1. He is known for his unscrupulous ways. He always sheds______ tears to deceive people.
(A) fox’s
(B) crocodile’s
(C) crocodile
(D) fox
Answer: (C)
2. Jofra Archer, the England fast bowler, is ____ than accurate.
(A) more fast
(B) faster
(C) less fast
(D) more faster
Answer: (A)
3. Select the word that fits the analogy:
Build : Building :: Grow : ______
(A) Grown
(B) Grew
(C) Growth
(D) Growed
Answer: (C)
4. I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.
What does the phrase “having said that” mean in the given text?
(A) as opposed to what I have said
(B) despite what I have said
(C) in addition to what I have said
(D) contrary to what I have said
Answer: (B)
5. Define [x] as the greatest integer less than or equal to x, for each x ∈ (−∞, ∞). If y = [x], then area under y for x ∈ [1, 4] is _______.
(A) 1
(B) 3
(C) 4
(D) 6
Answer: (D)
Q6 – Q10 carry two marks each.
6. Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.
Based on the above paragraph, which of the following is correct about crowd funding?
(A) Funds raised through unwilling contributions on web-based platforms.
(B) Funds raised through large contributions on web-based platforms.
(C) Funds raised through coerced contributions on web-based platforms.
(D) Funds raised through voluntary contributions on web-based platforms.
Answer: (D)
7. P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as ______.
(A) βα and αβ
(B) ββ and αα
(C) αβ and ββ
(D) βα and ββ
Answer: (D)
8. The sum of the first n terms in the sequence 8, 88, 888, 8888, … is ______.
(A)
(B)
(C)
(D)
Answer: (D)
9. Select the graph that schematically represents BOTH y = xm and y = x1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1.
Answer: (A)
10. The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is ________.
(A) 58.5%
(B) 58.8%
(C) 59.0%
(D) 59.3%
Answer: (C)
ME1: Mechanical Engineering
Q1 – Q25 carry one mark each.
1. Multiplication of real valued square matrices of same dimension is
(A) associative
(B) commutative
(C) always positive definite
(D) not always possible to compute
Answer: (A)
2. The value of is
(A) c
(B) c + 1
(C)
(D)
Answer: (C)
3. The Laplace transform of a function f(t) is Then, f(t) is
(A)
(B)
(C)
(D)
Answer: (C)
4. Which of the following function f(z), of the complex variable z, is NOT analytic at all the points of the complex plane?
(A) f(z) = z2
(B) f(z) = ez
(C) f(z) = sin z
(D) f(z) = log z
Answer: (D)
5. The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load P > 0 with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are
(A) BF and DH only
(B) BF, DH and GC only
(C) BF, DH, GC, CD and DE only
(D) BF, DH, GC, FG and GH only
Answer: (C)
6. A single-degree-freedom oscillator is subjected to harmonic excitation F(t) = F0 cos(ωt) as shown in the figure.
The non-zero value of ω, for which the amplitude of the force transmitted to the ground will be F0, is
Answer: (C)
7. The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa. If one unit on the σ – τ plane is 1 MPa, the Mohr’s circle representation of the state-of-stress is given by
(A) a circle with a radius equal to principal stress and its center at the origin of the σ – τ plane
(B) a point on the σ axis at a distance of 10 units from the origin
(C) a circle with radius of 10 units of the σ – τ plane
(D) a point on the τ axis at a distance of 10 units from origin
Answer: (B)
8. A four bar mechanism is shown below.
For the mechanism to be a crank-rocker mechanism, the length of the link PQ can be
(A) 80 mm
(B) 200 mm
(C) 300 mm
(D) 350 mm
Answer: (A)
9. A helical gear with 20° pressure angle and 30° helix angle mounted at the mid-span of a shaft that is supported between two bearings at the ends. The nature of the stress induced in the shaft is
(A) normal stress due to bending only
(B) normal stress due to bending in one plane and axial loading; shear stress due to torsion
(C) normal stress due to bending in two planes and axial loading; shear stress due to torsion
(D) normal stress due to bending in two planes; shear stress due to torsion
Answer: (A OR C)
10. The crystal structure of γ iron (austenite phase) is
(A) BCC
(B) FCC
(C) HCP
(D) BCT
Answer: (B)
11. Match the following.
(A) P-2, Q-3, R-4, S-1
(B) P-1, Q-1, R-3, S-2
(C) P-3, Q-3, R-1, S-3
(D) P-4, Q-3, R-2, S-1
Answer: (A)
12. The base of a brass bracket needs rough grinding. For this purpose, the most suitable grinding wheel grade specification is
(A) C30Q12V
(B) A50G8V
(C) C90J4B
(D) A30D12V
Answer: (A)
13. In the Critical Path Method (CPM), the cost-time slope of an activity is given by
Answer: (D)
14. Froude number is the ratio of
(A) buoyancy forces to viscous forces
(B) inertia forces to viscous forces
(C) buoyancy forces to inertia forces
(D) inertia forces to gravity forces
Answer: (D)
15. Match the following non-dimensional numbers with the corresponding definitions:
(A) P-1, Q-3, R-2, S-4
(B) P-3, Q-1, R-2, S-4
(C) P-4, Q-3, R-1, S-2
(D) P-3, Q-1, R-4, S-2
Answer: (D)
16. The velocity filed of an incompressible flow in a Cartesian system is represented by Which one of the following expressions for v is valid?
(A) −4xz + 6xy
(B) −4xy − 4xz
(C) 4xz – 6xy
(D) 4xy + 4xz
Answer: (B)
17. For an ideal gas, the value of the Joule-Thomson coefficient is
(A) positive
(B) negative
(C) zero
(D) indeterminate
Answer: (C)
18. For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature (T) versus specific entropy (s) diagram. CP is the specific heat at constant pressure and CV is the specific heat at constant volume. The ratio of the slopes of the constant pressure and constant volume lines at the point of intersection is
(A)
(B) CP/CV
(C)
(D) CV/CP
Answer: (D)
19. For three vectors and are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of is _______.
Answer: (6 to 6)
20. A flywheel is attached to an engine to keep its rotational speed between 100 rad/s and 110 rad/s. If the energy fluctuation in the flywheel between these two speeds is 1.05 kJ then the moment of inertia of the flywheel is _______ kg.m2 (round off to 2 decimal places).
Answer: (0.98 to 1.02)
21. A balanced rigid disc mounted on a rigid roto has four identical point masses, each of 10 grams, attached to four points on the 100 mm radius circle shown in the figure.
The rotor is driven by a motor at uniform angular speed of 10 rad/s. If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is _______ N (round off to 2 decimal places).
Answer: (0.09 to 0.11)
22. A sheet metal with a stock hardness of 250 HRC has to be sheared using a punch and a die having a clearance of 1 mm between them. If the stock hardness of the sheet metal increases to 400 HRC, the clearance between the punch and the die should be _______mm.
Answer: (1.0 to 1.3)
23. A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is _______ (round off to 2 decimal places).
Answer: (0.90 to 0.95)
24. The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of 6 in two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the inlet temperature of the first stage, before its entry to the second stage. Air enters the compressors at 300 K and 100 KPa. If the properties of gas are constant, the intercooling pressure for minimum compressor work is ________kPa (round off to 2 decimal places).
Answer: (MTA)
25. In a concentric tube counter-flow heat exchanger, hot oil enters at 102°C and leaves at 65° Cold water enters at 25°C and leaves at 42°C. The log mean temperature difference (LMTD) is __________°C (round of to one decimal place)
Answer: (48.8 to 49.8)
Q26 – Q55 carry two marks each.
26. The evaluation of the definite integral by using Simpson’s 1/3rd (one-third) rule with step size h = 0.6 yields
(A) 0.914
(B) 1.248
(C) 0.581
(D) 0.592
Answer: (D)
27. A vector field is defined as
where are unit vectors along the axes of right-handed rectangular /Cartesian coordinate system. The surface integral is an elemental surface area vector) evaluated over the inner and outer surfaces of a spherical shell formed by two concentric spheres with origin as the center, and internal and external radii of 1 and 2, respectively, is
(A) 0
(B) 2π
(C) 4π
(D) 8π
Answer: (A)
28. Bar of square and circular cross-section with 0.5 m length are made of a material with shear strength of 20 MPa. The square bar cross-section dimension is 4 cm × 4 cm and the cylindrical bar cross-section diameter is 4 cm. The specimens are loaded as shown in the figure.
Which specimen(s) will fail due to the applied load as per maximum shear stress theory?
(A) Tensile and compressive load specimens
(B) Torsional load specimen
(C) Bending load specimen
(D) None of the specimens
Answer: (A)
29. The 2 kg block shown in figure (top view) rests on a smooth horizontal surface and is attached to massless elastic cord that has a stiffness 5 N/m.
The cord hinged at O is initially unstretched and always remains elastic. The block is given a velocity v of 1.5 m/s perpendicular to the cord. The magnitude of velocity in m/s of the block at the instant the cord is stretched by 0.4 m is
(A) 0.83
(B) 1.07
(C) 1.36
(D) 1.50
Answer: (C)
30. The truss shown in the figure has four members of length l and flexural rigidity EI, and one member of length l√2 and flexural rigidity 4EI. The truss is loaded by a pair of forces of magnitude P, as shown in the figure.
The smallest value of P, at which any of the truss members will buckle is
Answer: (C)
31. A rigid mass-less rod of length L is connected to a disc (pulley) of mass m and radius r = L/4 through a friction-less revolute joint. The other end of that rod is attached to a wall through a friction-less hinge. A spring of stiffness 2k is attached to the rod at its mid-span. An inextensible rope passes over half the disc periphery and is securely tied to a spring of stiffness k at point C as shown in the figure. There is no slip between the rope and the pulley. The system is in static equilibrium in the configuration shown in the figure and the rope is always taut.
Neglecting the influence of gravity, the natural frequency of the system for small amplitude vibration is
Answer: (C)
32. A strip of thickness 40 mm is to be rolled to a thickness of 20 mm using a two-high mill having rolls of diameter 200 mm. Coefficient of friction and arc length in mm, respectively are
(A) 0.45 and 38.84
(B) 0.39 and 38.84
(C) 0.39 and 44.72
(D) 0.45 and 44.72
Answer: (D)
33. For an assembly line, the production rate was 4 pieces per hour and the average processing time was 60 minutes. The WIP inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by 30 percent. As a result of this change in the processing time, the WIP inventory
(A) decreases by 25%
(B) increases by 25%
(C) decreases by 30%
(D) increases by 30%
Answer: (C)
34. A small metal bead (radius 0.5 mm), initially at 100°C, when placed in a stream of fluid at 20°C, attains a temperature of 28°C in 4.35 seconds. The density specific heat of the metal are 8500 kg/m3 and 400 J/kg.K, respectively. If the bead is considered as lumped system, the convective heat transfer coefficient (in W/m2.K) between the metal bead and the fluid steam is
(A) 283.3
(B) 299.8
(C) 149.9
(D) 449.7
Answer: (B)
35. Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is ________ (round off to 2 decimal places).
Answer: (-1.00 to -0.98)
36. An analytic function of a complex variable z = x + iy(i = √−1) is defined as f(z) = x2 – y2 + iψ(x, y), where iψ(x, y) is a real function. The value of imaginary part of f(z) at z = (1+ i) is ________( round off to 2 decimal places).
Answer: (1.99 to 2.01)
37. In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm and 50 mm, respectively. An axial force F1 is needed to transmit a torque by a new clutch. However, to transmit the same torque, one needs an axial force F2 when the clutch wears out. If contact pressure remains uniform during operation of a new clutch while the wear is assumed to be uniform for an old clutch, and the coefficient of friction does not change, then the ratio F1/F2 is _______ (round off to 2 decimal places).
Answer: (0.85 to 0.89)
38. A cam with a translating flat-face follower is desired to have the follower motion y(θ) = 4[2πθ – θ2], 0 ≤ θ ≤ 2π. Contact stress considerations dictate that the radius of curvature of the cam profile should not be less than 40 mm anywhere. The minimum permissible base circle radius is _______ mm (round off to one decimal place).
Answer: (47.9 to 48.1)
39. A rectangular steel bar of length 500 mm, width 100 mm, and thickness 15 mm is cantilevered to a 200 mm steel channel using 4 bolts, as shown.
For an external load of 10 kN applied at the ip of the steel bar, the resultant shear load on the bolt at B, is _______ kN (round off to one decimal place).
Answer: (15.9 to 16.1)
40. The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modeled as cantilever.
Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10 m/s2, the maximum absolute bending moment developed in the cantilever is ______kN∙m (round off to the nearest integer).
Answer: (104 to 106)
41. The magnitude of reaction force at joint C o the hinge-beam shown in the figure is _______ kN (round off to 2 decimal places).
Answer: (19.95 to 20.05)
42. A slot of 25 mm × 25 mm is to be billed in a workpiece of 300 mm length using a side and face milling cutter of diameter 100 mm, width 25 mm and having 20 teeth.
For a depth of cut 5 mm, feed per tooth 0.1 mm, cutting speed 35 m/min and approach and over travel distance of 5 mm each, the time required for milling the slot is _____ minutes (round off to one decimal place).
Answer: (7 to 9)
43. The following data applies to basic shaft system:
tolerance for hole = 0.002 mm,
tolerance for shaft = 0.001 mm,
allowance = 0.003 mm,
basic size = 50 mm.
The maximum hole size is ____ mm (round off to 3 decimal places).
Answer: (50.005 to 50.005)
44. A steel part with surface area of 125 cm2 is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation :
I = 12 + 0.2t
where, I = current (A) and t = time (minutes). The part is a submerged in the plating solution for a duration of 20 minutes for plating purpose. Assuming the cathode efficiency of chromium to be 15% and the plating constant of chromium acid sulphate to be 2.50 × 10−2 mm3/A∙s, the resulting coating thickness on the part surface is _______ μm (round off to one decimal place).
Answer: (0 to 0)
45. In a turning process using orthogonal tool geometry, a chip length of 100 mm is obtained for an uncut chip length of 250 mm.
The shear plane angle is _______ degrees (round off to one decimal place).
Answer: (22 to 25)
46. The thickness of a steel plate with material strength coefficient of 210 MPa, has to be reduced from 20 mm to 15 min in a single pass in two-high rolling mill with a roll radius of 450 mm and rolling velocity of 28 m/min. If the plate has a width of 200 mm and its strain hardening exponent, n is 0.25, the rolling force required for the operation is ______ kN (round off to 2 decimal places).
Answer: (1164 to 1168)
47. Two business owners Shveta and Ashok run their businesses in two different states. Each of them, independent of the other, produces two products A and B, sells them at Rs. 2,000 per kg and Rs. 3,000 per kg, respectively, and uses Linear Programming to determine the optimal quantity of A and B to maximize their respective daily revenue. Their constraints are as follows: i) for each business owner, the production process is such that the daily production of A has to be at least as much as B, and the upper limit for production of B is 10 kg per day, and (ii) the respective state regulations restrict Shveta’s production of A to less than 20 kg per day, and Ashok’s production of A to less than 15 kg per day. The demand of both A and B in both the states is very high and everything produced is sold.
The absolute value of the difference in daily (optimal) revenue of Shveta and Ashok is _________ thousand Rupees (round off to 2 decimal places).
Answer: (9.90 to 10.10)
48. Consider two cases as below.
Case 1: A company buys 1000 pieces per year of a certain part from vendor ‘X’. The changeover time is 2 hours and the price is Rs. 10 per piece. The holding cost rate per part is 10% per year.
Case 2: For the same part, another vendor ‘Y’ offers a design where the changeover time is 6 minutes, with a price of Rs. 5 per piece, and a holding cost rate per part of 100% per year. The order size is 800 pieces per year from ‘X’ and 200 pieces per year from ‘Y’.
Assume the cost of downtime as Rs. 200 per hour. The percentage reduction in the annual cost for Case 2, as compared to Case 1 is ______ (round off to 2 decimal places).
Answer: (8.19 to 8.23)
49. Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter D. We know that the velocity profile forms a paraboloid about the pipe centre line, given by: where C is a constant. The rate of kinetic energy (in J/s) at the control surface A-B, as shown in the figure, is proportional to Dn. The value of n is ______.
Answer: (8 to 8)
50. Air discharges steadily through a horizontal nozzle and impings one a stationary vertical plate as shown in figure.
The inlet and outlet area of the nozzle are 0.1 m2 and 0.02 m2, respectively. Take air density as constant and equal to 1.2 kg/m3. If the inlet gauge pressure of air is 0.36 kPa, the gauge pressure at point O on the plate is ______ kPa (round off to two decimal places)
Answer: (0.37 to 0.45)
51. Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ______ kJ/kg (round off to nearest integer).
Answer: (244 to 246)
52. One kg of air, initially at a temperature of 127°C, expands reversible at a constant pressure until the volume is doubled. If the gas constant of air is 287 J/kg.K, the magnitude of work transfer is ______ kJ (round off to 2 decimal places).
Answer: (114.6 to 115.0)
53. For an ideal Rankine cycle operating between pressures of 30 bar and 0.04 bar, the work output from the turbine is 903 kJ/kg and the work input to the feed pump is 3 kJ/kg. The specific steam consumption is _______ kg/kW.h (round of to 2 decimal places).
Answer: (3.98 to 4.02)
54. For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in figure.
The diameter at this section is 3 m. The hub and tip diameters of the blade are 2 n and 4 m, respectively. The water volume flow rate is 100 m3/s. The rotational speed of the turbine is 300 rpm. The blade outlet angle β is _____ degrees (round off to one decimal place).
Answer: (11.0 to 14.0)
55. The indicated power developed by an engine with compression ratio of 8, is calculated using an air-standard Otto cycle (constant properties). The rate of heat addition is 10 kW. The ratio of specific heats at constant pressure and constant volume is 1.4. The mechanical efficiency of the engine is 80 percent.
The brake power output of the engine is ______kW (round off to one decimal place).
1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.
(A) with, at
(B) on, in
(C) on, at
(D) to, at
Answer: (C)
2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.
(A) slim
(B) bright
(C) obvious
(D) uncertain
Answer: (B)
3. Select the word that fits the analogy:
Cover : Uncover :: Associate : _______
(A) Unassociate
(B) Inassociate
(C) Missassociate
(D) Dissociate
Answer: (D)
4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.
Which of the following statements can be inferred from the given passage?
(A) Officials declared that the food-grain production target will be met due to good rains.
(B) Officials want the food-grain production target to be met by the November-February period.
(C) Officials feel that the food-grain production target cannot be met due to floods.
(D) Officials hope that the food-grain production target will be met due to a good rabi produce.
Answer: (D)
5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.
(A) n2 – n
(B) n2 + n
(C) 2n2 – n
(D) 2n2 + n
Answer: (B)
Q6-Q10 carry two marks each.
6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.
Which of the following statements can be inferred from the above passage?
(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.
(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.
(C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.
(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.
Answer: (D)
7. P, Q, R, S, T, U, V, and W are seated around a circular table.
(I) S is seated opposite to W.
(II) U is seated at the second place to the right of R.
(III) T is seated at the third place to the left of R.
(IV) V is a neighbor of S.
Which of the following must be true?
(A) P is a neighbor of R.
(B) Q is a neighbor of R.
(C) P is not seated opposite to Q.
(D) R is the left neighbor of S.
Answer: (C)
8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?
(A) 66.6
(B) 75.2
(C) 88.2
(D) 116.5
Answer: (B)
9. For a matrix M = [mij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and mij = −mij. The minimum number of elements required to fully specify the matrix is_______.
(A) 0
(B) 6
(C) 12
(D) 16
Answer: (B)
10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.
(A) 15 : 17
(B) 16 : 17
(C) 17 : 15
(D) 17 : 16
Answer: (B)
MA: Mathematics
Q1 – Q25 carry one mark each.
1. Suppose that ℑ1 and ℑ2 are topologies on X induced by metrics d1 and d2, respectively, such that ℑ1 ⊆ ℑ2. Then which of the following statements is TRUE?
(A) If a sequence converges in (X, d2) then it converges in (X, d1)
(B) If a sequence converges in (X, d1) then it converges in (X, d2)
(C) Every open ball in (X, d1) is an open ball in (X, d2)
(D) The map x → x from (X, d1) to (X, d2) is continuous
Answer: (A)
2. Let D = [−1, 1] × [−1, 1]. If the function f : D → ℝ is defined by
then
(A) f is continuous at (0, 0)
(B) both the first order partial derivatives of f exist at (0, 0)
(C) ∬D |f(x, y)|1/2 dx dy is finite
(D) ∬D |f(x, y)| dx dy is finite
Answer: (C)
3. The initial value problem y′ = y3/5, y(0) = b has
(A) a unique solution if b = 0
(B) no solution if b = 1
(C) infinitely many solutions if b = 2
(D) a unique solution if b = 1
Answer: (D)
4. Consider the following statements:
I : log(|z|) is harmonic on ℂ\{0}
II: log(|z|) has a harmonic conjugate on ℂ\{0}
Then
(A) both I and II are true
(B) I is true but II is false
(C) I is false but II is true
(D) both I and II are false
Answer: (B)
5. Let G and H be defined by
G = ℂ\ {z = x + iy ∈ ℂ : x ≤ 0, y = 0},
H = ℂ\ {z = x + iy ∈ ℂ : x ∈ ℤ, x ≤ 0, y = 0}.
Suppose f: G → ℂ and g : H → ℂ are analytic functions. Consider the following statements:
I : ∫γ f dz is independent of pathys γ in G joining –i and i
II : ∫γ g dz is independent of paths γ in H joining –i and i
Then
(A) both I and II are true
(B) I is true but II is false
(C) I is false but II true
(D) both I and II are false
Answer: (B)
6. Let f (z) = e1/z, z ∈ ℂ \ {0} and let, for n ∈ ℕ,
If for a subset S of ℂ, denotes the closure of S in ℂ, then
Answer: (A or D)
7. Suppose that
Then, with respect to the Eclidean metric on ℝ2,
(A) both U and V are disconnected
(B) U is disconnected but V is connected
(C) U is connected but V is disconnected
(D) both U and V are connected
Answer: (C)
8. If (D1) and (D2) denote the dual problems of the linear programming problems (P1) and P2), respectively, where
(C) (D1) is infeasible and (D2) is feasible but unbounded
(D) (P1) is feasible but unbounded and (D1) is feasible
Answer: (A)
9. If (4, 0) and (0, −1/2) are critical points of the function
f(x, y) = 5 – (α + β) x2 + βy2 + (α + 1) y3 + x3,
where α, β ∈ ℝ, then
(A) (4, −1/2) is a point of local maxima of f
(B) (4, −1/2) is saddle point of f
(C) α = 4, β = 2
(D) (4, −1/2) is a point of local minima of f
Answer: (B)
10. Consider the iterative scheme
with initial point x0 > 0. Then the sequence {xn}
(A) converges only if x0 > 1
(B) converges only if x0 < 3
(C) converges for any x0
(D) does not converge for any x0
Answer: (C)
11. Let C[0, 1] denote the space of all real-valued continuous functions on [0, 1] equipped with the supremum norm || ∙ ||∞. Let T : C[0, 1] → C[0, 1] be the linear operator defined by
Then
(A) || T || = 1
(B) I – T is not invertible
(C) T is surjective
(D) ||I + T|| = 1+ ||T||
Answer: (D)
12. Suppose that M is a 5 × 5 matrix with real entries and p(x) = det(xI – M). Then
(A) p(0) = det(M)
(B) every eigenvalue of M is real if p(1) + (p)2 = 0 = p(2) + p(3)
(C) M−1 is necessarily a polynomial in M of degree 4 if M is invertible
(D) M is not invertible if M2 – 2M = 0
Answer: (C)
13. Let C[0, 1] denote the space of all real-valued continuous functions on [0, 1] equipped with the supremum norm || ∙ ||∞. Let f ∈[0, 1] be such that
|f(x) – f(y)| ≤ M |x – y|, for all x, y ∈ [0, 1] and for some M > 0.
For n ∈ ℕ, let fn(x) = f(x1+1/n). If S = {fn : n ∈ ℕ}, then
(A) the closure of S is compact
(B) S is closed and bounded
(C) S is bounded but not totally bounded
(D) S is compact
Answer: (A)
14. Let K : ℝ × (0, ∞) → ℝ be a function such that the solution of the initial value problem u(x, 0), = f(x), x ∈ ℝ, t > 0, is given by
for all bounded continuous functions f. Then the value of is ______
Answer: (1 to 1)
15. The number of cyclic subgroups of the quaternion group is _________
Answer: (5 to 5)
16. The number of elements of order 3 in the symmetric group S6 is _______
Answer: (80 to 80)
17. Let F be the field with 4096 elements. The number of proper subfields of F is ______
Answer: (5 to 5)
18. If (x1*, x2*) is an optimal solution of the linear programming problem, minimize x1 + 2x2 subject to
4x1 – x2 ≥8
2x1 + x2 ≥ 10
−x1 + x2 ≤ 7
x1, x2 ≥ 0
and (λ1*, λ2*, λ3*) in an optimal solution of its dual problem, then is equal to ______ (correct up to one decimal place)
Answer: (5.5 to 5.5)
19. Let a, b, c ∈ ℝ be such that the quadrature rule
is exact for al polynomials of degree less than or equal to 2. Then b is equal to ______ (rounded off to two decimal places)
Answer: (1.70 to 1.80)
20. Let f(x) = x4 and let p(x) be the interpolating polynomial of f at nodes 1, 2 and 3. Then p(0) is equal to _______
Answer: (36 to 36)
21. For n ≥ 2, define the sequence {xn} by
Then the sequence {xn} converges to ______ (correct up to two decimal places)
Answer: (0.25 to 0.25)
22. Let
equipped with the norm and let T be the linear functional on L2[0, 10] given by
Then ||T|| is equal to ______
Answer: (3 to 3)
23. If {x13 x22, x23 = 10, x31, x32, x34} is the set of basic variable of a balanced transportation problem seeking to minimize cost of transportation from origins to destinations, where the cost matrix is,
and λ, μ ∈ ℝ, then x32 is equal to ______
Answer: (5 to 5)
24. Let ℤ225 be the ring of integers modulo 225. If x is the number of prime ideals and y is the number of nontrivial units in ℤ225, then x + y is equal to _______
Answer: (121 to 121)
25. Let u(x, t) be the solution of
where f is a twice continuously differential function. If f(−2) = 4, f(0) = 0, and u(2, 2) = 8, then the value of u(1, 3) is ________
Answer: (10 to 10)
Q26 – Q55 carry two marks each.
26. Let be an orthonormal basis for a separable Hilbert space H with the inner product Define
Then
(A) the closure of the span {fn : n ∈ ℕ} equals H
(B) f = 0 if for all n ∈ ℕ
(C) is an orthogonal subset of H
(D) there does not exist nonzero f ∈ H such that
Answer: (A)
27. Suppose V is a finite dimensional non-zero vector space over ℂ and T : V → V is a linear transformation such that Range (T) = Nullspace (T). Then which of the following statements is FALSE ?
(A) The dimension of V is even
(B) 0 is the only eigenvalue of T
(C) Both 0 and 1 are eigenvalues of T
(D) T2 = 0
Answer: (C)
28. Let P ∈ Mm×n(ℝ). Consider the following statements:
I : If XPY = 0 for all X ∈ M1×m(ℝ), then P = 0.
II : If m = n, P is symmetric and P2 = 0, then P = 0.
Then
(A) both I and II are true
(B) I is true but II is false
(C) I is false but II is true
(D) both I and II are false
Answer: (A)
29. For n ∈ ℕ, let Tn : (l1, ||∙||1) → (l∞, ||∙||∞) and T : (l1, ||∙||∞) be the bounded linear operators defined by
and
T(x1, x2, …) = (x1, x2 …).
Then
(A) ||Tn|| does not converge to ||T|| as n → ∞
(B) ||Tn – T|| converges to zero as n → ∞
(C) for all x ∈ l1, ||Tn(x) – T(x)|| converges to zero as n → ∞
(D) for each non-zero x ∈ l1, there exists a continuous linear functional g on l∞ such that g(Tn(x)) does not converge to g(T(x)) as n → ∞
Answer: (C)
30. Let P(ℝ) denote the power set of ℝ, equipped with the metric
where χU and χV denote the characteristic functions of the subjects U and V, respectively of ℝ. The set {{m} : m ∈ ℤ} in the metric space (P(ℝ), d) is
(A) bounded but not totally bounded
(B) totally bounded but not compact
(C) compact
(D) not bounded
Answer: (A)
31. Let f : ℝ → ℝ be defined by
where χ(n n+1] is the characteristic function of the interval (n, n + 1]. for α ∈ ℝ, let Sα = {x ∈ ℝ : f(x) > α}. Then
(A) S1/2 is open
(B) S√5/2 is not measurable
(C) S0 is closed
(D) S1/√3 is measurable
Answer: (D)
32. For n ∈ ℕ, let fn, gn : (0, 1) → ℝ be functions defined by fn(x) = xn and gn(x) = xn (1 – x).
Then
(A) {fn} converges uniformly but {gn} does not converge uniformly
(B) {gn} converges uniformly but {fn} does not converge uniformly
(C) both {fn} and {gn} converge uniformly
(D) neither {fn} nor{gn} converge uniformly
Answer: (B)
33. Let u be a solution of the differential equation y′ + xy = 0 and let ϕ = uψ be a solution of the differential equation y′′ + 2xy′ + (x2 + 2) y = 0 satisfying ϕ(0) = 1 and ϕ′(0) = 0. Then ϕ(x) is
Answer: (B)
34. For n ∈ ℕ ⋃ {0}, let yn be a solution of the differential equation xy′′ + (1 – x)y′ + ny = 0 satisfying yn(0) = 1. For which of the following functions w(x), the integral is equal to zero?
Answer: (B)
35. Suppose that
are metric spaces with metrics induced by the Euclidean metric of ℝ2. Let BX and BY be the open unit balls around (0 0) in X and Y, respectively. Consider the following statements:
I : The closure of BX in X is compact.
II : The closure of BY is compact.
Then
(A) both I and II are true
(B) I is true but II is false
(C) I is false but II is true
(D) both I and II are false
Answer: (C)
36. If f : ℂ \ {0} → ℂ is a function such that and its restriction to the unit circle is continuous, then
(A) f is continuous but not necessarily analytic
(B) f is analytic but not necessarily a constant function
(C) f is a constant function
(D)
Answer: (A)
37. For a subset S of a topological space, let Int(S) and denote the interior and closure of S, respectively. Then which of the following statements is TRUE?
(A) If S is open, then
(B) If the boundary of S is empty, then S is open
(C) If the boundary of S is empty, then S is open
(D) If is a proper subset of the boundary of S, then S is open
Answer: (B)
38. Suppose ℑ1, ℑ2, and ℑ3 are the smallest topologies on ℝ containing S1, S2 and S3, respectively, where
Then
(A) ℑ3 ⊋ ℑ1
(B) ℑ3 ⊋ ℑ2
(C) ℑ1 = ℑ2
(D) ℑ1 ⊋ ℑ2
Answer: (C)
39. Let Consider the following statements:
I: There exists a lower triangular matrix L such that M = LLt, where Lt denotes transpose of L.
II : Gauss-Seidel method of Mx = b (b ∈ ℝ3) converges for any initial choice x0 ∈ ℝ3.
Then
(A) I is not true when α > 9/2, β = 3
(B) II is not true when α > 9/2, β =−1
(C) II is not true when α = 4, β = 3/2
(D) I is true when α = 5, β = 3
Answer: (D)
40. Let I and J be the ideals generated by {5, √10} and {4, √10} in the ring ℤ[√10] = {a+ b√10|a, b ∈ ℤ}, respectively. Then
(A) both I and J are maximal ideals
(B) I is a maximal ideal but J is not a prime ideal
(C) I is not a maximal ideal but J is a prime ideal
(D) neither I nor J is a maximal ideal
Answer: (B)
41. Suppose V is finite dimensional vector space over ℝ. If W1, W2 and W3 are subspaces of V, then which of the following statements is TRUE?
(A) If W1 + W2 + W3 = V then span (W1 ⋃ W2) ⋃ span(W2 ⋃ W3) ⋃ span(W3 ⋃ W1) = V
(B) If W1 ⋂ W2 = {0} and W1 ⋂ W3 = {0}, then W1 ⋂ (W2 + W3) = {0}
(C) If W1 + W2 = W1 + W3, then W2 = W3
(D) If W1 ≠ V, then span(V\W1) = V
Answer: (D)
42. Let α, β ∈ ℝ, α ≠ The system
x1 – 2x2 + αx3 = 8
x1 – x2 + x4 = β
x1, x2, x3, x4 ≥ 0
has NO basic feasible solution if
(A) α < 0, β > 8
(B) α > 0, 0 < β < 8
(C) α > 0, β < 0
(D) α < 0, β < 8
Answer: (D)
43. Let 0 < p < 1 and let
Then
(A) |∙| defines a norm on X
(B) |f + g|p ≤ |f|p + |g|p for all f, g ∈ X
(C) |f +g|pp ≤ |f|pp + |g|pp for all, f, g ∈ X
(D) if fn converges to f pointwise on ℝ, then
Answer: (C)
44. Suppose the ϕ1 and ϕ2 are linearly independent solutions of the differential equation 2x2y′′ – (x + x2)y′ + (x2 – 2)y = 0, and ϕ1(0) = 0. Then the smallest positive integer n such that is _______
Answer: (3 to 3)
45. Suppose that z ∈ ℂ and γ(t) = e2it, t ∈[0, 2π]. If then the value of α is equal to ________
Answer: (56 to 56)
46. If t ∈ [0, 2] and then β is equal to _______ (correct up to one decimal place)
Answer: (0.5 to 0.5)
47. Let where ω is a primitive cube root of unity. Then the degree of extension of K over ℚ is _______
Answer: (4 to 4)
48. Let α ∈ ℝ. If (3, 0, 0, β) is an solution of the linear programming problem minimize x1 + x2 + x3 – αx4 subject to
2x1 – x2 + x3 = 6
−x1 + x2 + x4 = 3
x1, x2, x3, x4 ≥ 0
then the maximum value of β – α is _________
Answer: (7 to 7)
49. Suppose that T : ℝ4 → ℝ[x] is a linear transformation over ℝ satisfying T(−1, 1, 1, 1) = x2 + 2x4, T(1, 2, 3, 4) = 1 – x2, T(2, −1, −1, 0) = x3 – x4. Then the coefficient of x4 in T(−3, 5, 6, 6) is ________
Answer: (5 to 5)
50. Let and let S be the surface of the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 1.If is the unit outward normal to the tetrahedron, then the value of is _______ (rounded off to two decimal places)
Answer: (1.30 to 1.40)
51. Let and let S be the surface x2 + y2 + z = 1, z ≥ If is a unit normal to S and Then α is equal to _____
Answer: (2 to 2)
52. Let G be a non-cyclic group of order 57. Then the number of elements of order 3 in G is _______
Answer: (38 to 38)
53. The coefficient of (x – 1)5 in the Taylor expansion about x = 1 of the function is _______ (correct up to two decimal places)
Answer: (0.04 to 0.04)
54. Let u(x, y) be the solution of the initial value problem u(x, 0) = 1 + x2. Then the value of u(0, 1) is ______ (rounded off to three decimal places
Answer: (1.610 to 1.625)
55. The value of is _______ (rounded off to three decimal places)
1. He is known for his unscrupulous ways. He always sheds ______ tears to deceive people.
(A) fox’s
(B) crocodile’s
(C) crocodile
(D) fox
Answer: (C)
2. Jofra Archer, the England fast bowler, is _____ than accurate.
(A) more fast
(B) faster
(C) less fast
(D) more faster
Answer: (A)
3. Select the word that fits the analogy:
Build : Building :: Grow :______
(A) Grown
(B) Grew
(C) Growth
(D) Growed
Answer: (C)
4. I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.
What does the phrase “having said that” mean in the given text?
(A) as opposed to what I have said
(B) despite what I have said
(C) in addition to what I have said
(D) contrary to what I have said
Answer: (B)
5. Define [x] as the greatest integer less than or equal to x, for each x ∈ (−∞, ∞). If y = [x], then are under y for x ∈ [1, 4] is _____.
(A) 1
(B) 3
(C) 4
(D) 6
Answer: (D)
Q6 – Q10 carry two marks each.
6. Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.
Based on the above paragraph, which of the following is correct about crowd funding?
(A) Funds raised through unwilling contributions on web-based platforms.
(B) Funds raised through large contributions on web-based platforms.
(C) Funds raised through coerced contributions on web-based platforms.
(D) Funds raised through voluntary contributions on web-based platforms.
Answer: (D)
7. P, Q, R and S are to the uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as _______.
(A) βα and αβ
(B) ββ and αα
(C) αβ and ββ
(D) βα and ββ
Answer: (D)
8. The sum of the first n terms in the sequence, 8, 88, 888, …. is _______.
(A)
(B)
(C)
(D)
Answer: (D)
9. Select the graph that schematically represents BOTH y = xm and y = x1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1.
Answer: (A)
10. The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. Te average of success rates (in percentage) of these four schools is _______.
(A) 58.5%
(B) 58.8%
(C) 59.0%
(D) 59.3%
Answer: (C)
IN: Instrumentation Engineering
Q1 – Q25 carry one mark each.
1. The unit vectors along the mutually perpendicular x, y and z axes are, Consider the plane z = 0 and two vectors on that plane such that for any scalar α. A vector perpendicular to both is ______.
(A)
(B)
(C)
(D)
Answer: (A)
2. Consider the recursive equation Xn+1 = Xn – h(F(Xn) – Xn), with initial condition X0 = 1 and h > 0 being a very small valued scalar. This recursion numerically solves the ordinary differential equation_____
(A) Ẋ = −F(X), X(0) = 1
(B) Ẋ = −F(X) + X, X(0) = 1
(C) Ẋ = F(X), X(0) =1
(D) Ẋ = F(X) + X, X(0) = 1
Answer: (B)
3. A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ Will it be possible to solve for x and obtain a unique solution by multiplying both left and right sides of the equation by AT (the super script T denotes the transpose) and inverting the matrix ATA? Answer is _______
(A) Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.
(B) No, it is not possible to get a unique solution for any 2 × 4 matrix A.
(C) Yes, can obtain a unique solution provided the matrix ATA is well conditioned
(D) Yes, can obtain a unique solution provided the matrix A is well conditioned
Answer: (B)
4. In the circuit shown below, the safe maximum value for the current I is ______
(A) 1.0 A
(B) 0.5 A
(C) 0.1 A
(D) 0.05 A
Answer: (C)
5. A differentiator has a transfer function whose
(A) phase increases linearly with frequency
(B) magnitude remains constant
(C) magnitude increases linearly with frequency
(D) magnitude decreases linearly with frequency
Answer: (C)
6. A phase lead network has the transfer function The angular frequency at which the maximum phase shift for the network occurs is _____
(A) 10 rad/s
(B) 20 rad/s
(C) 100 rad/s
(D) 200 rad/s
Answer: (A)
7. If the diodes in the circuit shown are ideal and the breakdown voltage VZ of the Zener diode is 5 V, the power dissipated in the 100 Ω resistor (in watts) is _______
(A) 0
(B) 1
(C) 25/100
(D) 225/100
Answer: (A)
8. Given f(A, B, C, D) = ∑m(0, 1, 2, 6, 8, 9, 10, 11) + ∑d(3, 7, 14, 15) is a Boolean function, where m represents min-terms and d represents don’t-cares. The minimal sum of products expression for f is______
(A)
(B)
(C)
(D)
Answer: (B)
9. A Q meter is best suited for the measurement of the ______
(A) Quality factor of a capacitance.
(B) Distributed capacitance of a coil.
(C) Quality factor of piezoelectric sensor.
(D) Turns-ratio of a transformer
Answer: (B)
10. If I is the current flowing through a Hall effect sensor and B is the magnetic flux density perpendicular to the direction of the current (in the plane of the Hall effect sensor), the Hall voltage generated is______
(A) Directly proportional to I and inversely proportional to B
(B) Directly proportional to both I and B
(C) Inversely proportional to both I and B
(D) Inversely proportional to I and directly proportional to B
Answer: (B)
11. The Boolean expression for the shaded regions as shown in the figure is _______
(A)
(B)
(C)
(D)
Answer: (A)
12. The Boolea operation performed by the following circuit at the output O is ______
(A) O = S1 ⊕ S0
(B)
(C) O = S1 + S0
(D)
Answer: (A)
13. Consider the Signal x[n] = sin(2πn) u[n], where The period of this signal x[n] is _____
(A) 4
(B) 3
(C) 2
(D) 1
Answer: (D)
14. The closed loop transfer function of a control system is given by For the input r(t) = sin t, the steady state response c(t) is _____
(A) 1
(B)
(C)
(D)
Answer: (D)
15. Let The value of the integral ∮f(z) dz over a circle C with center (−a, 0) and radius R > 0 evaluated in the anti-clockwise direction is ____
(A) 0
(B) 2πi
(C) −2πi
(D) 4πi
Answer: (B)
16. A player throws a ball at a basket kept at a distance. The probability that the ball falls into the basket in a single attempt is 0.1. The player attempts to throw the ball twice. Considering each attempt to be independent, the probability that this player puts the ball into the basket only in the second attempt (rounded off to two decimal places) is ____
Answer: (0.09 to 0.09)
17. Assuming ideal opamps, the output voltage at V1 in the figure shown (in volts) is ______
Answer: (7 to 7)
18. Three 400 Ω resistors are connected in delta and powered by a 400 V (rms), 50 Hz, balanced, symmetrical R-Y-B sequence, three-phase three-wire mains. The rms value of the line current (in amperes, rounded off to one decimal place) is _______
Answer: (1.7 to 1.8)
19. Consider the signal x(t) = e−|t|. Let be the Fourier transform of x(t). The value of X(j0) is _____
Answer: (2 to 2)
20. A second order system has closed loop poles located at s = −3 ± The time t at which the maximum value of the step response occurs (in seconds, rounded off to two decimal places)
Answer: (0.78 to 0.79)
21. Assume that the opamp in the circuit shown is ideal.
The value of Vx/Ix (in kΩ) is ____
Answer: (-4 to -4)
22. A sinusoid of 10 kHz is sampled at 15 k samples/s. The resulting signal is passed through an ideal low pass filter (LPF) with cut-off frequency of 25 kHz. The maximum frequency component at the output of the LPF (in kHz) is _____
Answer: (25 to 25)
23. A 200 mV full-scale dual-slope analog to digital converter (DS-ADC) has a reference voltage of 100 mV. The first integration time is set as 100 ms. The DS-ADC is operated in the continuous conversion mode. The conversion time of the DS-ADC for an input voltage of 123.4 mV (in ms, rounded off to one decimal place) is______
Answer: (223.3 to 223.5)
24. The capacitance Cx of a capacitive type sensor is (1000 x) pF, where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage 10 sin (100 πt) V. The other terminal of the sensor is tied to the input of a high input impedance amplifier through a shielded cable, with shield connected to ground. The cable capacitance is 100 pF. The peak of the voltage VA at the input of the amplifier when x = 0.1 (in volts) is
Answer: (5 to 5)
25. Two 100 Ω resistors having tolerance 3% and 4% are connected in series. The effective tolerance of the series combination (in n% rounded off to one decimal place) is ______
Answer: (2.5 to 2.5 OR 3.5 to 3.5)
Q26 – Q55 carry two marks each.
26. Consider the matrix One of the eigenvectors of M is
(A)
(B)
(C)
(D)
Answer: (D)
27. Consider the differential equation with the initial condition x(0) = 0. The solution to this ordinary differential equation is _______
(A) x(t) = 0
(B) x(t) = sin(t)
(C) x(t) = cos(t)
(D) x(t) = sin(t) – cos(t)
Answer: (A)
28. A straight line drawn on an x-y plane intercepts the x-axis at −5 and the y-axis at 1. The equation that describes this line is _____
(A) y = −0.5x + 1
(B) y = x – 0.5
(C) y = 0.5x – 1
(D) y = 2x + 1
Answer: (D)
29. The loop transfer function of a negative feedback system is The Nyquist plot for the above system____
(A) encircles (−1 + j0) point once in the clockwise direction
(B) encircles (−1 + j0) point once in the counterclockwise direction
(C) does not encircle (−1 + j0) point
(D) encircles (−1 + j0) point twice in the counterclockwise direction
Answer: (A)
30. I1, I2, I3 in the figure below are mesh currents. The correct set of mesh equations for these currents, in matrix form, is ______
Answer: (A)
31. Consider the function f(x, y) = x2 + y2. The minimum value the function attains on the line x + y = 1 (rounded off to one decimal place) is ______
Answer: (0.5 to 0.5)
32. Consider two identical gas B1 and B2 each containing 10 balls o identical shapes and sizes. Bag B1 contains 7 Red and 3 Green balls, while bag B2 contains 3 Red and 7 Green balls. A bag is picked at random and a ball is drawn from it, which was found to be Red. The probability that the Red ball came from bag B1 (rounded off to ne decimal place) is ______
Answer: (0.7 to 0.7)
33. The rms of the phasor current I in the circuit shown (in amperes) is ______
Answer: (1 to 1)
34. In the circuit shown, the rms value of the voltage across the 100 Ω resistor (in volts) is _____
Answer: (115 to 116)
35. Let and Consider y[n] = h[n] ⊗ g[n], where ⊗ denotes the convolution operator. The value of y[2] is ______
Answer: (0 to 0)
36. The loop transfer function of a negative feedback system is given by where K > 0. The value of K at the breakaway point of the root locus for the above system (rounded off to one decimal place) is ______
Answer: (5.0 to 5.1)
37. The system shown in Fig. (a) has a time response y(t) to an input r(t) = 10 u(t) as shown in Fig. (b), u(t) being the unit step input. Both K, τ are positive. The gain K of the system is ________
Answer: (4 to 4)
38. Assuming that the opamp used in the circuit shown in ideal, the reading of the 1 Hz bandwidth, permanent magnet moving coil (PMMC) type voltmeter (in volts) is ______
Answer: (1 to 1)
39. If the opamps in the circuit shown are ideal and Vx = 0.5 mV, the steady state value of VO (in volts, rounded off to two decimal places) is _____
Answer: (0.45 to 0.55)
40. Two T-flip flops are interconnected as shown in the figure. The present state of the flip flops are: A = 1, B = 1. The input x is given as 1, 0, 1 in the next three clock cycles. The decimal equivalent of (ABy)2 with A being the MSB and y being the LSB, after the 3rd clock cycle is ________
Answer: (7 to 7)
41. The address lines A9 …. A2 of a 10 bit, 1.023 V full-scale digital to analog converter (DAC) is connected to the data lines D7 to D0 of an 8-bit microprocessor, with A1 and A0 of the DAC grounded. Now, D7 … D0 is changed from 1010 1010 to 1010 1011. The corresponding change in the output of the DAC (in mV, rounded off to one decimal place) is _____
Answer: (3.5 to 4.5)
42. The real power drawn by a balanced load connected a 400 V, 50 Hz balanced, symmetrical 3-phase, 3-wire, RYB sequence mains is measured using the two-wattmeter method. Wattmeter W1 is connected in the R line and wattmeter W2 is connected in the B line. The line current is measured as 1/√3 A. If the wattmeter W1 reads zero, the reading on W2(in watt) is ____
Answer: (199 to 201)
43. A 6½ digit timer-counter is set in the ‘time period’ mode of operation and the range is set as ‘ns’. For an input signal, the timer-counter displays 1000000. With the same input signal, the timer-counter is changed to ‘frequency’ mode of operation and the range is et as ‘Hz’. The display will show the number_____
Answer: (999 to 1001)
44. The circuit shown uses ideals opamp powered from a supply VCC = 5 V. If the charge qp generated by the piezoelectric sensor is o the form qp = 0.1 sin(10000πt) μC, the peak detector output after 10 cycles of qp (in volts, rounded off to one decimal place) is _____
Answer: (3.4 to 3.6)
45. A metallic strain gauge of resistance Rx with a gauge factor is 2 is bonded to a structure made of a metal with modulus of elasticity of 200 GN/m2. The value of Rx is 1 kΩ when no stress is applied. Rx is a part of quarter bridge with three identical fixed resistors of 1 kΩ The bridge is excited from a DC voltage of 4 V. The structure is subjected to a stress of 100 MN/m2. Magnitude of the output of the bridge (in mV, rounded off to two decimal places is _____
Answer: (0.95 to 1.05)
46. A laser beam of 10 mm beam diameter is focused onto an optical fibre using a thin biconvex lens as shown in the figure. The refractive index of the lens is 1.5. The refractive indices of the core and cladding of the fibre are 1.55 and 1.54 respectively. The minimum value of the focal length of the lens to attain the maximum coupling to the fibre (in mm, rounded off to one decimal place) is ______
Answer: (27.5 to 28.5)
47. As shown in the figure, a slab of finite thickness t with refractive index n2 = 1 .5, has air (n1 = 1) above and below it. Light of free space wavelength 600 nm is incident normally from air as shown. For a destructive interference to be observed at R, the minimum value of thickness of the slab t (in mm) is _____
Answer: (200 to 200)
48. Consider the finite sequence X = (1, 1, 1). The Inverse Discrete Fourier Transform (IDFT) of X is given as (x90), x(1), x(2)). The value of x(2) is ______
Answer: (0 to 0)
49. A circuit consisting of capacitors, DC voltage source and an amplifier having a voltage gain G = −5 is shown in the figure. The effective capacitance across the nodes A and B (in μF, rounded off to one decimal place) is _____
Answer: (14.5 to 15.0)
50. Consider the following state variable equations:
The initial conditions are x1(0) = 0 and x2(0) = 1. At t = 1 second, the value of x2(1) (rounded off to two decimal places) is ______
Answer: (-0.13 to -0.11)
51. Assume the diodes in the circuit shown are ideal. The current Ix flowing through the 3 kΩ resistor (in mA, rounded off to one decimal place) is ____
Answer: (1.8 to 1.8)
52. A 1000/1 A, 5VA, UPF bar-primary measuring current transformer has 1000 secondary turns. The current transformer exhibits a ratio error of −1% and a phase error of 3.438 minutes when the primary current is 1000 A. At this operating condition, the rms value of the magnetization current of the current transformer (in amperes, rounded off to two decimal places) is ____
Answer: (0.95 to 1.05)
53. The mutual inductances between the primary coil and the secondary coils of a linear variable differential transformer (LVDT) shown in the figure are M1 and M2. Assume that the self-inductances LS1 and LS2 remain constant and are independent of x. When x = 0, M1 = M2 = M0. When x is in the range ±10 mm, M1 and M2 change linearly with x. At x = +10 mm or −10 mm, the change in the magnitudes of M1 and M2 is 0.25 M0. For a particular displacement x = D, the voltage across the detector becomes zero when |V2| = 1.25|V1|. The value of D (in mm, rounded off to one decimal place) is _____
Answer: (4.3 to 4.6)
54. In the Maxwell-Wien bridge shown, the detector D reads zero when C1 = 100 nF and R1 = 100 kΩ. The Q factor of the coil is____
Answer: (10 to 10)
55. The loop transfer function of a negative feedback system is The phase margin of the system (in degrees, rounded off to one decimal place) is ____
1. The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die ______ diseases like cardio vascular disease, cancer, etc.
(A) in, of
(B) from, of
(C) during, from
(D) from, from
Answer: (A)
2. He was not only accused of theft ______ of conspiracy.
(A) rather
(B) but also
(C) but even
(D) rather than
Answer: (B)
3. Select the word that fits the analogy:
Explicit : Implicit : : Express: _______
(A) Impress
(B) Repress
(C) Compress
(D) Suppress
Answer: (B)
4. The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements is English lasting 15 seconds, as opposed to informal 5 second messages in French.
The French-speaking couple were upset at ______.
(A) the in-flight announcements being made in English.
(B) the English announcements being clearer than the French ones.
(C) the English announcements being longer than the French ones.
(D) equal importance being given to English and French.
Answer: (C)
5. A superadditive function f (∙) satisfies the following property
f(x1 + x2) ≥ f(x1) + f(x2)
Which of the following functions is a superadditive function for x > 1?
(A) ex
(B) √x
(C) 1/x
(D) e−x
Answer: (A)
Q6 – Q10 carry two marks each.
6. The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.
Which one of the following sequences shows the correct precedence as per the given passage?
(A) East Asian crisis → subprime lending crisis → banking crisis global financial crisis.
(B) Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.
(C) Banking crisis → subprime lending crisis → global financial crisis → East Asian crisis.
(D) Global financial crisis → East Asian crisis → Banking crisis → subprime lending crisis.
Answer: (A)
7. It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.
(A) 0°
(B) 7.5°
(C) 15°
(D) 22.5°
Answer: (B)
8. A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is ______.
(A) πa2 – a2
(B) πa2 – √2a2
(C) πa2 – 2a2
(D) πa2 – 3a2
Answer: (C)
9. a, b, c are real numbers. The quadratic equation ax2 – bx + c = 0 has equal roots, which is β, then
(A) β = b/a
(B) β2 = ac
(C) β3 = bc/(2a2)
(D) b2 ≠ 4ac
Answer: (C)
10. The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is ______ .
(A) 8 : 23
(B) 23 : 8
(C) 23 : 31
(D) 31 : 23
Answer: (B)
Part A- Compulsory Section For All Candidates
Q1 – Q25 carry cone mark each.
1. A plagioclase with is
(A) albite
(B) anorthite
(C) oligoclase
(D) bytownite
Answer: (C)
2. Tillite is an important constituent of the
(A) Talchir Formation
(B) Barakar Formation
(C) Pachmarhi Formation
(D) Lameta Formation
Answer: (A)
3. If the ratio of gravity to total magnetic field at the equator of t he Earth is X, then the ratio of gravity to total magnetic field at the pole of the Earth will be close to
(A) 2X
(B) X/2
(C) 4X
(D) X/8
Answer: (B)
4. Which of the following is NOT a point group?
(A) 222
(B) 422
(C) 432
(D) 632
Answer: (D)
5. Mississippian is an Epoch within the
(A) Permian Period
(B) Carboniferous Period
(C) Triassic Period
(D) Jurassic Period
Answer: (B)
6. The given stereoplot of the axial plane and the axis of a fold represents an/a
(A) upright fold
(B) vertical fold
(C) reclined fold
(D) recumbent fold
Answer: (D)
7. A siliciclastic sedimentary rock with <5% matrix and QFL composition of 60% quartz, 30% rock fragments and 10% feldspar, is called
(A) quartz wacke
(B) lithic arenite
(C) quartz arenite
(D) feldspathic wacke
Answer: (B)
8. Which one of the following pairs of geophysical methods is most suitable to delineate chromite ore deposits occurring at a shallow depth in a granitic terrain?
(A) Gravity and Electrical methods
(B) Electrical and Electromagnetic methods
(C) Seismic and Gravity methods
(D) Seismic and Magnetic methods
Answer: (A)
9. The ratio of bridging to non-bridging oxygen atoms is zero in case of
(A) nesosilicates
(B) inosilicates
(C) phyllosilicates
(D) tectosilicates
Answer: (A)
10. Lahar is geomorphic feature associated with
(A) wind activity
(B) river activity
(C) glacial activity
(D) volcanic activity
Answer: (D)
11. Kepler’s second law of planetary motion follows the principle of conservation of
(A) energy
(B) momentum
(C) angular momentum
(D) moment of inertia
Answer: (C)
12. Which one of the following options shows the internal structural units of the Earth arranged in the CORRECT sequence of increasing volume?
13. Which one of the following is NOT an earthquake intensity scale?
(A) Richter scale
(B) JMA scale
(C) Modified Mercalli scale
(D) Rossi-Forel scale
Answer: (A)
14. The dimension of transmissivity of an aquifer is
(A) M0L1T−1
(B) M0L0T0
(C) M1L−1T−2
(D) M0L2T−1
Answer: (D)
15. During ‘K-capture’ nuclear transmutation process
(A) both atomic number atomic mass increase
(B) atomic number decreases but atomic mass remains the same
(C) atomic number increases but atomic mass remains the same
(D) both atomic number and atomic mass decrease
Answer: (B)
16. Which one amongst the following logs has the maximum depth of investigation?
(A) Neutron log
(B) Natural Gamma-ray log
(C) Lateral log
(D) Density log
Answer: (C)
17. The scale factor of an aerial photo of a planar ground surface, taken vertically downwards by a camera with a focal length of 300 mm, from a flying height of 3000 m is ______.
Answer: (10000 to 10000 OR 0.0001 to 0.0001)
18. In a soil sample, specific gravity of soil particles is 2.5 and the void ratio is 0.5. The density of the soil sample when it is fully saturated with water is _______ kg/m3. (Assume density of water = 1000 kg/m3, and no volume change of the soil sample with saturation)
Answer: (2000 to 2000)
19. Nuclide A decays to nuclide B exclusively through α and β decay, such that the mass number is reduced by 32 and the atomic number is reduced by 10. The number of β particles emitted during the decay of nuclide A to nuclide B is ________.
Answer: (6 to 6)
20. A cylindrical specimen (diameter = 54.7 mm; length = 110 mm) of basalt shows linear elastic behavior under uniaxial compression. At an axial stress of 100 Mega-Pascal (MPa), the absolute value of the measured axial strain is 0.2%. The Young’s modulus is calculated to be __________ Giga-Pascal (GPa).
Answer: (50 to 50)
21. A Mid-Oceanic-Ridge has symmetric magnetic anomalies about the ridge axis as shown below. Using the information given in the figure, the average relative velocity between the Plates A and B is calculated to be _______ cm/year.
Answer: (10 to 10)
22. The transmission coefficient for the vertically incident seismic wave at the interface between Layer and Layer 2 given in the figure is __________. (Round off to 2 decimal places)
Answer: (0.71 to 0.81)
23. The ‘geometrical factor’ for the electrode configuration given below will be ________ m. (Round off to 2 decimal places) (Use π = 3.14)
(C1 and C2 are current electrodes; P1 and P2 are potential electrodes)
Answer: (186.00 to 192.00)
24. In an electromagnetic measurement, the resultant field shows a phase lag of 30° with respect to the primary field at the receiver coil. The ratio of Inphase to Quadrature component of the resultant field is _________. (Round off to 2 decimal places)
Answer: (1.70 to 1.75)
25. A 4 km-high plateau is isostatically compensated as shown in the figure. Assuming Pratt’s hypothesis of isostasy, the calculated density of the plateau is ________ kg/m3.
Answer: (2450 to 2450)
Part B (Section 1): For Geology Candidates Only
Q1 – Q30 carry two marks each.
1. “Point Group” in crystallography is characterized by a set of symmetry operations such that
(A) all points in a crystal are affected by it
(B) no point in a crystal is affected by bit
(C) at least one point in a crystal is affected by it
(D) at least one point in a crystal is unaffected by it
Answer: (D)
2. What are the Miller indices of a plane that intercepts each of the crystallographic axes X, Y and Z at 20 Å? (Assume a primitive unit-cell with the dimensions a = 5 Å, b = 2 Å and c = Å.)
(A) (111)
(B) (524)
(C) (425)
(D) (542)
Answer: (B)
3. Which one of the following processes is associated with the emission of X-rays?
(A) alpha decay
(B) beta decay
(C) electron capture decay
(D) positron decay
Answer: (C)
4. Which one of the following radioisotopes has the longest half-life?
(A) 87Rb
(B) 147Sm
(C) 232Th
(D) 238U
Answer: (B)
5. The given geological map represents
(A) culmination of an antiformal anticline
(B) culmination of an antiformal syncline
(C) depression of a synformal anticline
(D) culmination of a synformal syncline
Answer: (MTA)
6. On a fault plane, the net slip is parallel to the bedding trace. Then, the apparent movement will be recognizable
(A) both in horizontal and vertical sections
(B) in horizontal, but not in vertical section
(C) in vertical, but not in horizontal section
(D) neither in horizontal nor in vertical section
Answer: (D)
7. The CORRECT sequence of the given electromagnetic radiations in order of increasing wavelength is
8. Choose the CORRECT combination of foraminiferal tests and types of coiling.
(A) Test 1 – Trochospiral, Test 2 – Planispiral, Test 3 – Milioline
(B) Test 1 – Milioline, Test 2 – Planispiral, Test 3 – Trochospiral
(C) Test 1 – Milioline, Test 2 – Trochospiral, Test 3 – Planispiral
(D) Test 1 – Trochospiral, Test 2 – Milioline, Test 3 – Planispiral
Answer: (B)
9. The figure below represents an isobaric binary liquidus phase diagram, with the solid phases A, B and C. What are the degrees of freedom associated with equilibrium phase assemblages represented by the bulk compositions w, x, y and z, in the fields indicated in the figure?
(A) w = 2, x = 1, y = 1, z = 1
(B) w = 2, x = 1, y = 0, z = 2
(C) w = 1, x = 1, y = 0, z = 1
(D) w = 1, x = 1, y = 1, z = 2
Answer: (A)
10. Match the basins (Group I) with the corresponding stratigraphic units (Group II).
(A) P-3, Q-4, R-1, S-2
(B) P-2, Q-4, R-1, S-3
(C) P-3, Q-1, R-4, S-2
(D) P-2, Q-3, R-4, S-1
Answer: (A)
11. In the metamorphic reaction Quartz + Muscovite = X + Sillimanite + Water, ‘X’ represents
(A) Garnet
(B) Staurolite
(C) Orthoclase
(D) Cordierite
Answer: (C)
12. The talc-kyanite assemblage can stabilize in
(A) greenschist facies marly rocks
(B) amphibolites facies mafic rocks
(C) eclogite facies politic rocks
(D) sanidinite facies ultramafic rocks
Answer: (C)
13. Which one of the following statements about igneous rocks is CORRECT ?
(A) Tholeiitic and calc-alkaline rocks are both alkaline in nature.
(B) Tholeiitic rocks are subalkline, but calc-alkaline rocks are alkaline in nature.
(C) Tholeiitic rocks are subalkaline, but calc-alkaline rocks are alkaline in nature.
(D) Tholeiitic and calc-alkaline rocks are both subalkaline in nature.
Answer: (D)
14. Based on the three statements given below, choose the CORRECT option.
Statement I: Barchans are crescent-shaped dunes that close in the downwind direction.
Statement II : Parabolic dunes are U-shaped dunes that close in the downwind direction.
Statement III: Barchanoid dunes are sinuous transverse ridges, the crestline sinuousity of successive bed forms are either in-phase or out-phase.
(A) All the statements are correct
(B) Statement I is correct, but statements II and III are incorrect
(C) Statements I and II are correct, but statement III is incorrect
(D) Statements II and III are correct, but statement I is incorrect
Answer: (D)
15. Based on the three statements given below, choose the CORRECT option.
Statement I: Barapasaurus is known from the Jurassic Kota Formation.
Statement II: Morganucodon is known from the Tatrot Formation.
Statement III: Lystrosaurus is known from the Lameta Formation.
(A) All the three statements are correct
(B) Statement I is correct but statements II and III are incorrect
(C) Statements I and II are correct but statement III is incorrect
(D) Statements II and III are correct but statement I is correct
Answer: (B)
16. Which one of the following assemblages of plant fossils is known from the Barakar Formation?
(A) Glossopteris, Gangamopteris, Dicroidium
(B) Glossopteris, Gangamopteris, Noeggerathiopsis
(C) Glossopteris, Gangamopteris, Ptilophyllum
(D) Schizoneura, Noeggerathiopsis, Ptilophyllum
Answer: (B)
17. Match the features (Group I) with the corresponding invertebrate genera (Group II).
(A) P-3, Q-4, R-1, S-2
(B) P-3, Q-4, R-2, S-1
(C) P-4, Q-3, R-2, S-1
(D) P-2, Q-1, R-4, S-3
Answer: (B)
18. If the orthogonal thickness is constant along a folded layer, as per Ramsay’s morphological classification of folds, it is a
(A) Class IA fold
(B) Class IB fold
(C) Class 2 fold
(D) Class 3 fold
Answer: (B)
19. If density of quartz is 2650 kg/m3 and that of orthoclase is 2550 kg/m3, the lithostatic pressure due to granite with 68 modal % orthoclase at a depth of 10 km will be _______ kbar. (Round off to 2 decimal places) (Acceleration due to gravity g = 9.8 m/s2
Answer: (2.56 to 2.58)
20. The unit-cell of an orthorhombic mineral was compressed during deformation from 5 Å to 4.5 Å along the c-axis, with the other two dimensions remaining unaffected. The absolute value of the shift in the position of the (001) peak in its XRD pattern is _______ °2θ. (Round off to 3 decimal places) (Wavelength of X-ray used = 1.5418 Å. For orthorhombic system: 1/d2 = h2/a2 + k2/b2 + l2/c2).
Answer: (1.98 to 2.00)
21. The grade of iron in an ore body containing 80 wt. % hematite and 20 wt. % gangue is _______ %. (Round off to 2 decimal places) (Atomic wt. of Fe = 55.85, atomic weight of O = 16)
Answer: (55.90 to 55.97)
22. The abundances of the isotopes 35Cl (atomic mass = 34.96885 amu) and 37Cl (atomic mass = 36.96590 amu) are 75.77% and 24.23%, respectively. The calculated atomic weight of Cl is ______ amu. (Round off to 3 decimal places)
Answer: (35.451 to 35.454)
23. A vertical profile perpendicular to the rest line of an asymmetrical ripple is given in the figure. The calculated Ripple Index is ________.
Answer: (4 to 4)
24. A source rock undergoes melting. Assuming batch melting, 5% partial melting and bulk distribution coefficient of 0.045, the enrichment factor (C1/C0) of Rb in the melt will be _______. (Round off to 2 decimal places)
Answer: (10.75 to 10.87)
25. If the ∆H of formation of CaSiO3, SiO2 and CaO from Ca, Si and O are respectively −1635, −911 and −635 kJ/mol, the enthalpy of formation of CaSiO3 from CaO and SiO2 is ________ kJ/mol.
Answer: (-89 to -89)
26. The tip-line of an actively propagating thrust fault is located at a depth of 1 km from the horizontal ground surface. The average density of the material from the ground surface to this depth is assumed to be uniform and can be taken as 2700 kg/m3. The rock at this depth follows the failure criterion given by the equation: σ1 = 10 MPa + 3σ3, where σ1 and σ3 are the maximum and minimum principal stresses. Considering Anderson’s theory of faulting, the calculated maximum principal stress at this depth is _______ Mega-Pascal (MPa). (Assume the acceleration due to gravity (g) to be 10 m/s2.)
Answer: (91 to 91)
27. During a rockslide, a 20 kg granite block gets dislodged from the top of a planar hill slope and starts sliding down the slope as shown in the figure. The slope angle is 30° with the horizontal. After travelling a distance of 40 m in the same direction on the slope, the block hits the road. Assuming zero cohesion and zero friction, and considering acceleration due to gravity (g) as 10 m/s2, the velocity with which the block hits the road is ________ m/s.
Answer: (20 to 20)
28. Liquid limit and plastic limit of a soil are 40% and 20%, respectively. If the natural (i.e. in situ) water content of the soil is 30%. the liquidity index is ___________.
Answer: (0.5 to 0.5)
29. A confined aquifer has a uniform area (‘A’) perpendicular to the water flow. The hydraulic gradient and coefficient of permeability are given as 0.005 and 2 m/day, respectively. The total daily flow of water is 250 m3. Using Darcy’s law, the calculated value of ‘A’ is ________m2.
Answer: (25000 to 25000)
30. The apparent dip amount of a sandstone bed is 45°. The angle between the true dip direction and the apparent dip direction is 60°. The true dip amount of the bed is ________ degree (°). (Round off to 2 decimal places)
Answer: (63.42 to 63.44)
PART B (Section 2): Fro Geophysics Candidates only)
Q1 – Q30 carry two marks each.
1. International gravity formula is based on which one of the following models?
(A) Non-rotating homogeneous spherical Earth model
(B) Non-rotating homogenous oblate spheroidal Earth model
(C) Rotating homogeneous oblate spheroidal Earth model
(D) Rotating inhomogeneous spherical Earth model
Answer: (C)
2. Heat flow equation is valid when
[T = Temperature, z is coordinate along z-axis]
(A) steady state heat conduction is considered in an isotropic medium without heat source
(B) steady state heat conduction is considered in an isotropic medium with heat source
(C) steady state heat convection is considered in an isotropic medium without heat source
(D) steady state heat convection is considered in an isotropic medium with heat source
Answer: (A)
3. Assuming the inner core of the Earth to be one-third of its present size, which one of the following statements is CORRECT? (Radius of the Earth and outer core remain unchanged)
(A) Shadow zone of P-wave increases but that of S-wave decreases
(B) Shadow zone of P-wave increases and that S-wave remains unchanged
(C) Shadow zone of P-wave increases and that S-wave increases
(D) Shadow zone of P-wave decreases but that of S-wave remains unchanged
Answer: (MTA)
4. Match the following instruments (Group I) with their corresponding physical principle (Group II)
(A) P-4, Q-1, R-2, S-3
(B) P-4, Q-3, R-2, S-1
(C) P-3, Q-1, R-4, S-2
(D) P-3, Q-2, R-4, S-1
Answer: (C)
5. The sensitivity of LaCoste-Romberg gravimeter is proportional to the line period (T) of the spring as
(A) T2
(B) 1/T2
(C) √T
(D) 1/√T
Answer: (A)
6. Match the following gravity/magnetic data interpretation techniques (Group I) with the corresponding terms (Group II)
(A) P-4, Q-1, R-2, S-3
(B) P-3, Q-4, R-1, S-2
(C) P-4, Q-2, R-1, S-3
(D) P-3, Q-1, R-4, S-2
Answer: (B)
7. Assuming uncorrelated noise, the improvement in the signal to noise ratio in a reflection seismic survey with ‘n’ geophones spaced equally along the profile is proportional to
(A) n
(B) 1/n
(C) √n
(D) 1/√n
Answer: (C)
8. A waveform with amplitude spectrum A(ω) and phase spectrum ϕ(ω) is auto-correlated. Which one of the options given below correctly represents the information about t he original waveform that can be retrieved from the autocorrelated waveform?
(A) A(ω) can be retrieved but not ϕ(ω)
(B) ϕ(ω) can be retrieved but not A(ω)
(C) Both A(ω) and ϕ(ω) can be retrieved
(D) Both A(ω) and ϕ(ω) cannot retrieved
Answer: (A)
9. The convolution A(4, 2, −1, 2) with B(1, 0, −1) gives
(A) {−4, 2, −5, 0, 1 2}
(B) {4, 2, −5, 0, 1, −2}
(C) {−4, −2, 5, 0, −1, −2}
(D) 4, 2, 5, 0, −1, 2}
Answer: (B)
10. Which one of the following does NOT contribute to the suppression of SP log response for a thin, shaly, gas-bearing sandstone formation? (Resistivity of mud filtrate > resistivity of formation water)
(A) Increase in shale content
(B) Increase in hydrocarbon content
(C) Decrease in the thickness of the bed
(D) Increase in the salinity of formation water
Answer: (D)
11. The crossover observed for a hydrocarbon-bearing sandstone formation in the plot of Neutron and Density porosity logs (∅n – Neutron Density porosity is due to
(A) increase in ∅d and decrease in ∅n
(B) decrease in ∅d and increase in ∅n
(C) increase in both ∅d and ∅n
(D) decrease in both ∅d and ∅n
Answer: (A)
12. In which one of the following electromagnetic methods are the amplitude ratio and relative phase difference measured between two receiver coils?
(A) Fixed vertical loop method
(B) Compensator method
(C) TURAM method
(D) Slingram method
Answer: (C)
13. If four impedance tensors Zxx, Zyy, Zxy and Zyx are computed for a 2D body in magneto-telluric method (x is the strike direction), then
(A) Zxx = 0, Zyy ≠ 0, Zxy = Zyx
(B) Zxx ≠ 0, Zyy ≠ 0, Zxy = Zyx
(C) Zxx ≠ 0, Zyy ≠ 0, Zxy ≠ Zyx
(D) Zxx = 0, Zyy = 0, Zxy ≠ Zyx
Answer: (D)
14. Match the inversion methods (Group I) with the associated terms (Group II)
(A) P-3, Q-2, R-1, S-4
(B) P-4, Q-3, R-1, S-2
(C) P-2, Q-1, R-4, S-3
(D) P-2, Q-3, R-4, S-1
Answer: (D)
15. Ten equispaced metal electrodes are arranged along a profile for multi-electrode 2D resistivity imaging survey. If Wenner array is used for data recording, the maximum number of observations will be
(A) 7
(B) 11
(C) 12
(D) 13
Answer: (C)
16. P and R are Jacobian matrices for two different geophysical inverse problems. If their generalized inverses are written as P−1 = (PTP)−1PT and R−1 = RT(RRT)−1, then
(A) both P and R deal with over-determined problems
(B) both P and R deal with under-determined problems
(C) P deals with over-determined and R deals with under-determined problem
(D) P deals with under-determined and R deals with over-determined problem
Answer: (C)
17. In a 3D seismic survey, there are 512 groups of receivers in one line of a patch. Eight groups are moved per line from one patch to the next along the swath. What is the inline fold?
(A) 32
(B) 16
(C) 8
(D) 4
Answer: (A)
18. The magnetic potential of a uniform vertically magnetized buried spherical body with uniform density is given as Then, the vertical magnetic field Bz is proportional to
[I = intensity of magnetization, ρ = density, gz = vertical component of gravity field, G = Universal gravitational constant, μ0 = magnetic permeability of three space, coordinate of the center of the body is (0, z) and that of the observation point is (x, 0)]
(A)
(B)
(C)
(D)
Answer: (A)
19. A sample of granite is observed to have a P-wave velocity of 5 km/s and density of 2600 kg/m3. The bulk modulus of the granite, assuming it to be a Poisson’s solid, is ________kilo-Pascal (kPa). (Round off to 2 decimal places)
Answer: (35000000 to 37000000)
20. The half-life of a parent radionuclide is 100 yrs. If the parent radionuclide decays to a daughter radionuclide which itself decays with a decay constant of 1/4th that of the parent radionuclide, then radioactive equilibrium will be reached after ______ (Round of to 2 decimal places) (Assume at time t = 0 the number of daughter radionuclide is zero)
Answer: (265.00 to 270.00)
21. Current and potential electrodes in resistivity survey over an inhomogeneous ground is shown in the figure below. If 100 mA current flow between C1 and C2 generates 50 mV potential difference between P1 and P2, then the apparent resistivity of the medium will be _______Ω (Round off to 2 decimal places) (Use π = 3.14)
Answer: (37.00 to 41.00)
22. Skin depths in homogeneous media of resistivity ρ1 and ρ2 are 100 m and 200 m, respectively, at 1000 Hz frequency. The ratio ρ1/ρ2 will be _______.(Round of to 2 decimal places)
Answer: (0.23 to 0.27)
23. The mean resistivity of a horizontally stratified cuboid rock sample is 100 Ωm and coefficient of electrical anisotropy is 1.15. The transverse resistivity of the rock sample is _______ Ω (Round off to 2 decimal places)
Answer: (113.00 to 117.00)
24. A seismic reflection survey is carried out over a 1500 m thick horizontal layer with a P-wave velocity of 2000 m/s. The travel time of a reflected wave at a surface detector placed 1000 m from a surface source is ________ milliseconds.
Answer: (1576 to 1586)
25. A seismic reflection survey is carried out using a 10 milliseconds seismic wavelet over a subsurface medium having an average P-wave velocity of 1600 m/s. The best resolution which is obtained on the basis of Rayleigh criteria is _______ m. (Assume seismic wavelet contains one cycle)
Answer: (4 to 4)
26. To detect a 0.01 nT change in magnetic field using a proton precession magnetometer, the sensitivity required in the frequency measurement of the instrument is ______ × 10−4 (Round off to 2 decimal places) (Assume gyromagnetic ratio of proton as 2.67515 × 108 s−1T−1)
Answer: (4.24 to 4.28)
27. A micro-gravity survey with appropriate station spacing is performed to detect a subsurface spherical cavity in a bedrock of density 2500 kg/m3. The depth to the center of the cavity is 4 m from the surface and the elevation measurement accuracy of the surveying instrument is 0.1 m. The smallest cavity that can be detected by the survey must have a radius greater than _______m. (Round of to 1 decimal place) (Assume G = 6.673 × 10−11 m3kg−1s−2)
Answer: (1.6 to 2.1)
28. The gravity anomaly over a spherical ore body is shown in the figure below. The calculated excess mass due to the ore body will be ________ × 1010 (Round off to 1 decimal place) (Assume z = 1.3 × x1/2; G = 6.673 × 10−11 m3kg−1s−2)
Answer: (2.1 to 2.5)
29. A scalar potential field in 3D space is expressed as U(x, y, z) = x2 + yz2. The magnitude of the maximum rate of change in U(x, y, z) at a point (1, 1, 2) is ________.
Answer: (6 to 6)
30. A 10 Hz seismic wave propagates for 40 km through a material with a P-wave velocity of 5 km/s and quality factor (Q) of 100. The percentage of the initial amplitude retained in the attenuated wave is _______. (Round off to 1 decimal place) (Use π = 3.14)
1. This book, including all its chapters, ______ interesting. The students as well as the instructor ______ in agreement about it.
(A) is, was
(B) are, are
(C) is, are
(D) were, was
Answer: (C)
2. People were prohibited ______ their vehicles near the entrance of the main administrative building.
(A) to park
(B) from parking
(C) parking
(D) to have parked
Answer: (B)
3. Select the word that fits the analogy:
Do : Undo :: Trust : ________
(A) Entrust
(B) Intrust
(C) Distrust
(D) Untrust
Answer: (C)
4. Stock markets ________ at the news of the coup.
(A) poised
(B) plunged
(C) plugged
(D) probed
Answer: (B)
5. If P, Q, R, S are four individuals, how many teams of size exceeding one can be formed, with Q as a member ?
(A) 5
(B) 6
(C) 7
(D) 8
Answer: (C)
Q6 – Q10 carry two marks each.
6. Non-performing Assets (NPAs) of a bank in India is defined as an asset, which remains unpaid by a borrower for a certain period of time in terms of interest, principal, or both. Reserve Bank of India (RBI) has changed the definition of NPA thrice during 1993-2004, in terms of the holding period of loans. The holding period was reduced by one quarter each time. In 1993, the holding period was four quarters (360 days).
Based on the above paragraph, the holding period of loans in 2004 after the third revision was ______ days.
(A) 45
(B) 90
(C) 135
(D) 180
Answer: (B)
7. Select the next element of the series: Z, WV, RQP, ______
(A) LKJI
(B) JIHG
(C) KJIH
(D) NMLK
Answer: (C)
8. In four-digit integer numbers from 1001 to 9999, the digit group “37” (in the same sequence) appears ______ times.
(A) 270
(B) 279
(C) 280
(D) 299
Answer: (C)
9. Given a semicircle with O as the centre, as shown in the figure, the ratio is ______. where are chords.
(A) √2
(B) √3
(C) 2
(D) 3
Answer: (A)
10. The revenue and expenditure of four different companies P, Q, R and S in 2015 are shown in the figure. If the revenue of company Q in 2015 was 20% more than that in 2014, and company Q had earned a profit of 10% on expenditure in 2014, then its expenditure (in million rupees) in 2014 was _______.
(A) 32.7
(B) 33.7
(C) 34.1
(D) 35.1
Answer: (C)
EY: Ecology and Evolution
Q1 – Q25 carry one mark each.
1. Who among the following was a strong public supporter of Darwin’s theory of evolution by natural selection?
(A) Jean-Baptiste Lamarck
(B) Carl Linnaeus
(C) Thomas Huxley
(D) Gregor Mendel
Answer: (C)
2. Analysis of variance (ANOVA) can be used to compare multiple groups of samples. Select the correct option that reflects the principle behind ANOVA.
(A) The sum of the squares of the variances is calculated for the groups being compared.
(B) The variance ratio is calculated by subtracting each value from the overall mean, squaring the difference, and summing the resulting squared deviations.
(C) The variation between groups is compared with the variation within groups.
(D) The F value I statistically significant if the mean values between the groups are the same.
Answer: (C)
3. Which of the following information is provided by phylogenetic tree?
(A) The topology and the branch lengths of the related taxa.
(B) The topology and sequence length of the gene.
(C) The sequence length of the gene and tree length.
(D) The sequence type ad sequence variations within each taxa.
Answer: (A)
4. Myrmecochory refers to seed dispersal by which of the following agents?
(A) Bats
(B) Ants
(C) Lizards
(D) Birds
Answer: (B)
5. Which of the following is NOT capable of photosynthesis ?
(A) Diatoms
(B) Phytoplankton
(C) Pteridophytes
(D) Ascomycetes
Answer: (D)
6. Which of the following sensory mechanisms do most frugivorous bats primarily use while foraging?
(A) Olfaction
(B) Electromagnetism
(C) Vibration
(D) Echolocation
Answer: (A)
7. What direct effect does Follicle Stimulating Hormone (FSH) have in vertebrates?
(A) It causes follicles of the duodenum to contract.
(B) It causes follicles o the ovaries to grow.
(C) It causes follicles of the liver to enlarge.
(D) It causes follicles of muscles to contract.
Answer: (B)
8. Juvenile rhesus macaques, who have never seen a leopard before, can learn to show fear response if they see an adult react fearfully to a leopard. What kind of behavioural response is this?
(A) Imprinting
(B) Instinct
(C) Cultural transmission
(D) Mimicry transmission
Answer: (C)
9. In a tropical rainforest during the day, which of the following factors does NOT affect the spectral irradiance at the forest floor?
(A) Angle of the sun on the horizon.
(B) Weather conditions of the atmosphere.
(C) Structure of the canopy vegetation.
(D) Spectral reflectance of the leaf litter.
Answer: (D)
10. What would evolutionary biologist hypothesize as the ultimate cause for the presence of colouful dewlaps in lizards?
(A) Colour of dewlaps are formed by pigments in the skin.
(B) Colourful dewlaps are formed by folds in the skin.
(C) Colourful dewlaps increase mating success.
(D) Colourful dewlaps are regions where motor neurons control head movement.
Answer: (C)
11. Which of the following is true about comparisons between herbivorous and carnivorous mammals?
(A) Herbivores have longer digestive tracts and smaller caecum for the given body size than carnivores.
(B) Carnivores have longer digestive tracts and smaller caecum for a given body size than herbivores.
(C) Herbivores have shorter digestive tracts and smaller caecum for a given body size than carnivores.
(D) Carnivores have shorter digestive tracts and smaller caecum for a given body size than herbivores.
Answer: (D)
12. Two isolated populations X and Y have 100 ad 10000 individuals respectively. Both populations have the same starting allele frequencies of p = 0.5 and q = 0.5. After 1000 generations of genetic drift, which of the following statements is true about the heterozygosity at this locus in these two populations?
(A) The heterozygosity of population X will be more than population Y.
(B) The heterozygosity of population Y will be more than in population X.
(C) The heterozygosity of both the populations will be identical.
(D) The heterozygosity of these populations will not depend on their population sizes.
Answer: (B)
13. Which of the following criteria is used to define species under the biological species concept?
(A) Niche partitioning
(B) Reproductive isolation
(C) Morphological divergence
(D) Genetic distance
Answer: (B)
14. The abundances of three species (P, Q and R) were measured along a resource gradient. The resultant pattern in summarized in the figure. Which of the following statements can be inferred from niche theory?
(A) P is generalist; Q and R are specialists.
(B) Q is a generalist; P and R specialists.
(C) P and Q are generalists; R is a specialist.
(D) P and R are generalists; Q is a specialist.
Answer: (B)
15. In the last 3 to 4 decades, the average CO2 concentration in the Earth’s atmosphere has increased from_______.
(A) 3 ppm to 4 ppm
(B) 30 ppm to 40 ppm
(C) 300 ppm to 400 ppm
(D) 3000 ppm to 4000 ppm
Answer: (C)
16. What effect does myelination have on neurons?
(A) It increases the transmembrane resistance.
(B) It increases the membrane capacitance.
(C) It changes the direction of signal propagation.
(D) It protects synapse from damage.
Answer: (A)
17. Which of the following processes contributes to an increase in genetic variation?
(A) Genetic drift
(B) Directional selection
(C) Inbreeding
(D) Immigration
Answer: (D)
18. What characteristic do the plant species, sundew (Drosera capensis) and Venus fly trap (Dionaea muscipla), share?
(A) They are thigmonastic.
(B) They are nyctinastic.
(C) They are epiphytic.
(D) They are endophytic.
Answer: (A)
19. What is the study of fish known as?
(A) Malacology
(B) Herpetology
(C) Physiology
(D) Ichthyology
Answer: (D)
20. On one side of a house, a 50 watt bulb attracts moths at a rate of 30 individuals/minute. On the other side of the house, a 15 watt bulb attracts moths at a rate of 10 individuals/minute. There are 20 bats in the area who are foraging for these moths. According to Ideal Free Distribution, the number of bats near the 15 watt bulb should be _______.
Answer: (5 to 5)
21. The Simpson’s index of diversity is expressed as:
Where pi is the proportion of the ith species, and n is the total number of species.
The Simpson’s index of diversity for this dataset is ____ (round off to three decimal places).
Answer: (0.440 to 0.454)
22. In a botanical garden, tree species P had an average height of 1.5 m, while tree species Q had n average height of 1.8 m Pooled together, these two tree species had an average height of 1.7 m. From this, one can infer that the number of trees of species Q in the garden was _______ times the number of trees of species P.
Answer: (2 to 2)
23. A fragment of double stranded DNA has 30% Adenine. The % GC content in this fragment is _______.
Answer: (40 to 40)
24. A researcher traps rodents in a small, isolated forest patch. In the first trapping session she captures 24 mice ad marks them by notching their ears. In the second trapping session she captures 16 mice, of which 8 are already marked. Assuming that the population is closed (no immigration, emigration, birth, or death), the estimated number mice in the patch is_______.
Answer: (48 to 48)
25. A raptor sitting on a tree sees a rodent on the ground below as shown in the figure (not to scale). If the raptor views the rodent from a height of 10 metres, and the rodent subtends a visual angle of 45° on the raptor’s eye, the straight line distance from the raptor to the rodent in metres is ______ (round off to two decimal places).
Answer: (14.00 to 14.28)
Q26 – Q55 carry two marks each.
26. Beetles of one species have the option of eating plant species X or Y in their environment. Plant species X and Y have the same nutritional quality. When beetle diets comprise a greater proportion of a plant X, the population size of beetles increase faster than when beetle diets are dominated by plant Y. Which of the following is NOT a probable explanation for this outcome?
(A) Xenobiotics in X are physiologically easier for the beetles to detoxify than t hose in Y.
(B) Sequestration of xenobiotics from Y by the beetles confers greater protection from bird predators than those from Y.
(C) X attracts parasites of the beetles while Y does not.
(D) X provides greater protection from bird predators during foraging than does Y.
Answer: (C)
27. A researcher was documenting the number of tree species in landscape. Within each of three forest types (P, Q and R), she laid 100 quadrats and documented all the species found in each quadrat. She then plotted the cumulative species richness for these forest types as shown in the figure. Which of the following statements is FALSE?
(A) There are more species of trees in P than in R.
(B) There are more species of trees in Q than in R.
(C) More quadrats are required to estimate species richness in P than in Q.
(D) More quadrats are required to estimate species richness in Q than in R.
Answer: (C)
28. Which of the following ha an endemic species represented in the Andaman and Nicobar Islands for all taxonomic groups in that column?
(A) Column P
(B) Column Q
(C) Column R
(D) Column S
Answer: (D)
29. The theory of island biogeography predicts that the number of species o islands is determined by: (i) the rate of colonization, which depends on the distance of the island from the mainland and (ii) the rate of extinction which depends on the size of the island. A researcher surveyed two islands with similar habitats and geological history, and found that both islands have the same number of species. Which of the following statement(s) can explain this observation?
(P) The islands are of the same size and are at the same distance from the mainland.
(Q) The islands are of different sizes and are at the same distance from the mainland.
(R) The islands are of the same size and are at different distance from the mainland.
(S) The islands are of different sizes and are of different distances from t he mainland.
(A) Only P.
(B) Only Q.
(C) Both P and S.
(D) Both Q and R.
Answer: (C)
30. In marine fauna, Pelagic Larval Duration (PLD) or the amount of time that larvae spend swimming or drifting in the water column affects their dispersal distance. Successful establishment of the larvae on a substrate also depends on finding a suitable habitat after dispersal, which is influenced by whether that habitat is patchy or continuous. Which of the following species will have the lowest population genetic structure (FST) across the same spatial scale?
(A) Species with high PLD inn patchy habitats.
(B) Species with high PLD in continuous habitats.
(C) Species with low PLD in patchy habitats.
(D) Species with low PLD in continuous habitats.
Answer: (B)
31. Every lake in Wakanda has three species of fish: P, Q and R. Species P is a bottom dweller and substrate feeder, species Q is a mid-column dweller and herbivore, and species R is a surface dweller and piscivore. Which of the following processes best explains this distribution pattern?
(A) Speciation within one lake followed by dispersal to other lakes.
(B) Dispersal between lakes followed by speciation within lakes.
(C) Independent speciation events within all the takes.
(D) Speciation within a lake with no dispersal between lakes.
Answer: (A)
32. Group living can have both benefits (such as protection from predators) and costs (such as competition for resources). The figure depicts net benefit to individuals as a function of group size. Consider a population with more than hundred individuals, where groups do not split, and individuals can choose to either join a group or remain solitary. Given this information, what is the typical group size predicted?
(A) Less than 6
(B) Equal to 6
(C) Between 6 and 12
(D) Greater than 12
Answer: (C)
33. Two species of snails, P and Q, are found in rivers across a range of temperatures that vary from upstream a downstream. An experiment was conducted in which P was removed from a river and the distribution of Q was measured after a few weeks. In another similar river, the reciprocal experiment was conducted I which Q was removed, and the distribution of P was measured after a few weeks. In the graph below, the filled bars plot the distribution of P and Q when both species are present in a river. The open bars plot the distribution of P when Q is removed, and Q when P is removed. Which of the following statements is true?
(A) The realized niche of P is smaller than its fundamental niche.
(B) The realized niche of Q is smaller than its fundamental niche.
(C) The realized niche is smaller than the fundamental niche for both species.
(D) The realized niches of both species are equal.
Answer: (A)
34. In plants with bisexual flowers (hermaphrodites), mate-choice by females is expected to be important under which of the following cases?
(i) Seed set is pollen-limited rather than resource-limited.
(ii) Obligate self-pollination is present.
(iii) Seed set is resource-limited rather than pollen-limited.
(iv) Obligate cross-pollination is present.
(A) (i) and (ii)
(B) (ii) and (iii)
(C) (iii) and (iv)
(D) (i) and (iv)
Answer: (C)
35. Match the breeding system of the plants with their pollen : ovule ratio.
(A) P-i, Q-iii, R-ii, S-iv
(B) P-ii, Q-i, R-iv, S-iii
(C) P-iv, Q-iii, R-i, S-ii
(D) P-iii, Q-iv, R-i, S-ii
Answer: (C)
36. A particular gene sequence from two different species shows molecular clock-like evolution. Which of the following statements is consistent with this observation?
(A) The two sequences will show a linear decrease in their genetic distance with time.
(B) The genetic distance between the two sequences remains constant over time.
(C) The rate of evolution for this gene sequence is not constant over time.
(D) The two sequences will show a linear increase in their genetic distance with time.
Answer: (D)
37. An internal parasite of a mammal does not generate its own heat and yet it can maintain a constant body temperature. Which characteristics describe this parasite?
(A) Homeothermic ectotherm
(B) Homeothermic endotherm
(C) Poikilothermic ectotherm
(D) Poikilothermic endotherm
Answer: (A)
38. In a population of infinite size, the frequency of two alleles. A1 and A2 at a neutral locus are the same. What are the expected genotype frequencies (A1A1, A1A2, A2A2) after 100 generations of random mating?
(A) 0.25, 0.5, 0.25
(B) 0.5, 0.25, 0.25
(C) 0.25, 0.25, 0.5
(D) 0.05, 0.5, 0.45
Answer: (A)
39. A certain rodent species shows territoriality, competes for space and food, and their population is at carrying capacity. In the figures, the area within the rectangle (i) to (iv) represents a completely homogenous habitat where resources are distributed throughout, and the grey polygons represent rodent home ranges. Which of the following patterns best represents the expected distribution of home ranges of the rodent species if individuals vary in competitive ability?
(A) (i)
(B) (ii)
(C) (iii)
(D) (iv)
Answer: (D)
40. For a given gene there is 5% DNA sequence divergence between two species, however the protein coded by this gene has identical sequences in the two species. Which of the following types of mutations best explains this pattern in the DNA sequence?
(A) Nonsense mutation
(B) Synonymous substitution
(C) Non-synonymous substitution
(D) Frame-shift mutation
Answer: (B)
41. A researcher collects data on plant species composition in two habitats (P and Q) by using 10 quadrats each in both habitats. She calculates the average α-diversity and the β-diversity of each habitat from this data (shown below). Which of the following can be inferred about these habitats?
(A) p and Q have the same total diversity (γ) and P is more heterogeneous than Q.
(B) Q has lower total diversity (γ) and is more heterogeneous than P.
(C) P has greater total diversity (γ) and is more heterogeneous than Q.
(D) Q has greater total diversity (γ) and is more heterogeneous than P.
Answer: (C)
42. Among four related bird species P, Q, R and S, species P and Q are nectar feeding with long thin beaks, whereas species R and S are seed eaters with short thick beaks. Which o the following phylogenies unambiguously suggests that seed eating habit was the ancestral state?
(A) (i)
(B) (ii)
(C) (iii)
(D) (iv)
Answer: (B)
43. A population of unicorns is growing over time, but its rate of growth is declining. Which of the following graphs best represents this pattern of growth?
(A) (i)
(B) (ii)
(C) (iii)
(D) (iv)
Answer: (A)
44. In a polyploidization event, tetraploid progeny were formed by diploid parents. Hybridization between the tetraploid and diploid parent gave rise to sterile triploids. Which of the following best explains why these triploids were sterile?
(A) Many mutations during polyploidization have no phenotypic effect.
(B) Some chromosomes are without homologs during meiosis.
(C) Some chromosomes are without homologs during mitosis.
(D) All chromosomes have homologs during mitosis.
Answer: (B)
45. Blood tests are often used to screen for potential diseases. For a particular disease:
(i) Of 1000 persons who tested negative (T’), 1 person had the disease (D); Pr(D|T’).
(ii) of 10 persons who tested positive (T’), 1 person had the disease (D); Pr(D|T’).
From this we can calculate
What can be inferred from t his value ?
(A) 100 people have the disease but they will not test positive.
(B) 1 in 100 people have the disease and they will test positive.
(C) 100 in 1000 people have the disease and their blood tests will be inconclusive.
(D) People with positive tests are 100 time more likely t have the disease than people with negative tests.
Answer: (D)
46. The relative frequency distributions of vales of a trait in two samples, P and Q, are shown in figure. Which of the following statements is consistent with the figure?
(A) P has higher mean than Q; Q has higher variance than P.
(B) P has a higher mean than Q: P has a higher variance than Q.
(C) P and Q have the same mean; Q has higher variance than P.
(D) P and Q have the same mean; P has higher variance than Q.
Answer: (C)
47. Consider the function f(x) = |(eβx)/(β)|
Which of the following graphs represents the relationship between x and f(x)?
(A) (i)
(B) (ii)
(C) (iii)
(D) (iv)
Answer: (A)
48. In a nocturnal moth species (X), individuals with longer antennae have smaller eyes. This indicates a sensory trade-off. In a closely related but diurnal moth species (Y), individuals exhibit the same obligate sensory trade-off. Which of the following figures describes the relationship between these two traits in moth species Y, if it relies more on vision than olfaction?
(A) (i)
(B) (ii)
(C) (iii)
(D) (iv)
Answer: (A)
49. A researcher compared grass species richness in a 10 m × 10 m plot immediately before (T0) and 100 days after (T100) a fire. She observed that species richness was higher at T100 than at T0. Which of the following data is required for her to conclude that species richness increased because of the fire?
(A) Grass species richness of a 10 m × 10 m plot in a nearby area that also burned.
(B) Grass species richness of a 10 m × 10 m plot only at T100 in nearby area that did not burn.
(C) Grass species richness of a 10 m × 10 m plot at both T0 and T100 in a nearby area that did not burn.
(D) Grass species richness of the same 10 m × 10 m plot every 10 days after the fire until T100.
Answer: (C)
50. Following a gene duplication event, the duplicated copy often loses function and is called a pseudogene. In the absence of positive selection, which of the following is true about these genes?
(A) The functional gene will accumulate mutations more rapidly than the pseudogene.
(B) The pseudogene will accumulate mutations more rapidly than the functional gene.
(C) Both the functional gene and pseudogene will accumulate mutations at the same rate.
(D) The pseudogene will not accumulate mutations.
Answer: (B)
51. Which of the figures represents the expected relationship between parental care and the number of offspring produced across taxa?
(A) (i)
(B) (ii)
(C) (iii)
(D) (iv)
Answer: (C)
52. Match the following plant traits with the correct plant group/family:
(A) P-iv, Q-v, R-i, S-ii
(B) P-ii, Q-iv, R-iii, S-i
(C) P-i, Q-ii, R-iii, S-iv
(D) P-iii, Q-v, R-i, S-ii
Answer: (D)
53. In a population of 100 individuals of a diploid organism with 1:1 sex ratio, the probability of fixation of a new neutral mutation is ______ (round off to three decimal places).
Answer: (0.005 to 0.005)
54. The binomial probability of obtaining exactly k successes in n trials, where the probability of success in a single trial is p, is given by :
Here, rotation refers to number of combinations for k successes among n trials. With a fair and unbiased coin, the probability of getting 2 HEADS in a trial with 5 tosses is __________ (round off to two decimal places).
Answer: (0.30 to 0.35)
55. The petrified wood fossil was discovered with 8 g of 14 The decay of 14C over time is given by:
NT = N0e−0.0001216T
I the half-life of 14C is 5700 years, and the fossil initially had 2 g of 14C, the age of the fossil in years is ________.
1. This book, including all its chapters, ______ interesting. The students as well as the instructor ______ in agreement about it.
(A) is, was
(B) are, are
(C) is, are
(D) were, was
Answer: (C)
2. People were prohibited ______ their vehicles near the entrance of the main administrative building.
(A) to park
(B) from parking
(C) parking
(D) to have parked
Answer: (B)
3. Select the word that fits the analogy:
Do : Undo :: Trust : ________
(A) Entrust
(B) Intrust
(C) Distrust
(D) Untrust
Answer: (C)
4. Stock markets ________ at the news of the coup.
(A) poised
(B) plunged
(C) plugged
(D) probed
Answer: (B)
5. If P, Q, R, S are four individuals, how many teams of size exceeding one can be formed, with Q as a member ?
(A) 5
(B) 6
(C) 7
(D) 8
Answer: (C)
Q6 – Q10 carry two marks each.
6. Non-performing Assets (NPAs) of a bank in India is defined as an asset, which remains unpaid by a borrower for a certain period of time in terms of interest, principal, or both. Reserve Bank of India (RBI) has changed the definition of NPA thrice during 1993-2004, in terms of the holding period of loans. The holding period was reduced by one quarter each time. In 1993, the holding period was four quarters (360 days).
Based on the above paragraph, the holding period of loans in 2004 after the third revision was ______ days.
(A) 45
(B) 90
(C) 135
(D) 180
Answer: (B)
7. Select the next element of the series: Z, WV, RQP, ______
(A) LKJI
(B) JIHG
(C) KJIH
(D) NMLK
Answer: (C)
8. In four-digit integer numbers from 1001 to 9999, the digit group “37” (in the same sequence) appears ______ times.
(A) 270
(B) 279
(C) 280
(D) 299
Answer: (C)
9. Given a semicircle with O as the centre, as shown in the figure, the ratio is ______. where are chords.
(A) √2
(B) √3
(C) 2
(D) 3
Answer: (A)
10. The revenue and expenditure of four different companies P, Q, R and S in 2015 are shown in the figure. If the revenue of company Q in 2015 was 20% more than that in 2014, and company Q had earned a profit of 10% on expenditure in 2014, then its expenditure (in million rupees) in 2014 was _______.
(A) 32.7
(B) 33.7
(C) 34.1
(D) 35.1
Answer: (C)
EE: Electrical Engineering
Q1 – Q25 carry one mark each.
1. ax3 + bx2 + cx + d is a polynomial on real x over real coefficients a, b, c, d wherein a ≠ Which of the following statements is true?
(A) d can be chosen to ensure that x = 0 is a root for any given set a, b, c.
(B) no choice of coefficients can make all roots identical.
(C) a, b, c, d can be chosen to ensure that all roots are complex.
(D) c alone cannot ensure that all roots are real.
Answer: (A OR D)
2. Which of the following is true for all possible non-zero choices of integers m, n; m ≠ n, or all possible non-zero choices of real numbers p, q; p ≠ q, as applicable?
(A)
(B)
(C)
(D)
Answer: (C)
3. Which of the following statements is true about the two sided Laplace transform?
(A) It exists for every signal that may or may not have a Fourier transform.
(B) It has no poles for any bounded signal that is non-zero only inside a finite time interval.
(C) The number of finite poles and finite zeroes must be equal.
(D) If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.
Answer: (B)
4. Consider a signal where 1[n] = 0 if n < 0, and 1 [n] = 1 if n ≥ The z-transform of x[n – k], k > 0 is with region of convergence being
(A) |z| < 2
(B) |z| > 2
(C) |z| < 1/2
(D) |z| > 1/2
Answer: (D)
5. The value of the following complex integral, with C representing the unit circle centered at origin in the counterclockwise sense, is:
(A) 8πi
(B) −8πi
(C) −πi
(D) πi
Answer: (C)
6. xR and xA are, respectively, the rms and average values of x(t) = x(t – T), and similarly, yR and yA are, respectively, the rms and average values of y(t) = kx(t). k, T are independent of t. Which of the following is true?
(A) yA = kxA; yR = kxR
(B) yA = kxA; yR ≠ kxR
(C) yA ≠ kxA; yR = kxR
(D) yA ≠ kxA; yR ≠ kxR
Answer: (A)
7. A three-phase cylindrical rotor synchronous generator has a synchronous reactance Xs and a negligible armature resistance. The magnitude of per phase terminal voltage is VA and the magnitude of per phase induced emf is EA. Considering the following two statements, P and Q.
P: For any three-phase balanced leading load connected across the terminals of this synchronous generator, VA is always more than EA
Q: For any three-phase balanced lagging load connected across the terminals of this synchronous generator, VA is always less than EA
Which of the following options is correct?
(A) P is false Q is true.
(B) P is true and Q is false.
(C) P is false and Q is false.
(D) P is true and Q is true.
Answer: (A)
8. A lossless transmission line with 0.2 pu reactance per phase uniformly distributed along the length of the line, connecting a generator bus to a load bus, is protected up to 80% of its length by a distance relay placed at the generator bus. The generator terminal voltage is 1 pu. There is no generation at the load bus. The threshold pu current for operation of the distance relay for a solid three phase-to-ground fault on the transmission line is closest to:
(A) 1.00
(B) 3.61
(C) 5.00
(D) 6.25
Answer: (D)
9. Out of the following options, the most relevant information needed to specify the real power (P) at the PV buses in a load flow analysis is
(A) solution of economic load dispatch
(B) rated power output of the generator
(C) rated voltage of the generator
(D) base power of the generator
Answer: (A)
10. Consider a linear time-invariant system whose input r(t) and output y(t) are related by the following differential equation:
The poles of this system are at
(A) +2j, −2j
(B) +2, −2
(C) +4, −4
(D) +4j, −4j
Answer: (A)
11. A single-phase, full-bridge diode rectifier fed from a 230 V, 50 Hz sinusoidal source supplies a series combination of finite resistance, R, and a very large inductance, L. The two most dominant frequency components in the source current are:
(A) 50 Hz, 0 Hz
(B) 50 Hz, 100 Hz
(C) 50 Hz, 150 Hz
(D) 150 Hz, 250 Hz
Answer: (C)
12. Thyristor T1 is triggered at an angle α (in degree), and T2 at angle 180° + α, in each cycle of the sinusoidal input voltage. Assume both thyristors to be ideal. To control the load power over the range 0 to 2 kW, the minimum range of variation in α is:
(A) 0° to 60°
(B) 0° to 120°
(C) 60° to 120°
(D) 60° to 180°
Answer: (MTA)
13. Which of the options is an equivalent representation of the signal flow graph shown here?
Answer: (C)
14. A common-source amplifier with a drain resistance, RD = 4.7 kΩ, is powered using a 10 V power supply. Assuming that the transconductance, gm, is 520 μA/V, the voltage gain of the amplifier is closest to:
(A) −2.44
(B) −1.22
(C) 1.22
(D) 2.44
Answer: (A)
15. A sequence detector is designed to detect precisely 3 digital inputs, with overlapping sequences detectable. For the sequence (1, 0, 1) and input data (1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0)
(A) 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0
(B) 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0
(C) 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0
(D) 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
Answer: (B)
16. Consider the initial value problem below. The value of y at x = ln 2, (rounded off to 3 decimal places) is ______.
Answer: (0.8774 to 0.8952)
17. A three-phase, 50 Hz, 4-pole induction motor runs at no-load with a slip of 1%. With full load, the slip increases to 5%. The % speed regulation of the motor (rounded off to 2 decimal places) is _______.
Answer: (4.10 to 4.40)
18. Currents through ammeters A2 and A3 in the figure are 1∠10° and 1∠70°, respectively. The reading of the ammeter A1(rounded off to 3 decimal places) is _______A.
Answer: (1.700 to 1.750)
19. The Thevenin equivalent voltage, VTH, in V (rounded off to 2 decimal places) of the network shown below, is ________
Answer: (13.80 to 14.20)
20. A double pulse measurement for an inductively loaded circuit controlled by the IGBT switch is carried out to evaluate the reverse recovery characteristics of the diode, D, represented approximately as a piecewise linear plot of current vs time at diode turn-off. Lpar is a parasitic inductance due to the wiring of the circuit, and in series with the diode. The point on the plot (indicate your choice by entering 1, 2, 3 or 4) at which the IGBT experiences the highest current stress is ________.
Answer: (3 to 3)
21. A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________ W (rounded off to 2 decimal places).
Answer: (162.41 to 162.59)
22. A single-phase inverter is fed from a 100 V dc source and is controlled using a quasi-square wave modulation scheme to produce an output waveform. v(t), as shown. The angle σ is adjusted to entirely eliminate the 3rd harmonic component from the output voltage. Under this condition, for v(t), the magnitude of the 5th harmonic component as a percentage of the magnitude of the fundamental component is ________ (rounded off to 2 decimal places).
Answer: (19.90 to 20.20)
23. A single 50 Hz synchronous generator on droop control was delivering 100 MW power to a system. Due to increase in load, generator power had to be increased by 10 MW, as a result of which, system frequency dropped to 49.75 Hz. Further increase in load in the system resulted in a frequency of 49.25 Hz. At this condition, the power in MW supplied by the generator is ________ (rounded off to 2 decimal places).
Answer: (123.00 to 135.00)
24. Consider a negative unity feedback system with forward path transfer function where K, a, b, c are positive real numbers. For a Nyquist path enclosing the entire imaginary axis and right half of the s-plane in the clockwise direction, the Nyquist plot of (1+ G(s)), encircles the origin of (1+G(s)-plane) once in the clockwise direction and never passes through this origin for a certain value of K. Then, the number of poles of lying in the open right half of the s-plane is ________.
Answer: (2 to 2)
25. The cross-section of a metal-oxide-semiconductor structure is shown schematically. Starting from an uncharged condition, a bias of +3 V is applied to the gate contact with respect to the body contact. The charge inside the silicon dioxide layer is then measured to be +Q. The total charge contained within the dashed box shown, upon application of bias, expressed as a multiple of Q (absolute value in Coulombs, rounded off to nearest integer( is __________.
Answer: (0 to 0)
Q26 – Q55 carry two marks each.
26. For real numbers, x and y, with y = 3x2 + 3x + 1, the maximum and minimum value of y for x ∈ [−2, 0] are respectively_______.
(A) 7 and 1/4.
(B) 7 and 1.
(C) −2 and −1/2.
(D) 1 and 1/4.
Answer: (A)
27. The vector function expressed by F = ax (5y – k1z) + ay (3z + k2x) + az (k3y – 4x) represents a conservative field, where ax, ay, az are unit vectors along x, y and z directions, respectively. The values of constants k1, k2, k3 are given by:
(A) k1 = 3, k2 = 3, k3 = 7
(B) k1 = 3, k2 = 8, k3 = 5
(C) k1 = 4, k2 = 5, k3 = 3
(D) k1 = 0, k2 = 0, k3 = 0
Answer: (C)
28. A 250 V dc shunt motor has an armature resistance of 0.2 Ω and a field resistance of 100 Ω. When the motor is operated on no-load at rated voltage, it draws an armature current of 5 A and runs at 1200 rpm. When a load is coupled to the motor, it draws total line current of 50 A at rated voltage, with a 5% reduction in the air-gap flux due to armature reaction. Voltage drop across the brushes can be taken as 1 V per brush under all operating conditions. The speed of the motor, in rpm, under this loaded condition, is closest to:
(A) 1200
(B) 1000
(C) 1220
(D) 900
Answer: (C)
29. Two buses, i and j, are connected with a transmission line of admittance Y, at the two ends of which there are ideal transformers with turns ratios as shown. Bus admittance matrix for the system is:
Answer: (C)
30. Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic where n > 1, VT > 0, VD is the voltage across the diode and ID is the current through it. The circuit is biased so that voltage, V > 0 and current, I < 0. If you had to design this circuit to transfer maximum power from the current source (I1) to a resistive load (not shown) at the output, what values of R1 and R2 would you choose?
(A) Large R1 and large R2.
(B) Small R1 and small R2.
(C) Large R1 and small R2.
(D) Small R1 and large R2.
Answer: (D)
31. A non-ideal diode is biased with a voltage of −03 V, and a diode current of I1 is measured. The thermal voltage is 26 m V and the ideality factor for the diode is 15/13. The voltage, in V, at which the measured current increases to 1.5I1 is closest to:
(A) −0.02
(B) −0.09
(C) −1.50
(D) −4.50
Answer: (B)
32. A benchtop dc power supply acts as an ideal 4 A current source as long as its terminal voltage is below 10 V. Beyond this point, it begins to behave as an ideal 10 V voltage source for all load currents going down to 0 A. When connected to an ideal rheostat, find the load resistance value at which maximum power is transferred, and the corresponding load voltage and current.
(A) Short, ∞ A, 10 V
(B) Open, 4 A, 0 V
(C) 2.5 Ω, 4 A, 10 V
(D) 2.5 Ω, 4 A, 5 V
Answer: (C)
33. The static electric field inside a dielectric medium with relative permittivity, εr = 2.25, expressed in cylindrical coordinate system is given by the following expression where ar, aφ, az are unit vectors along r, φ and z directions, respectively. If the above expression represents a valid electrostatic field inside the medium, then the volume charge density associated with this field in terms of free space permittivity, ε0, in SI units is given by:
(A) 3ε0
(B) 4ε0
(C) 5ε0
(D) 9ε0
Answer: (D)
34. Consider a permanent magnet dc (PMDC) motor which is initially at rest. At t = 0, a dc voltage of 5 V is applied to the motor. Its speed monotonically increases from 0 rad/s to 6.32 rad/s in 0.5 s and finally settles to 10 rad/s. Assuming that the armature inductance of the motor is negligible, the transfer function for the motor is
Answer: (B)
35. Which of the following options is correct for the system shown below?
(A) 4th order and stable
(B) 3rd order and stable
(C) 4th order and unstable
(D) 3rd order and unstable
Answer: (C)
36. Consider a negative unity feedback system with the forward path transfer function where K is a positive real number. The value of K for which the system will have some of its poles on the imaginary axis is_______.
(A) 9
(B) 8
(C) 7
(D) 6
Answer: (B)
37. Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) * h (t) = y(t). Further, if |x(t)| * |h(t)| = z(t), which of the following statements is true?
(A) For all t ∈ (−∞, ∞) z(t) ≤ y(t)
(B) For some but not all t ∈ (−∞, ∞), z(t) ≤ y(t)
(C) For all t ∈ (−∞, ∞), z(t) ≥ y(t)
(D) For some but not all t ∈ (−∞, ∞), z(t) ≥ y(t)
Answer: (C)
38. The casual realization of a system transfer function H(s) having poles at (2, −1), (−2, 1) and zeroes at (2, 1) (−2, −1) will be
(A) stable, real, allpass
(B) unstable, complex, allpass
(C) unstable, real, highpass
(D) stable, complex, lowpass
Answer: (B)
39. Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:
y[n] – ay[n – 1] = b0x[n] – b1x[n – 1]
(A) y[n] is unaffected by the values of x[n – k]; k > 2.
(B) The system is necessarily casual.
(C) The system impulse response is non-zero at infinitely many instants.
(D) When x[n] = 0, n < 0, the function y[n]; n > 0 is solely determined by the function x[n].
Answer: (C)
40. Let ar, aϕ and az be unit vectors along, r, ϕ and z directions, respectively in the cylindrical coordinate system. For the electric flux density given b y D = (ar15 + aϕ2r – az3rz) Coulomb/m2, the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius 3 m and height 5 m oriented along the z-axis with its base at the origin is:
(A) 54 π
(B) 90 π
(C) 108 π
(D) 180 π
Answer: (D)
41. A stable real linear time-invariant system with single pole at p, has a transfer function with a dc gain of 5. The smallest positive frequency, in rad/s, at unity gain is closest to:
(A) 8.84
(B) 11.08
(C) 78.13
(D) 122.87
Answer: (A)
42. The number of purely real elements in a lower triangular representation of the given 3 × 3 matrix, obtained through the given decomposition is _______.
(A) 5
(B) 6
(C) 8
(D) 9
Answer: (MTA)
43. The figure below shows the per-phase Open Circuit Characteristics (measured in V) and Short Circuit Characteristics (measured in A) of a 14 kVA, 400 V, 50 Hz, 4-pole, 3-phase, delta connected alternator, driven at 1500 rpm. The field current, If is measured in A. Readings taken are marked as respective (x, y) coordinates in the figure. Ratio of the unsaturated synchronous impedances (Zs(unsat)/Zs(sat)) of the alternator is closest to:
(A) 2.100
(B) 2.025
(C) 2.000
(D) 1.000
Answer: (A)
44. Let ax and ay be unit vectors along x and y directions, respectively. A vector function is given by
F = axy – ayx
The line integral of the above function
along the curve C, which follows the parabola y = x2 as shown below is _______ (rounded off to 2 decimal places).
Answer: (-3.05 to -2.95)
45. A resistor and a capacitor are connected in series to a 10 V dc supply through a switch. The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ is the circuit time constant The absolute value of percentage change required in the initial capacitor voltage if the zero crossing has to happen at t = 0.2τ is ________(rounded off to 2 decimal places).
Answer: (54.00 to 56.00)
46. A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now ________ A (rounded off to 2 decimal places).
Answer: (123.00 to 127.00)
47. Bus 1 with voltage magnitude V1 = 1.1 pu is sending reactive power Q12 towards bus 2 with voltage magnitude V2 = 1 pu through a lossless transmission line of reactance X. Keeping the voltage at bus 2 fixed at 1 pu, magnitude of voltage at bus 1 is changed, so that the reactive power Q12 sent from bus 1 is increased by 20%. Real power flow through the line number both the conditions is zero. The new value of the voltage magnitude V1, in pu (rounded off to 2 decimal places),at bus 1 is _______.
Answer: (1.11 to 1.13)
48. Windings ‘A’, ‘B’ and ‘C’ have 20 turns each and are wound on the same iron core as shown, along with winding ‘X’ which has 2 turns. The figure shows the sense (clockwise/anti-clockwise) of each of the windings only and does not reflect the exact number of turns. If windings ‘A’, ‘B’ and ‘C’ are supplied with balanced 2-phase voltages at 50 Hz and there is no core saturation, the no-load RMS voltage (in V, rounded off to 2 decimal places) across winding ‘X’ is ________.
Answer: (MTA)
49. A cylindrical rotor synchronous generator has steady state synchronous reactance of 0.7 pu and subtransient reactance of 0.2 pu. It is operating at (1 + j0) pu terminal voltage with an internal emf of (1 + j0.7) pu. Following a three-phase solid short circuit fault at the terminal of the generator, the magnitude of the subtransient internal emf (rounded off to 2 decimal places) is _______pu.
Answer: (1.01 to 1.03)
50. In the dc-dc converter circuit shown, switch Q is switched at a frequency of 10 kHz with a duty ratio of 0.6. All components of the circuit are ideal, and the initial current in the inductor is zero. Energy stored in the inductor in mJ (rounded off to 2 decimal places) at the end of 10 complete switching cycles is ________.
Answer: (4.95 to 5.05)
51. A single-phase, full-bridge, fully controlled thyristor rectifier feeds a load comprising a 10 Ω resistance in series with a very large inductance. The rectifier is fed from an ideal 230 V, 50 Hz sinusoidal source through cables which have negligible internal resistance and a total inductance of 2.28 mH. If the thyristors are triggered at an angle α = 45°, the commutation overlap angle in degree (rounded off to 2 decimal p laces) is _______.
Answer: (4.51 to 5.10)
52. A non-ideal Si-based pn junction diode is tested by sweeping the bias applied across its terminals from −5 V to + 5 V. The effective thermal voltage, VT, for the diode is measured to be (29 ± 2) mV. The resolution of the voltage source in the measurement range is 1 mV. The percentage uncertainty (rounded off to 2 decimal places) in the measured current at a bias voltage of 0.02 V is ______.
Answer: (11.50 to 12.00)
53. The temperature of the coolant oil bath for a transformer is monitored using the circuit shown. It contains a thermistor with a temperature-dependent resistance, Rthermistor = 2(1 + αT) kΩ, where T is the temperature in ° The temperature coefficient, α, is –(4 ± 0.25)%/°C. Circuit parameters; R1 = 1 kΩ, R2 = 1.3 kΩ, R3 = 2.6 kΩ. The error in the output signal (in V, rounded off to 2 decimal places) at 150°C is _______.
Answer: (MTA)
54. An 8085 microprocessor accesses two memory locations (2001 H) and (2002 H), that contain 8-bit numbers 98H and B1H, respectively. The following program is executed:
LXIH,2001H
MVI A, 21H
INX H
ADD M
INX H
MOV M, A
HLT
At the end of this program, the memory location 2003H contains the number in decimal (base 10) form _______.
Answer: (210 to 210)
55. A conducting square loop of side length 1 m is placed at a distance of 1 m from a long straight wire carrying a current I = 2 A as shown below. The mutual inductance, in nH (rounded off to 2 decimal places), between the conducting loop and the long wire is _______.
1. The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die ______ diseases like cardio vascular disease, cancer, etc.
(A) in, of
(B) from, of
(C) during, from
(D) from, from
Answer: (A)
2. He was not only accused of theft ______ of conspiracy.
(A) rather
(B) but also
(C) but even
(D) rather than
Answer: (B)
3. Select the word that fits the analogy:
Explicit : Implicit : : Express: _______
(A) Impress
(B) Repress
(C) Compress
(D) Suppress
Answer: (B)
4. The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements is English lasting 15 seconds, as opposed to informal 5 second messages in French.
The French-speaking couple were upset at ______.
(A) the in-flight announcements being made in English.
(B) the English announcements being clearer than the French ones.
(C) the English announcements being longer than the French ones.
(D) equal importance being given to English and French.
Answer: (C)
5. A superadditive function f (∙) satisfies the following property
f(x1 + x2) ≥ f(x1) + f(x2)
Which of the following functions is a superadditive function for x > 1?
(A) ex
(B) √x
(C) 1/x
(D) e−x
Answer: (A)
Q6 – Q10 carry two marks each.
6. The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.
Which one of the following sequences shows the correct precedence as per the given passage?
(A) East Asian crisis → subprime lending crisis → banking crisis global financial crisis.
(B) Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.
(C) Banking crisis → subprime lending crisis → global financial crisis → East Asian crisis.
(D) Global financial crisis → East Asian crisis → Banking crisis → subprime lending crisis.
Answer: (A)
7. It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.
(A) 0°
(B) 7.5°
(C) 15°
(D) 22.5°
Answer: (B)
8. A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is ______.
(A) πa2 – a2
(B) πa2 – √2a2
(C) πa2 – 2a2
(D) πa2 – 3a2
Answer: (C)
9. a, b, c are real numbers. The quadratic equation ax2 – bx + c = 0 has equal roots, which is β, then
(A) β = b/a
(B) β2 = ac
(C) β3 = bc/(2a2)
(D) b2 ≠ 4ac
Answer: (C)
10. The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is ______ .
(A) 8 : 23
(B) 23 : 8
(C) 23 : 31
(D) 31 : 23
Answer: (B)
EC: Electronics and Communication Engineering
Q1- Q25 carry one mark each.
1. If v1, v2,….,v6 are six vectors in R4, which one of the following statements is FALSE
(A) It is not necessary that these vectors span R4.
(B) These vectors are not linearly independent.
(C) Any four of these vectors form a basis for R4.
(D) If {v1, v3, v5, v6} spans R4, then it forms a basis for R4
Answer: (C)
2. For a vector field , which one of the following is FALSE?
(A) is solenoidal if
(B) is another vector field.
(C) is irrotational if
(D)
Answer: (C)
3. The partial derivative of the function f(x, y, z) with respect to x at the point (1, 0, e) is
(A) −1
(B) 0
(C) 1
(D) 1/e
Answer: (B)
4. The general solution of is
(A) y = C1e3x + C2e−3x
(B) y = (C1 + C2x) e−3x
(C) y = (C1 + C2x)e3x
(D) y = C1e3x
Answer: (C)
5. The output y[n] of a discrete-time system for an input x[n] is The unit impulse response of the system is
(A) 0 for all n.
(B) 1 for all n.
(C) unit step signal u[n].
(D) unit impulse signal δ[n].
Answer: (C)
6. A single crystal intrinsic semiconductor is at a temperature of 300 K with effective density of states for holes twice that of electrons. The thermal voltage is 26 mV. The intrinsic Fermi level is shifted from mid-bandgap energy level by
(A) 18.02 meV.
(B) 9.01 meV.
(C) 13.45 meV.
(D) 26.90 meV.
Answer: (B)
7. Consider the recombination process via bulk traps in a forward biased pn homojunction diode. The maximum recombination rate is Umax. If the electron and the hole capture cross-sections are equal, which one of the following is FALSE?
(A) With all other parameters unchanged, Umax decreases if the intrinsic carrier density is reduced.
(B) Umax occurs at the edges of the depletion region in t he device.
(C) Umax depends exponentially on the applied bias.
(D) With all other parameters unchanged, Umax increases if the thermal velocity of the carriers increases.
Answer: (B)
8. The components in the circuit shown below are ideal. If the op-amp is in positive feedback and the input voltage Vi is a since wave of amplitude 1 V, the output voltage Vo is
(A) a non-inverted sine wave of 2 V amplitude.
(B) an inverted sine wave of 1 V amplitude.
(C) a square wave of 5 V amplitude.
(D) a constant of either +5V or −5V.
Answer: (D)
9. In the circuit shown below, the Thevenin voltage VTH is
(A) 2.4 V
(B) 2.8 V
(C) 3.6 V
(D) 4.5 V
Answer: (C)
10. The figure below shows a multiplexer where S1 and S0 are the select lines, I0 to I3 are the input data lines, EN is the enable line, and F(P, Q, R) is the output. F is
(A)
(B)
(C)
(D)
Answer: (A)
11. The pole-zero map of a rational function G(s) shown below. When the closed contour Γ is mapped into the G(s)-plane, then the mapping encircles
(A) the origin of the G(s)-plane once in the counter-clockwise direction.
(B) the origin of the G(s)-plane once in the clockwise direction.
(C) the point −1 + j0 of the G(s)-plane once in the counter-clockwise direction.
(D) the point −1 + j0 of the G(s)-plane once in the clockwise direction.
Answer: (B)
12. A digital communication system transmits a block of N bits. The probability of error in decoding a bit is α. The error event of each bit is independent of the error events of the other bits. The received block is erroneous if at least one of its bits is decoded wrongly. The probability that the received block is erroneous is
(A) N(1 – α)
(B) αN
(C) 1 – αN
(D) 1 – (1 – α)N
Answer: (D)
13. The impedances Z = jX, for all X in the range (−∞, ∞), map to the Smith chart as
(A) a circle of radius 1 with centre at (0, 0).
(B) a point at the centre of the chart.
(C) a line passing through the centre of the chart.
(D) a circle of radius 0.5 with centre at (0.5, 0).
Answer: (A)
14. Which one of the following pole-zero plots corresponds to the transfer function of an LTI system characterized by the input-output difference equation given below?
Answer: (A)
15. In the given circuit, the two-port network has the impedance matrix The value of ZL for which maximum power is transferred to the load is ________ Ω.
Answer: (48 to 48)
16. The current in the RL-circuit shown below is i(t) = 10 cos(5t – π/4) A. The value of the inductor (rounded off to two decimal places) is _______ H.
Answer: (2.80 to 2.85)
17. In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output V0(rounded off to two decimal places) is _______ V.
Answer: (644 to 657)
18. In the circuit shown below, all the components are ideal. If Vi is +2V, the current Io sourced by the op-amp is _______mA.
Answer: (6 to 6)
19. In an 8085 microprocessor, the number of address lines required to access a 16 K byte memory bank is _________.
Answer: (14 to 14)
20. A 10-bit D/A converter is calibrated over the full range from 0 to 10 V. If the input to the D/A converter is 13A (in hex), the output (rounded off to three decimal places) is _______V.
Answer: (3.050 to 3.080)
21. A transmission line of length 3λ/4 and having a characteristic impedance of 50 Ω is terminated with a load of 400 Ω. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is _______ Ω.
Answer: (6.25 to 6.25)
22. A binary random variable X takes the value +2 or − The probability P(X = +2) = α. The value of α (rounded off to one decimal place), for which the entropy of X is maximum, is _______.
Answer: (0.5 to 0.5)
23. The loop transfer function of a negative feedback system is The value of K, for which the system is marginally stable, is ________.
Answer: (160 to 160)
24. The random variable where and W(t) is a real white Gaussian noise process with two-sided power spectral density SW(f) = 3 W/Hz, for all f. The variance of Y is _______.
Answer: (6 to 6)
25. The two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min(M, N), the expected value E(X) (rounded off to two decimal places) is _______.
Answer: (0.25 to 0.25)
Q26 – Q55 carry two marks each.
26. Consider the following system of linear equations.
Which one of the following conditions ensures that a solution exists for the above system?
(A) b2 = 2b1 and 6b1 – 3b3 + b4 = 0
(B) b3 = 2b1 and 6b1 – 3b3 + b4 = 0
(C) b2 = 2b1 and 3b1 – 6b3 + b4 = 0
(D) b3 = 2b1 and 3b1 – 6b3 + b4 = 0
Answer: (A)
27. Which one of the following options contains two solutions of the differential equation
(A) ln|y – 1| = 0.5x2 + C and y = 1
(B) ln|y – 1| = 2x2 + C and y = 1
(C) ln|y – 1| = 0.5x2 + C and y = −1
(D) ln|y – 1| = 2x2 + C and y = −1
Answer: (A)
28. The current I in the given network is
(A) 0 A.
(B) 2.38 ∠−96.37° A.
(C) 2.38 ∠143.63° A.
(D) 2.38 ∠−23.63° A.
Answer: (C)
29. A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos (200 πt) at sampling instants t = n/400, n = 0, 1, …. , 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined as
Which one of the following statements is TRUE?
(A) All X[k] are non-zero.
(B) Only X[4] is non-zero.
(C) Only X[2] and X[6] are non-zero.
(D) Only X[3] and X[5] are non-zero.
Answer: (C)
30. For the given circuit, which one of the following is the correct state equation?
Answer: (A)
31. A one-sided abrupt pn junction diode has a depletion capacitance CD of 50 pF at a reverse bias of 0.2 V. The plot of 1/CD2 versus the applied voltage V for this diode is a straight line as shown in the figure below. The slope of the plot is ________× 1020 F−2 V−1.
(A) −5.7
(B) −3.8
(C) −1.2
(D) −0.4
Answer: (MTA)
32. The band diagram of a p-type semiconductor with a band-gap of 1 eV is shown. Using this semiconductor, a MOS capacitor having VTH of −16 V C′ox of 100 nF/cm2 and a metal work function of 3.87 eV is fabricated. There is no charge within the oxide. If the voltage across the capacitor is VTH, the magnitude of depletion charge per unit area (in C/cm2) is
(A) 1.70 × 10−8
(B) 0.52 × 10−8
(C) 1.41 × 10−8
(D) 0.93 × 10−8
Answer: (A)
33. The base of an npn BJT T1 has a linear doping profile NB(x) as shown below. The base of another npn BJT T2 has a uniform doping NB of 1017 cm−3. All other parameters are identical for both the devices. Assuming that the hole density profile is the same as that of doping, the common-emitter current gain of T2 is
(A) approximately 2.0 times that of T1.
(B) approximately 0.3 times that of T1.
(C) approximately 2.5 times that of T1.
(D) approximately 0.7 times that of T1.
Answer: (MTA)
34. A pn junction solar cell of area 1.0 cm2, illuminated uniformly with 100 nW cm−2, has the following parameters: Efficiency = 15%, open circuit voltage = 0.7 V, fill factor = 0.8, and thickness = 200 μ The charge of an electron is 1.6 × 10−19 C. The average optical generation rate (in cm−3 s−1) is
(A) 0.84 × 1019.
(B) 5.57 × 1019.
(C) 1.04 × 1019.
(D) 83.60 × 1019.
Answer: (A)
35. For the BJT in the amplifier shown below, VBE = 0.7 V, kT/q = 26 mV. Assume that BJT output resistance (r0) is very high and the base current is negligible. The capacitors are also assumed to be short circuited at signal frequencies. The input vi is direct coupled. The low frequency voltage gain v0/vi of the amplifier is
(A) −89.42
(B) −128.21
(C) −178.85
(D) −256.42
Answer: (A)
36. An enhancement MOSFET of threshold voltage 3 V is being used in the sample and hold circuit given below. Assume that the substrate of the MOS device is connected to −10 V. If the input voltage v1 lies between ±10 V, the minimum and the maximum values of vG required for proper sampling and holding respectively, are
(A) 3 V and −3 V.
(B) 10 V and −10 V.
(C) 13 V and −7 V.
(D) 10 V and −13 V.
Answer: (C)
37. Using the incremental low frequency small-signal model of the MOS device, the Norton equivalent resistance of the following circuit is
(A) rds + R + gmrdsR
(B)
(C)
(D) rds + R
Answer: (B)
38. P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) is
(A) 110101
(B) 110010
(C) 111101
(D) 111001
Answer: (A)
39. The state diagram of a sequence detector is shown below. State S0 is the initial state of the sequence detector. If the output is 1, then
(A) the sequence 01010 is detected.
(B) the sequence 01011 is detected.
(C) the sequence 01110 is detected.
(D) the sequence 01001 is detected.
Answer: (A)
40. The characteristic equation of a system is s3 + 3s2 + (K + 2)s + 3K = 0. In the root locus plot for the given system, as K varies from 0 to ∞, the break-way or break-in point(s) lie within
(A) (−1, 0).
(B) (−2, −1).
(C) (−3, −2).
(D) (−∞,−3).
Answer: (A)
41. The components in the circuit given below are ideal. If R = 2 kΩ and C = 1 μF, the –dB cutt-off frequency of the circuit in Hz is
(A) 14.92
(B) 34.46
(C) 59.68
(D) 79.58
Answer: (D)
42. For the modulated signal x(t) = m(t) cos (2πfct), the message signal m(t) = 4 cos(1000 πt) and the carrier frequency fc is 1 MHz. The signal x(t) is passed through a demodulator, as shown in the figure below. The output y(t) of the demodulator is
(A) cos(460 πt).
(B) cos(920 πt).
(C) cos(1000 πt).
(D) cos(540 πt).
Answer: (B)
43. For an infinitesimally small dipole in free space, the electric field Eθ in the far field is proportional to (e−jkr/r) sin θ, where k = 2π/λ. A vertical infinitesimally electric dipole (δl << λ) is placed at a distance h(h > 0) above an infinite ideal conducting plane, as shown in the figure. The minimum value of h, for which one of the maxima in the far field radiation pattern occurs at θ = 60°, is
(A) λ
(B) 0.5λ
(C) 0.25λ
(D) 0.75λ
Answer: (A)
44. In the voltage regulator shown below, V1 is the unregulated input at 15 V. Assume VBE = 0.7 V and the base current in negligible for both the BJTs. If the regulated output VO is 9 V, the value of R2 is ________ Ω.
Answer: (800 to 800)
45. The magnetic field of a uniform plane wave in vacuum is given by cos(ωt + 3x – y – z). The value of b is _______.
Answer: (1 to 1)
46. For a 2-port network consisting of an ideal lossless transformer, the parameter S21 (rounded off to two decimal places) for a reference impedance of 10 Ω, is _______.
Answer: (0.8 to 0.8)
47. SPM(t) and SFM(t) as defined below, are the phase modulated and the frequency modulated waveforms, respectively, corresponding to the message signal m(t) shown in the figure.
SPM(t) = cos(1000πt + Kpm(t))
where Kp is the phase deviation constant in radians/volt and Kf is the frequency deviation constant in radians/second/volt. If the highest instantaneous frequencies of SPM(t) and SFM(t) are same, then the value of the ratio kp/kff is _______ seconds.
Answer: (2 to 2)
48. In a digital communication system, a symbol S randomly chosen from the set {s1, s2, s3, s4} is transmitted. It is given that s1 = −3, s2 = −1, s3 = +1 and s4 = +2. The received symbol is Y = S + W. W is a zero-mean unit-variance Gaussian random variable and is independent of S. Pi is the conditional probability of symbol error for the maximum likelihood (ML) decoding when the transmitted symbol S = si. The index i for which the conditional symbol error probability Pi is the highest is _________.
Answer: (3 to 3)
49. A system with transfer function is subjected to an input 5 cos 3t. The steady state output of the system is The value of a is _______.
Answer: (3.95 to 4.05)
50. For the components in the sequential circuit shown below, tpd is the propagation delay, tsetup is the setup time, and thold is the hold time. The maximum clock frequency (rounded off to the nearest integer), at which the given circuit can operate reliably, is _________ MHz.
Answer: (76 to 77)
51. For the solid S shown below, the value of (rounded off to two decimal places) is ___________
Answer: (2.25 to 2.25)
52. X(ω) is the Fourier transform of x(t) shown below. The value of (rounded off to two decimal places) is _________.
Answer: (58.50 to 58.80)
53. The transfer function of a stable discrete-time LTI system is where K and α are real numbers. The value of α (rounded off to one decimal place) with |α| > 1, for which the magnitude response of the system is constant over all frequencies, is _______.
Answer: (-2 to -2)
54. X is a random variable with uniform probability density function in the interval [−2, 10]. For Y = 2X – 6, the conditional probability P(Y ≤ 7\X ≥ 5) (rounded off to three decimal places) is ________.
Answer: (0.299 to 0.301)
55. Consider the following closed loop control system
where If the steady state error for a unit ramp input is 0.1, then the value of K is _________.
1. While I agree _____ his proposal this time, I do not often agree _____ him.
(A) to, with
(B) with, to
(C) with, with
(D) to, to
Answer: (A)
2. The recent measures to improve the output would _______ the level of production to our satisfaction.
(A) increase
(B) decrease
(C) speed
(D) equalise
Answer: (A)
3. Select the word that fits the analogy:
White : Whitening : Light: ______
(A) Lightning
(B) Lightening
(C) Lighting
(D) Enlightening
Answer: (B)
4. In one of the greatest innings ever seen in 142 years of Test history, Ben Stokes upped the tempo in a five-and-a-half hour long stay of 219 balls including 11 fours and 8 sixes that saw him finish on a 135 not out as England squared the five-match series.
Based on their connotations in the given passage, which one of the following meanings DOES NOT match?
(A) upped = increased
(B) squared = lost
(C) tempo = enthusiasm
(D) saw = resulted in
Answer: (B)
5. There are five levels {P, Q, R, S, T} in a linear supply chain before a product reaches customers, as shown in the figure.
At each of the five levels, the price of the product is increased by 25%. If the product is produced at level P at the cost of Rs. 120 per unit, what is the price paid (in rupees) by the customers?
(A) 187.50
(B) 234.38
(C) 292.26
(D) 366.21
Answer: (D)
Q6 – Q10 carry two marks each.
6. Climate change and resilience deal with two aspects – reduction of sources of non-renewable energy resources and reducing vulnerability of climate change aspects. The terms ‘mitigation’ and ‘adaptation’ are used to refer to these aspects, respectively.
Which of the following assertions is best supported by the above in information?
(A) Mitigation deals with consequences of climate change.
(B) Adaptation deals with causes of climate change.
(C) Mitigation deals with actions taken to reduce the use of fossil fuels.
(D) Adaptation deals with actions taken to combat gree-house gas emissions.
Answer: (C)
7. Find the missing element in the following figure.
(A) d
(B) e
(C) w
(D) y
Answer: (A)
8. It was estimated that 52 men can complete a strip in a newly constructed highway connecting cities P and Q in 10 days. Due to an emergency, 12 men were sent to another project. How many number of days, more than the original estimate, will be required to complete the strip?
(A) 3 days
(B) 5 days
(C) 10 days
(D) 13 days
Answer: (A)
9. An engineer measures THREE quantities X, Y and Z in an experiment. She finds that they follow a relationship that is represented in the figure below : (the product of X and Y linearly varies with Z)
Then, which of the following statements is FALSE?
(A) For fixed Z; X is proportional to Y
(B) For fixed Y; X is proportional to Z
(C) For fixed X; Z is proportional to Y
(D) XY/Z is constant
Answer: (A)
10. The two pie-charts given below show the data of total students and only girls registered in different streams in a university. If the total number of students registered in the university is 5000, and the total number of the registered girls is 1500; then, the ratio of boys enrolled in Arts to the girls enrolled in Management is ______.
(A) 2:1
(B) 9:22
(C) 11:9
(D) 22:9
Answer: (D)
CY: Chemistry
Q1 – Q25 carry one mark each.
1. Among the following, the suitable reagents for the given transformation is:
(A) H2, Pd/C
(B) H2N-NH2/KOH, ∆
(C) NaBH4/CeCl3∙7H2O
(D) Li/Liq. NH3
Answer: (C)
2. Major product formed in the following reaction sequence is:
Answer: (C)
3. Major product formed in the following reaction is:
Answer: (A)
4. Major product formed in the following transformation is:
Answer: (C)
5. Absolute stereochemistry of the given compound is:
(A) 4aR, 8aS
(B) 4aR, 8aR
(C) 4aS, 8aS
(D) 4aS, 8aR
Answer: (D)
6. In the following reaction sequence,
the major product P and Q are :
Answer: (C)
7. Major product formed in the given reaction is:
Answer: (B)
8. The CORRECT statement regarding the substitution of coordinated ligands in Ni(CO)4 and CO(NO)(CO)3 is:
(Given Co―N―O bond is nearly linear; atomic numbers of Co and Ni are 27 and 28, respectively)
(A) Ni(CO)4 and Co(NO)(CO)3 follow associative and dissociative pathways, respectively.
(B) Ni(CO)4 and Co(NO)(CO)3 follow dissociative and associative pathways, respectively.
(C) Both Ni(CO)4 and Co(NO)(CO)3 follow associative pathway.
(D) Both Ni(CO)4 and Co(NO)(CO)3 follow dissociative pathway.
Answer: (B)
9. The CORRECT statement about hexagonal boron nitride is :
(A) It is a good electrical conductor.
(B) It has same layer stacking as that of graphite.
(C) It is reactive towards fluorine.
(D) It has lower thermal stability in air compared to that of graphite.
Answer: (C)
10. In oxyhemocyanin, the coordination number, mode of oxygen binding, color and the net magnetic behavior of copper ions, respectively are:
(Given: atomic number of Cu is 29)
(A) Four, μ-η1:η1-O2−, colorless and paramagnetic.
(B) Five, μ-η2:η2-O2−, colorless and paramagnetic.
(C) Five, μ-η2:η2-O22−, blue and diamagnetic.
(D) Four, μ-η1:η1-O22−, blue and diamagnetic.
Answer: (C)
11. Among the following species, the one that has pentagonal shape is:
(Given: atomic numbers of O, F, S, I and Xe are 8, 9, 16, 53 and 54, respectively)
(A) XeOF4
(B) IF5
(C) [SF5]−
(D) [XeF5]−
Answer: (D)
12. A solution containing a metal complex absorbs at 480 mm with molar extinction coefficient of 15,000 L mol−1 cm−1. If the path length of the cell is 1.0 cm and transmittance is 20.5%, the concentration (in mol L−1) of the metal complex is:
(A) 1.37 × 10−5
(B) 2.29 × 10−5
(C) 4.59 × 10−5
(D) 8.75 × 10−5
Answer: (C)
13. Among the following linear combination of atomic orbitals, the CORRECT representation of the lowest unoccupied π-molecular orbital of butadiene is:
14. The activity of ‘m’ molal CuSO4 solution can be expressed in terms of its mean activity coefficient (γ±) as:
(A) m2γ±2
(B) 4m3γ±3
(C) 16m4γ±4
(D) 108 m5γ±5
Answer: (A)
15. The character table for a pyramidal AB3 molecule of C3v point group is given below:
The reducible representation of pyramidal AB3 is
The CORRECT option representing all the normal Raman active modes of pyramidal AB3 is :
(A) A1 + A2 + 2E
(B) 3E
(C) 3A1 + A2 + E
(D) 2A1 + 2E
Answer: (D)
16. In the following reaction,
the number of peaks exhibited by the major product P in its broadband proton decoupled 13C NMR spectrum is_______
Answer: (8.0 to 8.0)
17. Among the following,
the total number of aromatic species is________
Answer: (4.0 to 4.0)
18. The maximum number of microstates of d2 electronic configuration is_________
Answer: (45 to 45)
19. In a uranium recovery process, an aqueous solution of uranyl ion is evaporated, dried in air at 400°C and subsequently reduced with hydrogen at 700°C to obtain a uranium compound (X). The oxidation state of uranium in X is __________
(Given : atomic number of U is 92)
Answer: (4 to 4)
20. For a cubic crystal system, the powder X-ray diffraction pattern recorded using Cu Kα source (λ = 1.54 Å) shows a peak at 33.60° (2θ) for (111) plane. The lattice parameter ‘a’ (in Å, rounded off to two decimal places) is _________
Answer: (4.60 to 4.64)
21. In an NMR spectrometer operating at a magnetic field strength of 16.45 T, the resonance frequency (in MHz, rounded off to one decimal place) of 19F nucleus is ________
(Given : g factor of 19F = 5.255; βN = 5.05 × 10−27 J T−1; h = 6.626 × 10−34 J s)
Answer: (658 to 659)
22. When three moles of helium is mixed with one mole of neon at constant temperature and pressure (25 °C, 1 atm), the entropy of mixing (in J K−1, rounded off to two decimal places) is ________
(Given : R = 8.314 J K−1 mol−1)
Answer: (18.60 to 18.80)
23. At 25°C, the emf(in volts, rounded off to three decimal places) of the cell, Ag | AgBr(s) | Br− (a = 0.20), Cu2+ (a = 0.48), Cu+(a = 0.24) | Pt is _______
(Given : The standard emf of the cell is 0.082 V; R = 8.314 J K−1 mol−1; F = 96500 C mol−1)
Answer: (0.058 to 0.060)
24. For an enzyme catalyzed reaction, the plot of inverse of initial rate against inverse of initial substrate concentration is linear with slope 0.16 s and intercept 2.12 mol−1 L s. The estimated value of Michaelis constant (in mol L−1, rounded off to two decimal places is ________
Answer: (0.07 to 0.08)
25. Fluorescence quantum yield and fluorescence lifetime of a molecule are 0.4 and 5 × 10−9 s, respectively. If the fluorescence decay rate constant is Y × 107 s−1, t he value of Y (rounded off to nearest integer) is _________
Answer: (8 to 8)
Q26 – Q55 carry two marks each.
26. Major product formed in the following reaction sequence is:
Answer: (C)
27. Major products P and Q, in the given reaction sequence, are:
Answer: (B)
28. Major products P and Q, formed in the reactions given below, are:
Answer: (C)
29. A compound with molecular formula C10H12O12 showed a strong IR band at ~ 720 cm−1 a peak at m/z 122 in the mass spectrum and the following 1H NMR signals: δ1 – 8.0 (2H, m), 7.6 – 7.5(1H, m), 7.5 – 7.3 (2H, m), 4.3(2H, t), 1.8 (2H sextet) and 1.0 (3H, t). The structure of the compound is:
Answer: (B)
30. Major product formed in the following synthetic sequence is:
Answer: (A)
31. The CORRECT statement with respect to the stereochemistry of α-hydroxy acids P and Q formed in the following reactions is:
(A) Both P and Q are formed with retention of configuration.
(B) Both P and Q are formed with inversion of configuration.
(C) P is formed with retention of configuration and Q with inversion of configuration.
(D) P is formed with inversion of configuration and Q with retention of configuration.
Answer: (D)
32. The rate of solvolysis of the given compounds is in the order
(A) T > R > Q > S > P
(B) Q > T > R > P > S
(C) R > T > Q > S > P
(D) T > Q > R > P > S
Answer: (A)
33. In the following reaction sequence, the major products Q and R are:
Answer: (B)
34. In the electronic absorption spectrum of an aqueous solution of [Ni(NH3)6]2+, a very weak band is observed between the bands due to the transitions 3A2g → 3T2g and 3A2g → 3T1g(F). The transition responsible for the very weak band is
(Given: atomic number of Ni is 28)
(A) 3A2g → 1T1g
(B) 3A2g → 1T2g
(C) 3A2g → 1Eg
(D) 3A2g → 1A2g
Answer: (C)
35. The experimental magnetic moment (3.4 BM) of a hydrated salt of Eu3+ at 27°C is significantly different from the calculated value. The difference is due to
(Given: atomic number of Eu is 63)
(A) population of electrons at higher J level(s) via thermal excitation.
(B) strong ligand field splitting of f-orbitals.
(C) strong spin-orbit coupling.
(D) pairing of electrons in f-orbitals.
Answer: (A)
36. The CORRECT combination of L1 and L2 among H−, NO−, MeCH2− and CO, that will satisfy the 18 electron rule for both metal centers in the following neutral molecule, is
(Given: atomic number of Ru is 44)
(A) H−, NO−
(B) MeCH2−, NO−
(C) MeCH2−, CO
(D) H−, CO
Answer: (C)
37. In the following reaction sequence,
the structure of B is
(Given: atomic number of Mo is 42)
Answer: (D)
38. The following table lists the reaction/conversion catalyzed by metalloenzymes.
The correct combination is
(A) P-II; Q-I; R-III; S-IV
(B) P-IV; Q-III; R-II; S-I
(C) P-II; Q-III; R-IV; S-I
(D) P-I; Q-IV; R-III; S-II
Answer: (C)
39. The fission of with thermal neutron is represented below.
are the primary fission fragment pair, which undergo series of radioactive decay to form stable nuclei X3 and X4 (chain enders). The X3 and Y4, respectively are:
(A)
(B)
(C)
(D)
Answer: (B)
40. The CORRECT ‘voltage (E) versus time’ excitation signal used in cyclic voltammetry is
Answer: (C)
41. The hydrogen-like radial wave function of the 3s orbital is given as
where ρ = 2Zr/a0; Z = atomic number, r = distance from the nucleus and a0 = Bohr radius. Positions of the radial nodes (in units of a0) of the 3s orbital are at
(A)
(B)
(C)
(D)
Answer: (C)
42. ∆Gf0 and ∆Hf0 for Fe(g) are 370.7 kJ mol−1 and 416.3 kJ mol−1 at 298 K, respectively. Assuming ∆Hf0 is constant in the interval 250 K to 375 K, ∆Gf0 (rounded off to the nearest integer) for Fe(g) at 375 K is:
(A) 359 kJ mol−1
(B) 338 kJ mol−1
(C) 325 kJ mol−1
(D) 310 kJ mol−1
Answer: (A)
43. Adsorption of N2 on TiO2 was carried out at 75 K. A plot of gives a straight line with an intercept, 4.0 × 10−6 mm−3 and slope, 1.0 × 10−3 mm−3. The volume (rounded off to the nearest integer) corresponding to the monolayer coverage is:
(A) 996 mm3
(B) 785 mm3
(C) 690 mm3
(D) 555 mm3
Answer: (A)
44. Among the following sets,
the total number of set(s) of diastereomeric pair(s) is _______
Answer: (4.0 to 4.0)
45. Among the following.
the total number of compounds showing characteristic carbonyl stretching frequency less than 1700 cm−1 in their IR spectra is _______
Answer: (3.0 to 3.0)
46. Consider the AgX crystallizes in rock salt structure. The density of AgX is 6477 kg/m3 and unit cell length is 577.5 pm. Atomic weight of Ag is 107.87 g mol−1. The atomic weight of X (in g mol−1, rounded off to two decimal places) is _______
Answer: (79.00 to 81.00)
47. The total number of g|| lines expected in the EPR spectrum of a solution of bis(salicylaldimine) copper(II) having pure 63Cu and 14N at 77 K is ________
(Given: I values of 63Cu, 14N and 1H are 3/2, 1 and 1/2, respectively)
Answer: (60 to 60)
48. Among the following,
[B12H12]2−, [Ni5(CO)12]2−, [C2B9H11]2−, Rh6(CO)16, Os6(CO)20, B5H11, B6H10 the total number of species having nido structure is________
(Given : atomic numbers of H, B, C, O, Ni, Rh and Os are 1, 5, 6, 8, 28, 45 and 76, respectively)
Answer: (3 to 3)
49. The frequency (in cm−1, rounded off to two decimal places) for pure rotational line in the spectrum of NO molecule due to change in the quantum number from J = 1 to J = 2 is _______
(Given: Moment of inertia of NO = 1.6427 × 10−46 kg m2; h = 6.626 × 10−34 J s; c = 3 × 108 m/s)
Answer: (6.80 to 6.82)
50. The % error (rounded off to two decimal places) in the ground state energy of a particle in a one dimensional box of length ‘a’ described by a trial variation function φ = x(a – x), where 0 ≤ x ≤ a, is ________
(Given: The true ground state energy of the above system is h2/8ma2;
Answer: (1.22 to 1.44)
51. Assuming no interaction between vibrational and rotational energy levels in HF, the frequency (in cm−1, rounded off to the nearest integer) of the R branch line originating from J = 4 in its IR spectrum is ________
(Given: Rotational constant of HF = 19.35 cm−1;
Answer: (4332 to 4332)
52. The van der Waals constants a and b for gaseous CO are given as 1.49 L2 atm mol−2 and 0.0399 L mol−1, respectively. The fugacity (in atm, rounded off to two decimal places) of CO at 35°C and 95 atm is ______
(Given: R = 0.082 L atm K−1 mol−1)
Answer: (88.11 to 88.60)
53. At 30°C, the vapor pressure and density of a 1.0 M aqueous solution of sucrose are 31.207 mm Hg and 1.1256 g/mL, respectively. If the vapor pressure of pure water at 30°C is 31.824 mm Hg, the activity coefficient (rounded off to three decimal places) of water in the given solution is _______
(Given: The molar mass of sucrose = 342.3 g mol−1)
Answer: (1.002 to 1.004)
54. For the ring opening reaction of cyclopropane to propene at 25°C, the pre-exponential factor is 4.3 × 1015 s−1. The entropy of activation (in J K−1 mol−1, rounded off to two decimal places) is _______.
55. In a reaction, reactant X is converted to products Y and Z consecutively with rate constants 6.0 × 10−2 min−1 and 9.0 × 10−3 min−1, respectively. If the initial amount of X is 12.5 moles, the number of moles (rounded off to one decimal place) of Y formed after 10 minutes is ________
1. Raman is confident of speaking English ______ six months as he has been practicing regularly ________ the last three weeks.
(A) during, for
(B) for, since
(C) for, in
(D) within, for
Answer: (D)
2. His knowledge of the subject was excellent but his classroom performance was _______.
(A) extremely poor
(B) good
(C) desirable
(D) praiseworthy
Answer: (A)
3. Select the word that fits the analogy:
Cook : Cook :: Fly :_____
(A) Flyer
(B) Flying
(C) Flew
(D) Flighter
Answer: (A)
4. The drawn of the 21st century witnessed the melting glaciers oscillating between giving too much and too little to billions of people who depend on them for fresh water. The UN climate report estimates that without deep cuts to man-made emissions, at least 30% of the northern hemisphere’s surface permafrost could melt by the end of the century. Given this situation of imminent global exodus of billions of people displaced by rising seas, nation-states need to rethink their carbon footprint for political concerns, if not for environmental ones.
Which one of the following statements can be inferred from the given passage?
(A) Nation-states do not have environmental concerns.
(B) Nation-states are responsible for providing fresh water to billions of people.
(C) Billions of people are responsible of man-made emissions.
(D) Billions of people are affected by melting glaciers.
Answer: (D)
5. There are multiple routes to reach from node 1 to node 2, as shown in the network.
The cost of travel on an edge between two nodes is given in rupees. Nodes ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, and ‘f’ are toll booths. The toll price at toll booths marked ‘a’ and ‘e’ is Rs. 200, and is Rs.100 for the other toll booths. Which is the cheapest route from node 1 to node 2?
(A) 1-a-c-2
(B) 1-f-b-2
(C) 1-b-2
(D) 1-f-e-2
Answer: (B)
Q6 – Q10 carry two marks each.
6. Goods and Services Tax (GST) is an indirect tax introduced in India in 2017 that is imposed on the supply of goods and services, and it subsumes all indirect taxes except few. It is a destination-based tax imposed on goods and services used, and it is not imposed at the point of origin from where goods come. GST also has a few components specific to state governments, central government and Union Territories (UTs).
Which one of the following statements can be inferred from the given passage?
(A) GST is imposed on the production of goods and services.
(B) GST includes all indirect taxes.
(C) GST does not have a component specific to UT.
(D) GST is imposed at the point of usage of goods and services.
Answer: (D)
7. If P = 3, R = 27, T = 243, then Q + S = _____.
(A) 40
(B) 80
(C) 90
(D) 110
Answer: (C)
8. The figure below shows an annular ring with outer and inner radii as b and a, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is ________.
(A)
(B) π[(b2 – a2) – n(b – a)2]
(C)
(D) π[(b2 – a2) + n(b – a)2]
Answer: (A)
9. Two straight lines are drawn perpendicular to each other in X-Y plane. If α and β are the acute angles the straight lines make with t he X-axis, then α + β is _______.
(A) 60°
(B) 90°
(C) 120°
(D) 180°
Answer: (B)
10. The total revenue of a company during 2014-2018 is shown in the bar graph. If the total expenditure of the company in each year is 500 million rupees, then the aggregate profit or loss (in percentage) on the total expenditure of the company during 2014-2018 is ______.
(A) 16.67% profit
(B) 16.67% loss
(C) 20% profit
(D) 20% loss
Answer: (C)
CS: Computer Science and Information Technology
Q1 – Q25 carry one mark each.
1. Consider the functions
(I) e−x
(II) x2 – sin x
(III)
Which of the above functions is/are increasing everywhere in [0, 1]?
(A) III only
(B) II only
(C) II and III only
(D) I and III only
Answer: (A)
2. For parameters a and b, both of which are ω(1), T(n) = T(n1/a) + 1, and T(b) = 1.
Then T(n) is
(A) Θ(loga logb n)
(B) Θ(logab n)
(C) Θ(logb loga n)
(D) Θ(log2 log2 n)
Answer: (A)
3. Consider the following statements.
(I) Daisy chaining is used to assign priorities in attending interrupts.
(II) When a device raises a vectored interrupt, the CPU does polling to identify the source of interrupt.
(III) In polling, the CPU periodically checks the status bits to know if any device needs its attention.
(IV) During DMA, both the CPU and DMA controller can be bus masters at the same time.
Which of the above statements is/are TRUE?
(A) I and II only
(B) I and IV only
(C) I and III only
(D) III only
Answer: (C)
4. Consider the following data path diagram.
Consider an instruction: R0 ← R1 + R2. The following steps are used to execute it over the given data path. Assume that PC is incremented appropriately. The subscripts r and w indicated read and write operations, respectively.
(1) R2r, TEMP1r, ALUadd, TEMP2w
(2) R1r, TEMP1w
(3) PCr, MARw, MEMr
(4) TEMP2r, R0w
(5) MIDRr, IRw
which one of the following is the correct order of execution of the above steps?
(A) 2, 1, 4, 5, 3
(B) 1, 2, 3, 4, 5
(C) 3, 5, 2, 1, 4
(D) 3, 5, 1, 2, 4
Answer: (C)
5. The preorder traversal of a binary search tree is 15, 10, 12, 11, 20, 18, 16, 19.
Which one of the following is the postorder traversal of the tree?
(A) 10, 11, 12, 15, 16, 18, 19, 20
(B) 11, 12, 10, 16, 19, 18, 20, 15
(C) 20, 19, 18, 16, 15, 12, 11, 10
(D) 19, 16, 18, 20, 11, 12, 10, 15
Answer: (B)
6. What is the worst case time complexity of inserting n2 elements into an AVL-tree with n elements initially?
(A) Θ(n4)
(B) Θ(n2)
(C) Θ(n2 log n)
(D) Θ(n3)
Answer: (C)
7. Which one of the following regular expressions represents at set of all binary strings with an odd number of 1’s?
(A) ((0 + 1)*1(0 + 1)*1)*10*
(B) (0*10*10*)*0*1
(C) 10*(0*10*10*)*
(D) (0*10*10*)*10*
Answer: (MTA)
8. Consider the following statements.
(I) If L1 ⋃ L2 is regular, then both L1 and L2 must be regular.
(II) The class of regular languages is closed under infinite union.
Which of the above statement is/are TRUE?
(A) I only
(B) II only
(C) Both I and II
(D) Neither I nor II
Answer: (D)
9. Consider the following statements.
(I) Symbol table is accessed only during lexical analysis and syntax analysis.
(II) Compilers for programming languages that support recursion necessarily need heap storage for memory allocation in the run-time environment.
(III) Errors violating the condition ‘any variable must be declared before its use’ are detected during syntax analysis.
Which of the above statements is/are TRUE?
(A) I Only
(B) I and III only
(C) II only
(D) None of I, II and III
Answer: (D)
10. Consider the language L = {an | n ≥ 0} ⋃ {anbn | n ≥ 0} and the following statements.
(I) L is deterministic context-free.
(II) L is context-free but not deterministic context-free.
(III) L is not LL(k) for any k.
Which of the above statements is/are TRUE?
(A) I only
(B) II only
(C) I and III only
(D) III only
Answer: (C)
11. Consider allocation of memory to a new process. Assume that none of the existing holes in the memory will exactly fit the process’s memory requirement. Hence, a new hole of smaller size will be created if allocation is made in any of the existing holes. Which one of the following statements is TRUE?
(A) The hole created by first fit is always larger than the hole created by next fit.
(B) The hole created by worst fit is always large than the hole created by first fit.
(C) The hole created by best fit is never larger than the hole created by first fit.
(D) The hole created by next fit is never larger than the hole created by best fit.
Answer: (C)
12. Consider the following statements about process state transitions for a system using preemptive scheduling.
(I) A running process can move to ready state.
(II) A ready process can move to running state.
(III) A blocked process can move to running state.
(IV) A blocked process can move to ready state.
Which of the above statements are TRUE?
(A) I, II, and III only
(B) II and III only
(C) I, II and IV only
(D) I, II, III, and IV
Answer: (C)
13. Consider a relational database containing the following schemas.
The primary key of each table is indicated by underlining the constituent fields.
The number of rows returned by the above SQL query is
(A) 4
(B) 5
(C) 0
(D) 2
Answer: (A)
14. Which of the following is used to represent the supporting many-one relationship of a weak entity set in an entity-relationship diagram?
(A) Diamonds with double/bold border
(B) Rectangles with double/bold border
(C) Ovals with double/bold border
(D) Ovals that contain underlined identifiers
Answer: (A)
15. Consider the following statements about the functionality of an IP based router.
(I) A router does not modify the IP packets during forwarding.
(II) It is not necessary for a router to implement any routing protocol.
(III) A router should reassemble IP fragments if the MTU of the outgoing link is larger than the size of the incoming IP packet.
Which of the above statement is/are TRUE?
(A) I and II only
(B) I only
(C) II and III only
(D) II only
Answer: (D)
16. What is the worst case time complexity of inserting n elements into an empty linked list, if the linked list needs to be maintained in sorted order?
(A) Θ(n)
(B) Θ(n log n)
(C) Θ(n2)
(D) Θ(1)
Answer: (C)
17. Let R be the set of all binary relations on the set {1, 2, 3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is _______.
Answer: (0.125 to 0.125)
18. Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is _______.
Answer: (7 to 7)
19. A multiplexer is placed between a group of 32 registers and an accumulator to regulate data movement such that at any given point in time the content of only one register will move to the accumulator. The minimum number of select lines needed for the multiplexer is
Answer: (5 to 5)
20. If there are m input lines and n output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of m + n is _______.
Answer: (1034 to 1034)
21. A direct mapped cache memory of 1 MB has a block size of 256 bytes. The cache has an access time of 3 ns and a hit rate of 94%. During a cache miss, it takes 20 ns to bring the first word of a block from the main memory, while each subsequent word takes 5 ns. The word size is 64 bits. The average memory access time in ns (round off to 1 decimal place) is _______.
Answer: (13.3 to 13.3 OR 13.5 to 13.5)
22. Consider the following C program.
The output of the program is ________
Answer: (19 to 19)
23. Consider a double hashing scheme in which the primary hash function is h1(k) = k mod 23, and the secondary hash function is h2(k) = 1 + k(mod 19). Assume that the table size is 23. Then the address returned by probe 1 in the probe sequence (assume that the probe sequence begins at probe 0) for key value k = 90 is _______.
Answer: (13 to 13)
24. Consider the following grammar.
S → aSB | d
B → b
The number of reduction steps taken by a bottom-up parser while accepting the string aaadbbb is ______.
Answer: (7 to 7)
25. Assume that you have made a request for a web page through your web browser to a web server. Initially the browser cache is empty. Further, the browser is configured to send HTTP requests in non-persistent mode. The web page contains text and five very small images. The minimum number of TCP connections required to display the web page completely in your browser is ________.
Answer: (6 to 6)
Q26 – Q55 carry two marks each.
26. Which of the following languages are undecidable? Note that indicates encoding of the Turing machine M.
(A) L1, L3, and L4 only
(B) L1 and L3 only
(C) L2 and L3 only
(D) L2, L3 and L4 ony
Answer: (A)
27. Let A and B be two n × n matrices over real numbers. Let rank(M) and det(M) denote that rank and determinant of a matrix M, respectively. Consider the following statements.
Which of the above statements are TRUE?
(A) I and II only
(B) I and IV only
(C) II and III only
(D) III and IV only
Answer: (C)
28. Consider the Boolean function z(a, b, c).
Which one of the following minterm list represents the circuit given above?
(A) z = ∑ (0, 1, 3, 7)
(B) z = ∑ (1, 4, 5, 6, 7)
(C) z = ∑ (2, 4, 5, 6, 7)
(D) z = ∑ (2, 3, 5)
Answer: (B)
29. Consider three registers R1, R2 and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x42200000 and 0xC1200000, respectively.
If what is the value stored in R3?
(A) 0x40800000
(B) 0xC0800000
(C) 0x83400000
(D) 0xC8500000
Answer: (B)
30. A computer system with a word length of 32 bits has a 16 MB byte-addressable main memory and a 64 KB, 4-way set associative cache memory with a block size of 256 bytes. Consider the following four physical addresses represented in hexadecimal notation.
31. Let G = (V, E) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighted edge (u, v) ∈ V × V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph is
(A) Θ(|E| + |V|)
(B) Θ(|E| |V|)
(C) Θ(|E| log|V|)
(D) Θ(|V|)
Answer: (D)
32. Consider the following languages.
L1 = {wxyx, |w, x, y ∈ (0 + 1)+}
L2 = {xy | x, y ∈ (a +b)*, |x| = |y|, x ≠ y}
Which one of the following is TRUE?
(A) L1 is regular and L2 is context-free
(B) L1 is context-free but not regular and L2 is context-free.
(C) Neither L1 nor L2 is context-free.
(D) L1 is context-free but L2 is not context-free.
Answer: (A)
33. Consider the productions A → PQ and A → Each of the five non-terminals A, P, Q, X, and Y has two attributes: s is a synthesized attribute, and i is an inherited attribute. Consider the following rules.
Rule 1 : P. i = A.i + 2, Q.i = P.i + A.i, and A.s = P.s + Q.s
Rule 2: X.i = A.i + Y.s and Y.i = X.s + A.i
Which one of the following is TRUE?
(A) Both Rule 1 and Rule 2 are L-attributed.
(B) Only Rule 1 is L-attributed.
(C) Only Rule is L-attributed.
(D) Neither Rule 1 nor Rule 2 is L-attributed.
Answer: (B)
34. Each of a set of n processes executes the following code using two semaphores a and b initialized to 0 and not used in CODE SECTION P.
What does the code achieve?
(A) It ensures that no process executes CODE SECTION Q before every process has finished CODE SECTION P.
(B) It ensures that at most two processes are in CODE SECTION Q at any time.
(C) It ensures that all processes execute CODE SECTION P mutually exclusively.
(D) It ensures that at mot n – n1 processes are in CODE SECTION P at any time.
Answer: (A)
35. Consider the following five disk access requests of the form (request id, cylinder number) that are present in the disk scheduler queue at a given time.
(P, 155), (Q, 85), (R, 110), (S, 30), (T, 115)
Assume the head is positioned at cylinder 100. The scheduler follows Shortest Seek Time First scheduling to service the requests.
Which one of the following statements is FALSE?
(A) T is serviced before P.
(B) Q is serviced after S, but before T.
(C) The head reverses its direction of movement between servicing of Q and P.
(D) R is serviced before P.
Answer: (B)
36. Consider a relational table R that is in 3NF, but not in BCNF. Which one of the following statements is TRUE?
(A) R has a nontrivial functional dependency X → A, where X is not a superkey and A is a prime attribute.
(B) R has nontrivial functional dependency X → A, where X is not superkey and A is non-prime attribute and X is not a proper subset of any key.
(C) R has a nontrivial functional dependency X → A, where X is not a superkey and A is a non-prime attribute and X is proper subset of some key.
(D) A cell in R holds a set instead of an atomic value.
Answer: (A)
37. Consider a schedule of transactions T1 and T2:
Here, RX stands for “Read (X)” and WX stands for “Write(X)”. Which one of the following schedules is conflict equivalent to the above schedule?
Answer: (A)
38. An organization requires a range of IP addresses to assign one to each of its 1500 computers. The organization has approached an Internet Service Provider (ISP) for this task. The ISP uses CIDR and serves the requests from the available IP address space 202.61.0.0/17. The ISP wants to assign an address space to the organization which will minimize the number of routing entries in the ISP’s router using route aggregation. Which of the following address spaces are potential candidates from which the ISP can allot any one to the organization?
(I) 202.61.84.0/21
(II) 202.61.104.0/21
(III) 202.61.64.0/21
(IV) 202.61.144.0/21
(A) I and II only
(B) II and III only
(C) III and IV only
(D) I and IV only
Answer: (B)
39. Which one of the following predicate formulae is NOT logically valid?
Note that W is a predicate formula without any free occurrence of x.
Answer: (C)
40. Let G = (V, E) be a directed, weighted graph with weight function w: E → ℝ. For some function f : V → ℝ, for each edge (u, v) ∈ E, define w’(u, v) as w(u, v) + f(u) – f(v).
Which one of the options completes the following sentence so that it is TRUE?
“The shortest paths in G under w are shortest paths under w’, too, _______”.
(A) for every f : V → ℝ
(B) if and only if ∀u ∈ V, f(u) is positive
(C) if and only if ∀u ∈V, f(u) is negative
(D) If and only if f(u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of G
Answer: (A)
41. In an balanced binary search tree with n elements, what is the worst case time complexity of reporting all elements in range [a, b]? Assume that the number of reported elements is k.
(A) Θ(log n)
(B) Θ(log n + k)
(C) Θ(k log n)
(D) Θ(n log k)
Answer: (B)
42. The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
Answer: (12 to 12)
43. Consider a non-pipelined processor operating at 2.5 GHz. It takes 5 clock cycles to complete an instruction. You are going to make a 5-stage pipeline out of this processor. Overheads associated with pipelining force you to operate the pipelined processor at 2 GHz. In a given program, assume that 30% are memory instructions, 60% are ALU instructions and the rest are branch instructions. 5% of the memory instructions cause stalls of 50 clock cycles each due to cache misses and 50% of the branch instructions cause stalls of 2 cycles each. Assume that there are not stalls associated with the execution of ALU instructions. For this program, the speedup achieved by the pipelined processor over the non-pipeline processor (round off to 2 decimal places) is ______.
Answer: (2.15 to 2.18)
44. A processor has 64 registers and uses 16-bit instruction format. It has two types of instructions: I-type and R-type. Each I-type instruction contains an opcode, a register name, and a 4-bit immediate value. Each R-type instruction contains an opcode and two register names. If there are 8 distinct I-type opcodes, then the maximum number of distinct R-type opcodes is _______.
Answer: (14 to 14)
45. For n > 2, let a ∈ {0, 1}n be a non-zero vector. Suppose that x is chosen uniformly at random from {0, 1}n. Then the probability that is an odd number is ______.
Answer: (0.5 to 0.5)
46. Consider the following C functions.
The return value of fun 2 (5) is ______.
Answer: (55 to 55)
47. Consider the array representation of a binary min-heap containing 1023 elements. The minimum number of comparisons required to find the maximum in the heap is ______.
Answer: (511 to 511)
48. Consider the following C functions.
The value returned by pp(3, 4) is _____.
Answer: (81 to 81)
49. Consider a graph G = (V, E), where V = {v1, v2 ….., v100}, E = {(vi, vj) |1 ≤ i < j ≤ 100}, and weight of the edge (vi, vj) is |i – j|. The weight of minimum spanning tree of G is ______.
Answer: (99 to 99)
50. Consider the following set of processes, assumed to have arrived at time 0. Consider the CPU scheduling algorithms Shortest Job First (SJF) and Round Robin (RR). For RR, assume that the processes are scheduled in the order P1, P2, P3, P4.
If the time quantum for RR is 4 ms, then the absolute value of the difference between the average turnaround times (in ms) of SJF and RR (round off to 2 decimal places) is ______.
Answer: (5.25 to 5.25)
51. Consider the following language.
L = {x ∈ {a, b}* | number of a’s in x is divisible by 2 but not divisible by 3}
The minimum number of states in a DFA that accepts L is ______.
Answer: (6 to 6)
52. Graph G is obtained by adding vertex s to K3, 4 and making s adjacent to every vertex of K3,4. The minimum number of colours required to edge-colour G is ______.
Answer: (7 to 7)
53. Consider a paging system that uses 1-level page table residing in main memory and a TLB for address translation. Each main memory access takes 100 ns and TLB lookup takes 20 ns. Each page transfer to/from the disk takes 5000 ns. Assume that the TLB hit ratio is 95%, page fault rate is 10%. Assume that for 20% of the total page faults, a dirty page has to be written back to disk before the required page is read in from disk. TLB update time is negligible. The average memory access time in ns(round of to 1 decimal places) is ______.
Answer: (154.5 to 155.5)
54. Consider a database implemented using B+ tree for file indexing and installed on a disk drive with block size of 4 KB. The size of search key is 12 bytes and the size of tree/disk pointer is 8 bytes. Assume that the database has one million records. Also assume that no node of the B+ tree and no records are present initially in main memory. Consider that each record fits into one disk block. The minimum number of disk accesses required to retrieve any record in the database is ________.
Answer: (4 to 4)
55. Consider a TCP connection between a client and a server with the following specifications: the round trip time is 6 ms, the size of the receiver advertised window is 50 KB, slow-start threshold at the client is 32 KB, and the maximum segment size is 2 KB. The connection is established at time t = 0. Assume that there are no timeouts and errors during transmission. Then the size of the congestion window (in KB) at time t + 60 ms after all acknowledgements are processed is _______.
1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.
(A) with, at
(B) on, in
(C) on, at
(D) to, at
Answer: (C)
2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.
(A) slim
(B) bright
(C) obvious
(D) uncertain
Answer: (B)
3. Select the word that fits the analogy:
Cover : Uncover :: Associate : _______
(A) Unassociate
(B) Inassociate
(C) Missassociate
(D) Dissociate
Answer: (D)
4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.
Which of the following statements can be inferred from the given passage?
(A) Officials declared that the food-grain production target will be met due to good rains.
(B) Officials want the food-grain production target to be met by the November-February period.
(C) Officials feel that the food-grain production target cannot be met due to floods.
(D) Officials hope that the food-grain production target will be met due to a good rabi produce.
Answer: (D)
5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.
(A) n2 – n
(B) n2 + n
(C) 2n2 – n
(D) 2n2 + n
Answer: (B)
Q6-Q10 carry two marks each.
6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.
Which of the following statements can be inferred from the above passage?
(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.
(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.
(C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.
(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.
Answer: (D)
7. P, Q, R, S, T, U, V, and W are seated around a circular table.
(I) S is seated opposite to W.
(II) U is seated at the second place to the right of R.
(III) T is seated at the third place to the left of R.
(IV) V is a neighbor of S.
Which of the following must be true?
(A) P is a neighbor of R.
(B) Q is a neighbor of R.
(C) P is not seated opposite to Q.
(D) R is the left neighbor of S.
Answer: (C)
8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?
(A) 66.6
(B) 75.2
(C) 88.2
(D) 116.5
Answer: (B)
9. For a matrix M = [mij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and mij = −mij. The minimum number of elements required to fully specify the matrix is_______.
(A) 0
(B) 6
(C) 12
(D) 16
Answer: (B)
10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.
(A) 15 : 17
(B) 16 : 17
(C) 17 : 15
(D) 17 : 16
Answer: (B)
Chemical Engineering
Q1 – Q26 carry one mark each.
1. Which one of the following methods requires specifying an initial interval containing the root (i.e., bracketing) to obtain the solution of f(x) = 0, where f(x) is a continuous non-linear algebraic function?
(A) Newton-Raphson method
(B) regula falsi method
(C) secant method
(D) fixed point iteration method
Answer: (B)
2. Consider the hyperbolic function s in Group-1 and their definitions in Group-2.
The correct combination is
(A) P-IV, Q-I, R-III, S-II
(B) P-II, Q-III, R-I, S-IV
(C) P-IV, Q-I, R-II, S-III
(D) P-I, Q-II, R-IV, S-III
Answer: (C)
3. Consider the following continuously differentiable function v(x, y, z) = 3x2yi + 8y2zj + 5xyzk where i, j and k represent the respective unit vectors along the x, y, and z directions in the Cartesian coordinate system. The curl of this function is
(A) −3x2i – 8y2j + 5z(x + y) k
(B) 6xyi – 16y j + 5xy k
(C) (5xz – 8y2)I – 5yzj – 3x2k
(D) y(11x + 16z)
Answer: (C)
4. Consider the following unit step function.
The Laplace transform of this function is
(A) e−3s/S
(B) e−3s/S2
(C) e−3s/3S
(D) e−6s/S
Answer: (A)
5. In a constant-pressure cake filtration with an incompressible cake layer, volume of the filtrate (V) is measured as a function of time t. The plot of t/V versus V results in a straight line with an intercept of 104 s m−3. Area of the filter is 0.05 m2, viscosity of the filtrate is 10−3 Pa, s and the overall pressure drop across the filter is 200 kPa. The value of filter-medium resistance (in m−1) is
(A) 1 × 109
(B) 1 × 1010
(C) 1 × 1011
(D) 1 × 1012
Answer: (C)
6. In a laboratory experiment, a unit pulse input of tracer is given to an ideal plug flow reactor operating at steady state with a recycle ratio, R = 1. The exit age distribution, E(t), of the tracer at the outlet of the reactor is measured. The first four pulses observed at t1, t2, t3, and t4 are shown below.
In addition, use the following data and assumptions
• R is defined as ratio of the volume of fluid returned to the entrance of the reactor to the volume leaving the system
• No reaction occurs in the reactor
• Ignore any dead volume in the recycle loop
If the space time of the plug flow reactor is τ seconds, which one of the following is correct?
Answer: (B)
7. The square of Thiele modulus, MT, is given by where L is the characteristic length of the catalyst pellet, k is the rate constant of a first order reaction, and Deff is the effective diffusivity of the species in the pores. MT2 is a measure of
Answer: (A)
8. Hot-wire anemometer is used for the measurement of
(A) composition
(B) flow
(C) pressure
(D) temperature
Answer: (B)
9. Pure gas P is being absorbed into a liquid, The dissolved P undergoes an irreversible reaction in the liquid film. The reaction is first order with respect to P. Which one of the following represents the concentration profile of P in the liquid film at steady state?
Answer: (B)
10. Consider a batch distillation process for a equimolar mixture of benzene and toluene atmospheric pressure. The mole fraction of benzene in the distillate collected after 10 minutes is 0.6. The process is further continued for additional 10 minutes. The mole fraction of benzene in the total distillate collected after 20 minutes of operation is
(A) less than 0.6
(B) exactly equal to 0.6
(C) exactly equal to 0.7
(D) greater than 0.7
Answer: (A)
11. Which one of the following is NOT CORRECT?
(A) nylon-6, 6 is produced by condensation polymerization
(B) phenol-formaldehyde resin is a thermosetting polymer
(C) high density polyethylene (HDPE) is produced by condensation polymerization
(D) poly (ethylene terephthalate) (PET) is a polyester
Answer: (C)
12. The operating temperature range for the Haber process is 350-500° It is used for the production of ammonia at
(A) 20 MPa using Fe catalyst in an exothermic reaction
(B) 0.1 MPa using Fe catalyst in an exothermic reaction
(C) 20 MPa using Fe catalyst in an endothermic reaction
(D) 20 MPa using zeolie catalyst in an endothermic reaction
Answer: (A)
13. Consider the refinery processes in Group-1 and the catalysts in Group-2.
The correct combination is
(A) P-II, Q-I, R-III
(B) P-III, Q-II, R-I
(C) P-III, Q-I, R-II
(D) P-I, Q-III, R-II
Answer: (C)
14. Consider the processes in Group-1 and the reactions in Group-2.
The correct combination is
(A) P-II, Q-I, R-III
(B) P-III, Q-II, R-I
(C) P-III, Q-I, R-II
(D) P-I, Q-III, R-II
Answer: (B)
15. Annual capacity of a plant producing phenol is 100 metric tons. Phenol sells at INR 200 per kg, and its production cost is INR 50 per kg. The sum of annual fixed charges, overhead costs and general expenses is INR 30,00,000. Taxes are payable at 18% on gross profit. Assuming the plant runs at full capacity and that all the phenol produced is sold, the annual net profit of the plant (in INR) is
(A) 1,39,40,000
(B) 1,50,00,000
(C) 98,40,000
(D) 1,20,00,000
Answer: (C)
16. A rigid spherical particle undergoes free settling in a liquid of density 750 kg m−3 and viscosity 9.81 × 10−3 Pa s. Density of the particle is 3000 kg m−3 and the particle diameter is 2 × 10−4 Acceleration due to gravity is 9.81 m s−2. Assuming Stoke’s law to be valid, the terminal settling velocity (in ms−1) of the particle is
(A) 2 × 10−3
(B) 3 × 10−3
(C) 4 × 10−3
(D) 5 × 10−3
Answer: (D)
17. Consider an compressible flow of a constant property fluid over a smooth, thin and wide flat plate. The free stream flows parallel to the surface of the plate along its length and its velocity is constant. Value of the Reynolds number at a distance of 2.0 m from the leading edge of the plate is 8000. The flow within the boundary layer at a distance of 1.0 m from the leading edge of the plate is
(A) laminar
(B) turbulent
(C) transitioning from laminar to turbulent
(D) inviscid
Answer: (A)
18. Ratio of momentum diffusivity to thermal diffusivity is
(A) Reynolds number
(B) Prandtl number
(C) Nusselt number
(D) Peclet number
Answer: (B)
19. Mole fraction and activity coefficient of component 1 in a binary liquid mixture are x1 and γ1, respectively. GE is excess molar Gibbs energy of the mixture, R is universal gas constant and T is absolute temperature of the mixture. Which one of the following is always true?
(A)
(B)
(C)
(D)
Answer: (A)
20. Leidenfrost phenomenon refers to
(A) the condensation of vapour on a cold surface
(B) the exchange of heat between two solids
(C) the melting of frost
(D) film boiling and evaporation of liquid droplets falling on a very hot surface
Answer: (D)
21. An irreversible gas phase reaction 2P → 4Q + R is conducted in an isothermal and isobaric batch reactor. Assume ideal gas behavior. The feed is an equimolar mixture of the reactant P and an inert gas. After complete conversion of P, the fractional change in volume is _______(round off to 2 decimal places).
Answer: (0.74 to 0.76)
22. Consider two Carnot engines C1 and C2 as shown in the figure.
The efficiencies of the engines C1 and C2 are 0.40 and 0.35, respectively. If the temperature of Reservoir R1 is 800 K, then the temperature (in K) of Reservoir R3 is ___________ (round off to nearest integer).
Answer: (311 to 313)
23. Consider the following closed loop system with Gp and Gc as the transfer functions of the process and the controller, respectively.
For a unit step change in the set point (ysp), the change in the value of response (y) at steady state is _______ (round off to 1 decimal place).
Answer: (0.9 to 1.1)
24. The decomposition of acetalydehyde (X) to methane and carbon monoxide follows four-step free radical mechanism. The overall rate of decomposition of X is where k1, k2, and k3 denote the rate constants of the elementary steps, with corresponding activation energies (in kJ mol−1) of 320, 40 and 0, respectively. The temperature dependency of the rate constants is described by Arrhenius equation. Cx denotes the concentration of acetaldehyde. The rate constant for the overall reaction is koverall. The activation energy for the overall reaction (in kJ mol−1) is ________ (round off to nearest integer).
Answer: (199 to 201)
25. Sum of the eigenvalues of the matrix is _______ (round off to nearest integer).
Answer: (14 to 14)
Q26 – Q55 carry two marks each.
26. In a box, there are 5 green balls and 10 blue balls. A person picks 6 balls randomly. The probability that the person has picked 4 green balls and 2 blue balls is
(A) 42/1001
(B) 45/1001
(C) 240/1001
(D) 420/1001
Answer: (B)
27. The maximum value of the function in the interval (0.5, 3.5) is
(A) 0
(B) 8
(C) 16
(D) 48
Answer: (C)
28. SO2 from air is absorbed by pure water in a counter current packed column operating at constant pressure. The compositions and the flow rates of the streams are shown in the figure.
In addition, use the following data and assumptions
• Column operates under isothermal conditions
• At the operating temperature of the column, y* = 40x, where yx is the mole fraction of SO2 in the gas that is the equilibrium with water containing SO2 at a mole fraction of x
• Solution is dilute and the operating line is linear
• Negligible amount of water evaporates
The number of transfer units (NTU) for this column is
(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
Answer: (D)
29. Two film theory applies for absorption of a solute from a gas mixture into a liquid solvent. The interfacial mass transfer coefficient (in mol m−2 s−1) for the gas side is 0.1 and for the liquid side is 3. The equilibrium relationship is y* = 2x, where x and y* are mole fractions of the solute in the liquid and gas phases, respectively. The ratio of the mass transfer resistance in the liquid film to the overall resistance is
(A) 0.0161
(B) 0.0322
(C) 0.0625
(D) 0.0645
Answer: (C)
30. Consider the equilibrium data for methanol-water system at 1 bar given in the figure below.
A distillation column operating at 1.0 bar is required to produce 92 mol % methanol. The feed is a saturated liquid. It is an equimolar mixture of methanol and water. The minimum reflux ratio is
(A) 0.33
(B) 0.50
(C) 0.54
(D) 1.17
Answer: (B)
31. Consider the gas phase reaction N2O4 ⇄ 2NO2 occurring in an isothermal and isobaric reactor maintained at 298 K and 1.0 bar. The standard Gibbs energy change of the reaction at 298 K is ∆G°298 = 5253 J mol−1. The standard states are those of pure ideal gases at 1.0 bar. The equilibrium mixture in the reactor behaves as an ideal gas. The value of the universal gas constant is 8.314 J mol−1 K−1. If one of pure N2O4 is initially charged to the reactor, the fraction of N2O4 that decomposes into NO2 at equilibrium is
(A) 0
(B) 0.17
(C) 0.38
(D) 1
Answer: (B)
32. A tank initially contains a gas mixture with 21 mol% oxygen and 79 mol% nitrogen. Pure nitrogen enters the tank, and a gas mixture of nitrogen and oxygen exits the tank. The molar flow rate of both the inlet and exit streams is 8 mol s−1.
In addition, use the following data and assumptions
• Assume the tank contents to be well mixed
• Assume ideal gas behavior
• The temperature and pressure inside the tank are held constant
• Molar density of the gas mixture in the tank is constant at 40 mol m−3
If the volume of the tank is 20 m3, then t he time (in seconds) required for oxygen content in the tank to decrease to 1 mol % is
(A) 100.45
(B) 304.45
(C) 3.445
(D) 10
Answer: (B)
33. Consider steady, laminar, fully developed flow of an incompressible Newtonian fluid through two horizontal straight pipes I and II, of circular cross section. The volumetric flow rates in both the pipes are the same. The diameter of pipe II is twice the diameter of pipe I, i.e., dII = 2dI. The ratio of the shear stress at the wall of pipe I to the shear stress at the wall of pipe II is
(A) 0.5
(B) 2
(C) 4
(D) 8
Answer: (D)
34. Equilibrium data for a binary mixture of E and F at two different pressures is shown in the figure
It is desired to process a feed containing 80 mol % E and 20 mol % F, and obtain a product with a purity of 99.5 mol % E. A sequence of two distillation columns, cone operating at pressure P1 and another at P2, is employed for this operation, as shown below.
Mole fraction of E in the distillate obtained from column 1 is 0.9. If the column pressures P1 and P2 are in kPa, which one of the following is correct?
(A) P1 = 100, P2 = 20, and high purity E is recovered from the top of column 2
(B) P1 = 100, P2 = 20, and high purity E is recovered from the bottom of column 2
(C) P1 = 20, P2 = 100, and high purity E is recovered from the top of column 2
(D) P1 = 20, P2 = 100, and high purity E is recovered from the bottom of column 2
Answer: (D)
35. A hollow cylinder of equal length and inner diameter (i.e., L = D) is sealed at both ends with flat plate, as shown in the figure. Its inner surfaces, A1, A2, and A3 radiate energy.
Fij denotes the fraction of radiation energy leaving the surface Ai which reaches the surface Aj. It is also known that F13 = 3 – 2√2. Which one of the following is correct?
(A) F21 = √2 – 1
(B)
(C)
(D)
Answer: (B)
36. A student performs a flow experiment with Bingham Plastic under fully developed laminar flow conditions in a tube of radius 0.01 m with a pressure drop (∆P) of 10 kPa over tube length (L) of 1.0 m. The velocity profile is flat for r < rc and parabolic for r ≥ rc, as shown in the figure.
Consider r and x as the radial and axial directions, and the shear stress is finite as r approaches zero. A force balance results in the following equation where τrx is the shear str3ess. If rc is 0.001 m, then t he magnitude of yield stress for this Bingham Plastic (in Pa) is
(A) 1
(B) 5
(C) 8
(D) 12
Answer: (B)
37. A feed stream containing pure species L flows into a reactor, where L is partly converted to M as shown in the figure.
The mass flow rate of the recycle stream is 20% of that of the product stream. The overall conversion of L (based on mass units) in the process is 30%. Assuming steady state operation, the one-pass conversion of L (based on mass units) through the reactor is
(A) 34.2%
(B) 30%
(C) 26.3%
(D) 23.8%
Answer: (C)
38. A U-tube manometer contains two manometric fluids of densities 1000 kg m−3 and 600 kg m−3. When both the limbs are open to atmosphere, the difference between the two levels is 10 cm at equilibrium, as shown in the figure.
The rest of manometer is filled with air of negligible density. The acceleration due to gravity is 9.81 ms−2 and the atmospheric pressure is 100 kPa. How much absolute pressure (in kPa) has to be applied on the limb ‘P’ to raise the fluid in the limb ‘Q’ by another 20 cm?
(A) 100.175
(B) 103.924
(C) 547.231
(D) 833.206
Answer: (B)
39. A pure gas obeys the equation of state given by where P is the pressure, T is the absolute temperature, V is the molar volume of the gas, R is the universal gas constant, and B, is a parameter independent of T and P. The residual molar Gibbs energy, GR, of the gas is given by the relation where Z is the compressibility factor and the integral is evaluated at constant T. If the value of B is 1 × 10−4 m3 mol−1, the residual molar enthalpy (in J mol−1) of the gas at 1000 kPa and 300 K is
(A) 100
(B) 300
(C) 2494
(D) 30000
Answer: (A)
40. Consider one mole of an ideal gas in a closed system. It undergoes a change in state from L to N through two different non-isothermal processes, as shown in the P-V diagram (where P is the pressure and V is the molar volume of the gas). Process I is carried out in a single step, namely LN, whereas process II is carried out in two steps, namely LM and MN. All the steps are reversible.
The net heat flowing into the system for process I is QI and that for process II is Qu. The value of QI – QII is
(A) 250
(B) 500
(C) 1000
(D) 1500
Answer: (B)
41. A fluid is heated from 40°C to 60°C in a countercurrent, double pipe heat exchanger. Hot fluid enters at 100°C and exits at 70° The log mean temperature difference, i.e. LMTD (in °C), is _______ (round off to 2 decimal places).
Answer: (34020 to 35.20)
42. Consider an infinitely long rectangular fin exposed to a surrounding fluid at a constant temperature Ta = 27°C
The steady state one dimensional energy balance on an element of the fin of thickness dx at a distance x from its base yields where θ = Tx – Ta, Tx is the temperature of the fin at the distance x from its base in °C. The value of m is 0.04 cm−1 and the temperature at the base is T0 = 227°C. The temperature (in °C) at x = 25 cm is _______ (round off to 1 decimal place).
Answer: (100.0 to 101.5)
43. Liquid water is pumped at a volumetric flow rate of 0.02 m3 s−1 form Tank I to Tank II, as shown in the figure.
Both the tanks are open to the atmosphere. The total frictional head loss for the pipe system is 1.0 m of water.
In addition, use the following data and assumptions
• Density of water is 1000 kg m−3
• Acceleration due to gravity is 9.81 m s−2
• Efficiency of the pump is 100%
• The liquid surfaces in the tanks have negligible velocities
The power supplied (in W) by the pump to lift the water is ________ (round off to 1 decimal place).
Answer: (1175.0 to 1180.0)
44. An elementary liquid phase reversible reaction P ⇄ Q is carried out in an ideal continuous stirred tank reactor (CSTR) operated at steady state. The rate of consumption of P, −rP (in mol liter−1 minute−1), is given by –rP = CP – 0.5CQ where CP and CQ are the concentrations (in mol liter−1) of P and Q, respectively.
The feed contains only the reactant P at a concentration of 1 mol liter−1, and the conversion of P at the exit of the CSTR is 75% of the equilibrium conversion. Assume that there is no volume change associated with the reaction, and the temperature of the reaction mixture is constant throughout the operation. The space time (in minutes) of the CSTR is ________ (round off to 1 decimal place).
Answer: (1.9 to 2.1)
45. An aqueous suspension at 60°C is fed to the first effect of a double effect forward feed evaporator with a mass flow rate of 1.25 kg s−1. The sum of the rates of water evaporated from the first and second effects is 1.0 kg s−1. Temperatures of the exit streams from the first and the second effects are 100°C, and 60°C, respectively. Consider the specific heat of the aqueous suspension, and the latent heat of phase change for water to be 4 kJ kg−1 K−1 and 2200 kJ kg−1, respectively, over this temperature range. The steam economy (in kg per kg) is _______ (round off to 2 decimal places).
Answer: (1.70 to 1.90)
46. A vertically held packed bed has a height of 1 m, and a void fraction of 0.1, when there is not flow through the bed. The incipient (minimum) fluidization is set in by injection of a fluid of density 1 kg m−3. The particle density (ρp) of the solids is 3000 kg m−3. Acceleration due to gravity is 9.81 ms−2. The pressure drop (in Pa) across the height of the bed is ________ (round off to nearest integer).
Answer: (26450 to 26500)
47. Two ideal cross-current stages operate to extract P from a feed containing P and Q, as shown below.
The mass flow rates of P and Q fed to Stage 1 are, 1,000 kg h−1 and 10,000 kg h−1, respectively. Pure solvent (S) is injected at mass flow rates of 5,000 kg h−1 and 15,000 kg h−1 to Stages 1 and 2, respectively. The components Q and S are immiscible. The equilibrium relation is given by Y* = 1.5X, where X is the mass o P per unit mass of Q in the raffinate, and Y* is the mass of P per unit mass of S in the extract, which is in equilibrium with the raffinate. The mass flow rate of P (in kg h−1) in the raffinate from Stage 2 is ______ (round off to nearest integer).
Answer: (171 to 181)
48. Consider a vertically falling film of water over an impermeable wall. The film is in contact with a static pool of non-reactive pure gas. The gas diffuses into the water film over the entire height of the falling film. The height of the film is 1.0 m, and its thickness is 10−4 The velocity of water, averaged over the film thickness, is 0.01 ms−1. The gas concentration (in kg m−3), averaged over the film thickness is where y is the vertical position in meters measured from the top of the wall.
In addition, use the following data and assumptions
• The flow is fully developed
• The width of the film is much larger than the thickness of the film, and the dissolved gas concentration is invariant over this width
• The solubility of the gas in water, CAi, is constant
• Pure water enters at y = 0
• The evaporation of water is negligible
The mass transfer coefficient on the liquid side (in mm s−1), averaged over the entire height of the falling film is ________ (round off to 3 decimal places).
Answer: (0.025 to 0.035)
49. An exothermic, aqueous phase, irreversible, first order reaction, Y → Z is carried out in an ideal continuous stirred tank reactor (CSTR) operated adiabatically at steady state. Rate of consumption of Y (in mol liter−1 minute−1) is given by where Cγ is the concentration of Y (in mol liter−1), and T is the temperature of the reaction mixture (in K). Reactant Y is fed at 50° Its inlet concentration is 1.0 mol liter−1, and its volumetric flow rate is 1.0 liter minute−1.
In additions, use the following data and assumptions
• Heat of the reaction = −42000 J mol−1
• Specific heat capacity of the reactions mixture = 4.2 J g−1 K−1
• Density of the reaction mixture = 1000 g liter−1
• Heat of the reaction, specific heat capacity and density of the reaction mixture do not vary with temperature
• Shaft work is negligible
If the conversion of Y at the exit of the reactor is 90%, the volume of the CSTR (in liter) is _______ (round off to 2 decimal places).
Answer: (2.40 to 3.00)
50. The liquid phase irreversible reactions, are carried out in an ideal continuous stirred tank reactor (CSTR) operating isothermally at steady state. The space time of the CSTR is 1 minute. Both the reactions are first order with respect to the reactant P, and k1 and k2 denote the rate constants of the two reactions. At the exit of the reactor, the conversion of reactant P is 60%, and the selectivity of Q with respect to R is 50%. The value of the first order rate constant k1 (in minute−1) is _______ (correct up to one decimal place).
Answer: (0.49 to 0.51)
51. A catalytic gas phase reaction P → Q is conducted in an isothermal packed bed reactor operated at steady state. The reaction is irreversible and second order with respect to the reactant P. The feed is pure P with a volumetric flow rate of 1.0 liter minute−1 and concentration of 2.0 mol liter−1.
In addition, use the following assumptions
• The reactant and product are ideal gases
• There is no volume change associated with the reaction
• Ideal plug flow conditions prevail in the packed bed
When the mass f catalyst in the reactor is 4 g, the concentration of P measured at the exit is 0.4 mol liter−1. The second order rate constant (in liter2 g−1catalyst mol−1 minute−1) is _______ (correct up to one decimal place).
Answer: (0.49 to 0.51)
52. Flow of water through an equal percentage vale is 900 liter h−1 at 30% opening, and 1080 liter h−1 at 35% opening. Assume that the pressure drop across the valve remains constant. The flow rate (in liter h−1) through the valve at 45% opening is ________ (round off to nearest integer).
Answer: (1540 to 1580)
53. Consider the following closed loop system.
Gc, Gf, and Gp are the transfer functions of the controller, the final control element and the process, respectively. y and ysp are the response and its set point, respectively. For a gain margin of 1.6, the design value of KC is _______ (correct up to one decimal place).
Answer: (0.49 to 0.51)
54. Given the value of y at x = 2 is _______ (round off to nearest integer).
Answer: (162 to 170)
55. Consider the following dataset.
The value of the integral using Simpson’s 1/3rd rule is ________ (round off to 1 decimal place).
1. Rescue team deployed _____ disaster hit areas combat _____ a lot of difficulties to save the people.
(A) with, at
(B) in, with
(C) with, with
(D) to, to
Answer: (B)
2. Select the most appropriate word that can replace the underlined word without changing the meaning of the sentence:
Now-a-days, most children have a tendency to belittle the legitimate concerns of their parents.
(A) disparage
(B) applaud
(C) reduce
(D) begrudge
Answer: (A)
3. Select the word that fits the analogy:
Partial : Impartial : : Popular : _____
(A) Impopular
(B) Dispopular
(C) Mispopular
(D) Unpopular
Answer: (D)
4. After the inauguration of the new building, the Head of the Department (HoD) collated faculty preferences for office space. P wanted a room adjacent to the lab. Q wanted to be close to the lift. R wanted a view of the playground and S wanted a corner office.
Assuming that everyone was satisfied, which among the following shows a possible allocation?
Answer: (C)
5. If f(x) = x2 for each x ∈ (−∞, ∞),then is equal to ______.
(A) f(x)
(B) (f(x))2
(C) (f(x))3
(D) (f(x))4
Answer: (C)
Q6 – Q10 carry two marks each.
6. Nominal interest rate is defined as the amount paid by the borrower to the lender for using the borrowed amount for a specific period of time. Real interest rate calculated on the basis of actual value (inflation-adjusted), is approximately equal to the difference between nominal rate and expected rate of inflation in the economy.
Which of the following assertions is best supported by the above information?
(A) Under high inflation, real interest rate is low and borrowers get benefited.
(B) Under low inflation, real interest rate is high and borrowers get benefited.
(C) Under high inflation, real interest rate is low and lenders get benefited.
(D) Under low inflation, real interest rate is low and borrowers get benefited.
Answer: (A)
7. For the year 2019, which of the previous year’s calendar can be used?
(A) 2011
(B) 2012
(C) 2013
(D) 2014
Answer: (C)
8. The ratio of ‘the sum of the odd positive integers from 1 to 100’ to ‘the sum of the even positive integers from 150 to 200’ is ______.
(A) 45 : 95
(B) 1 : 2
(C) 50 : 91
(D) 1 : 1
Answer: (C)
9. In a school of 1000 students, 300 students play chess and 600 students play football. If 50 students play both chess and football, the number of students who play neither is ______.
(A) 200
(B) 150
(C) 100
(D) 50
Answer: (B)
10. The monthly distribution of 9 Watt LED bulbs sold by two firm X and Y from January to June 2018 is shown in the pie-chart and the corresponding table. If the total number of LED bulbs sold by two firms during April-June 2018 is 50000, then the number of LED bulbs sold by the firm Y during April-June 2018 is ______.
(A) 11250
(B) 9750
(C) 8750
(D) 8250
Answer: (MTA)
CE2: Civil Engineering
Q1 – Q25 Carry one mark each.
1. The ordinary differential equation is
(A) linear and homogeneous
(B) linear and nonhomogeneous
(C) nonlinear and homogeneous
(D) nonlinear and nonhomogeneous
Answer: (B)
2. The value of is
(A) 7/9
(B) 1
(C) 3
(D) indeterminable
Answer: (C)
3. The integral is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson’s rules with a common step size. In this context, which one of the following statements is TRUE?
(A) Simpson’s rule as well as rectangular rule of estimation will give NON-zero error.
(B) Simpson’s rule, rectangular rule as well as trapezoidal rule of estimation will give NON-zero error.
(C) Only the rectangular rule of estimation will give zero error.
(D) Only Simpson’s rule of estimation will give zero error.
Answer: (D)
4. The following partial differential equation is defined for u: u (x, y)
The set of auxiliary conditions necessary to solve the equation uniquely, is
(A) three initial conditions
(B) three boundary conditions
(C) two initial conditions and one boundary condition
(D) one initial and two boundary conditions
Answer: (D)
5. The ratio of the plastic moment capacity of a beam section to its yield moment capacity is termed as
(A) aspect ratio
(B) load factor
(C) shape factor
(D) slenderness ratio
Answer: (C)
6. The state of stress represented by Mohr’s circle shown in the figure is
(A) uniaxial tension
(B) biaxial tension of equal magnitude
(C) hydrostatic stress
(D) pure shear
Answer: (D)
7. A weightless cantilever beam of span L is loaded as shown in the figure. For the entire span of the beam, the material properties are identical and the cross section is rectangular with constant width.
From the flexure-critical perspective, the most economical longitudinal profile of the beam to carry the given loads amongst the options given below, is
Answer: (C)
8. As per IS 456:2000, the pH value of water for concrete mix shall NOT be less than
(A) 4.5
(B) 5.0
(C) 5.5
(D) 6.0
Answer: (D)
9. The traffic starts discharging from an approach at an intersection with the signal turning green. The constant headway considered from the fourth or fifth headway position is referred to as
(A) discharge headway
(B) effective headway
(C) intersection headway
(D) saturation headway
Answer: (D)
10. Soil deposit formed due to transportation by wind is termed as
(A) aeolian deposit
(B) alluvial deposit
(C) estuarine deposit
(D) lacustrine deposit
Answer: (A)
11. A sample of 500 g dry sand, when poured into a 2 litre capacity cylinder which is partially filled with water, displaces 188 cm3 of water. The density of water is 1 g/cm3. The specific gravity of the sand is
(A) 2.72
(B) 2.66
(C) 2.55
(D) 2.52
Answer: (B)
12. Muskingum method is used in
(A) hydrologic reservoir routing
(B) hydrologic channel routing
(C) hydraulic channel routing
(D) hydraulic reservoir routing
Answer: (B)
13. Superpassage is a canal cross-drainage structure in which
(A) natural stream water flows with free surface below a canal
(B) natural stream water flows under pressure below a canal
(C) canal water flows with free surface below a natural stream
(D) canal water flows under pressure below a natural stream
Answer: (C)
14. A triangular direct runoff hydrograph due to a storm has a time base of 90 hours. The peak flow of 60 m3/s occurs at 20 hours from the start of the storm. The area of catchment is 300 km2. The rainfall excess of the storm (in cm), is
(A) 2.00
(B) 3.24
(C) 5.40
(D) 6.48
Answer: (B)
15. The velocity components in the x and y directions for an incompressible flow are given as u = (−5 + 6x) and v = −(9 + 6y), respectively. The equation of the streamline is
(A) (−5 + 6x) – (9 + 6y) = constant
(B)
(C) (−5 + 6x) (9 + 6y) = constant
(D)
Answer: (C)
16. The relationship between oxygen consumption and equivalent biodegradable organic removal (i.e., BOD) in a closed container with respect to time is shown in the figure
Assume that the rat of oxygen consumption is directly proportional to the amount of degradable organic matter and is expressed as where, Lt (in mg/litre) is the oxygen equivalent of the organics remaining at time t and k(in d−1) is the degradation rate constant. L0 is the oxygen equivalent of organic matter at time, t = 0.
In the above context, the correct expression is
(A) BOD5 = L5
(B) BODt = L0 – Lt
(C) L0 = Lte−kt
(D) Lt = L0(1 − e−kt)
Answer: (B)
17. A gas contains two types of suspended particles having average sizes of 2 μm and 50 μ Amongst the options given below, the most suitable pollution control strategy for removal of these particles is
(A) settling chamber followed by bag filter
(B) elstrostatic precipitator followed by venture scrubber
(C) electrostatic precipitator followed by cyclonic separator
(D) bag filter followed by electrostatic precipitator
Answer: (A)
18. A fair (unabised) coin is tossed 15 times. The probability of getting exactly 8 heads (round off to three decimal places), is _______.
Answer: (0.190 to 0.200)
19. The maximum applied load on a cylindrical concrete specimen of diameter 150 mm and length 300 mm tested as per the split tensile strength test guidelines of IS 5816:1999 is 157 kN. The split tensile strength (in MPa, round off to one decimal place) of the specimen is _______.
Answer: (2.0 to 2.4)
20. For an axle load of 15 tonne on a road, the Vehicle Damage Factor (round off to two decimal places), in terms of the standard axle load of 8 tonne, is _________.
Answer: (12.30 to 12.40)
21. 24-h traffic count at a road section was observed to be 1000 vehicles on a Tuesday in the month of July. If daily adjustment factor for Tuesday is 1.121 and monthly adjustment factor for July is 0.913, the Annual Average Daily Traffic (in veh/day, round off to the nearest integer) is ________.
Answer: (1021 to 1024)
22. A soil has dry unit weight of 15.5 kN/m3, specific gravity of 2.65 and degree of saturation of 72%. Considering the unit weight of water as 10 kN/m3, the water content of the soil (in %, round off to two decimal places) is ________.
Answer: (19.00 to 19.50)
23. A one-dimensional consolidation test is carried out on a standard 19 mm thick clay sample. The oedometer’s deflection gauge indicates a reading of 2.1 mm, just before removal of the load, without allowing any swelling. The void ratio is 0.62 at this stage. The initial void ratio (round of to two decimal places) of the standard specimen is________.
Answer: (0.78 to 0.88)
24. Velocity distribution in a boundary layer is given by where u is the velocity at vertical coordinate y, U∞ is the free stream velocity and δ is the boundary layer thickness. The values of U∞ and δ are 0.3 m/s and 1.0 m, respectively. The velocity gradient (in s−1, round off to two decimal places at y = 0, is _________.
Answer: (0.45 to 0.49)
25. Two identically sized primary settling tanks receive water for Type-I settling (discrete particles in dilute suspension) under laminar flow conditions. The Surface Overflow Rate (SOR) maintained in the two tanks are 30 m3/m2.d and 15 m3/m2.d. The lowest diameters of the particles, which shall be settled out completely under SORs of 30 m3/m2.d. and 15 m3/m2.d are designated as d30 and d15, respectively. The ratio d30/d15 (round off two decimal places), is_________.
Answer: (1.40 to 1.42)
Q26 – Q55 carry two marks each.
26. An ordinary differential equation is given below
The general solution of the above equation (with constant C1 and C2)
(A) y(x) = C1e−x/3 + C2ex/2
(B) y(x) = C1ex/3 + C2e−x/2
(C) y(x) = C1xe−x/3 + C2ex/2
(D) y(x) = C1e−x/3 + C2xex/2
Answer: (B)
27. A 4 × 4 matrix [P] is given below
The eigenvalues of [P] are
(A) 0, 3, 6, 6
(B) 1, 2, 3, 4
(C) 3, 4, 5, 7
(D) 1, 2, 5, 7
Answer: (D)
28. A prismatic linearly elastic bar of length of L, cross-sectional area A, and made up of a material with Young’s modulus, E, is subjected to axial tensile force as shown in the figures. When the bar is subjected to axial tensile forces P1 and P2, the strain energies stored in the bar are U1 and U2, respectively.
If U is the strain energy stored in the same bar when subjected to an axial tensile force (P1 + P2), the correct relationship is
(A) U = U1 + U2
(B) U = U1 – U2
(C) U < U1 + U2
(D) U > U1 + U2
Answer: (D)
29. The planar structure RST shown in the figure is roller-supported at S and pin-supported at R. Members RS and ST have uniform flexural rigidity (EI) and S is a rigid joint. Consider only bending deformation and neglect effects of self-weight and axial stiffening.
When the structure is subjected to a concentrated horizontal load P at the end, T, the magnitude of rotation at the support R, is
(A) PL3/12EI
(B) PL2/12EI
(C) PL2/6EI
(D) PL/6EI
Answer: (B)
30. Joints, I, J, K, L, Q and M of the frame shown in the figure (not down to the scale are pins. Continuous members IQ and LJ are connected through a pin at N. Continuous members JM and KQ are connected through a pin at P. the frame has hinge supports at joints R and S. The loads acting at joints I, J and K are along the negative Y direction and the loads acting at joints L and M are along the positive X direction.
The magnitude of the horizontal component of reaction (in kN) at S, is
(A) 5
(B) 10
(C) 15
(D) 20
Answer: (C)
31. The flow-density relationship of traffic on a highway is shown in the figure
The correct representation of speed-density relationship of the traffic on this highway is
Answer: (C)
32. Group-I gives a list of test methods for evaluating properties of aggregates. Group-II gives the list of properties to be evaluated.
The correct match test methods under Group-I to properties under Group-II, is
(A) P-4; Q-1; R-2; S-3
(B) P-2; Q-1; R-4; S-3
(C) P-3; Q-4; R-1; S-2
(D) P-2; Q-4; R-3; S-1
Answer: (B)
33. For the hottest month of the year at the proposed airport site, the monthly mean of the average daily temperature is 39° The monthly mean of the maximum daily temperature is 48°C for the same month of the year. From the given information, the calculated Airport Reference Temperature (in °C), is
(A) 36
(B) 39
(C) 42
(D) 48
Answer: (C)
34. Permeability tests were carried out on the samples collected from two different layers as shown in the figure (not drawn to the scale). The relevant horizontal (kh) and vertical (kv) coefficients of permeability are indicated for each layer.
The ratio of the equivalent horizontal to vertical coefficients of permeability, is
(A) 37.29
(B) 80.20
(C) 68.25
(D) 0.03
Answer: (A)
35. A 10 m high slope of dry clay soil (unit weight = 20 kN/m3), with a slope angle of 45° and the circular slip surface, is shown in the figure (not drawn to the scale). The weight of the slip wedge is denoted by W. The undrained unit cohesion (cu) is 60 kPa.
The factor of safety of the slope against slip failure, is
(A) 1.84
(B) 1.57
(C) 0.58
(D) 1.67
Answer: (MTA)
36. Crops are grown in a field having soil, which has field capacity of 30% and permanent wilting point of 13%. The effective depth of root zone is 80 cm. Irrigation water is supplied when the average soil moisture drops to 20%. Consider density of the soil as 1500 kg/m3 and density of water as 1000 kg/m3. If the daily consumptive use of water for the crops is 2 mm, the frequency of irrigating the crops (in days), is
(A) 7
(B) 10
(C) 11
(D) 13
Answer: (MTA)
37. Alkalinity of water, in equivalent/litre (eq/litre), is given by
{HCO3−} + 2 {CO32−} + {OH−] – {H+}
Where, {} represents concentration in mol/litre. For a water sample, the concentrations of HCO3− = 2 × 10−3 mol/litre, CO32− = 3.04 × 10−4 mol/litre and the pH of water = 9.0. The atomic weights are: Ca = 40; C = 12; and O = 16. If the concentration of OH− and H+ are NEGLECTED, the alkalinity of the water sample (in mg/litre as CaCO3), is
(A) 130.4
(B) 100.0
(C) 50.0
(D) 65.2
Answer: (A)
38. A theodolite was set up at a station P. The angle of depression to a vane 2 m above the foot of a staff held at another station Q was 45°. The horizontal distance between stations P and Q is 20 m. The staff reading at a benchmark S or RL 433.050 m is 2.905 m. Neglecting the errors due to curvature and refraction, the RL o the station Q (in m), is
(A) 413.050
(B) 413.955
(C) 431.050
(D) 435.955
Answer: (B)
39. The Fourier series to represent x – x2 for –π ≤ x ≤ π is given by
The value of a0 (round off to two decimal places), is _________.
Answer: (-6.61 to -6.55)
40. The diameter and height of a right circular cylinder are 3 cm and 4 cm, respectively. The absolute error in each of these two measurements is 0.2 cm. The absolute error in the computed volume (in cm3, round off to three decimal places), is ________.
Answer: (5.180 to 5.200)
41. A concrete beam of span 15 m, 150 mm wide and 350 mm deep is prestressed with a parabolic cable as shown in the figure (not drawn to the scale). Coefficient of friction for the cable is 0.35, and coefficient of wave effect is 0.0015 per meter.
If the cable is tensioned from one end only, the percentage loss (round off to one decimal place) in the cable force due to friction, is _______.
Answer: (3.8 to 4.7)
42. The plane truss has hinge supports at P and W and is subjected to the horizontal forces as shown in the figure (not drawn to the scale)
Representing the tensile force with ‘+’ sign and the compressive force with ‘−’ sign, the fore in member XW (in kN, round off to the nearest integer), is ________.
Answer: (-31 to -29)
43. The cross-section of the reinforced concrete beam having an effective depth of 500 mm is shown in the figure (not drawn to the scale). The grades of concrete and steel used are M35 and Fe550, respectively. The area of tension reinforcement is 400 mm2. It is given that corresponding to 0.2% proof stress, the material safety factor is 1.15 and the yield strain of Fe550 steel is 0.0044.
As per IS 456:2000, the limiting depth (in mm, round off to the nearest integer) of the neutral axis measured from the extreme compression fiber, is_______.
Answer: (220 to 224)
44. Two steel plates are lap jointed in a workshop using 6 mm thick fillet weld as shown in the figure (not drawn to the scale). The ultimate strength of the weld is 410 MPa.
As per limit State Design of IS 800:2007, the design capacity (in kN, round off to three decimal places) of the welded connection, is ______.
Answer: (400 to 420)
45. The design speed of a two-plane two-way road is 60 km/h and the longitudinal coefficient of friction is 0.36. The reaction time of a driver is 2.5 seconds. Consider acceleration due to gravity as 9.8 m/s2. The intermediate sight distance (in m, round off to the nearest integer) required for the road is _______.
Answer: (154 to 178)
46. A footing of size 2 m × 2 m transferring a pressure of 200 kN/m2, is placed at a depth of 1.5 m below the ground as shown in the figure (not drawn to the scale). The clay stratum is normally consolidated. The clay has specific gravity of 2.65 and compression index of 0.3.
Considering 2:1 (vertical to horizontal) method of load distribution and γw = 10 kN/m3, the primary consolidation settlement (in mm, round off to two decimal places) of the clay stratum is _______.
Answer: (74.00 to 76.00)
47. A constant-head permeability test was conducted on a soil specimen under a hydraulic gradient of 2.5. The soil specimen has specific gravity of 2.65 and saturated water content of 20%. If the coefficient of permeability of the soil is 0.1 cm/s, the seepage velocity (in cm/s, round off to two decimal places) through the soil specimen is ______.
Answer: (0.70 to 0.73)
48. A 5 m high vertical wall has a saturated clay backfill. The saturated unit weight and cohesion of clay are 18 kN/m3 and 20 kPa, respectively. The angle of internal friction of clay is zero. In order to prevent development of tension zone, the height of the wall is required to be increased. Dry sand is used as backfill above the clay for the increased portion of the wall. The unit weight and angle of internal friction of sand are 16 kN/m3 and 30°, respectively. Assume that the back of the wall is smooth and top of the backfill is horizontal. To prevent the development of tension zone, the minimum height (in m, round off to one decimal place) by which the wall has to be raised, is _______.
Answer: (2.4 to 2.6)
49. A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, round off to two decimal places) is ________.
Answer: (2.40 to 2.70)
50. A hydraulic jump occurs in a triangular (V-shaped) channel with side slopes 1:1 (vertical to horizontal). The sequent depths are 0.5 m and 1.5 m. The flow rate (in m3/s, round off to two decimal places) in the channel is ________.
Answer: (1.70 to 1.76)
51. A concrete dam holds 10 m of static water as shown in the figure (not drawn to the scale). The uplift is assumed to vary linearly from full hydrostatic head at the heel, to zero at the toe of dam. The coefficient of friction between the dam and foundation soil is 0.45. Specific weights of concrete and water are 24 kN/m3 and 9.81 kN/m3, respectively.
For NO sliding condition, the required minimum base width B (in m, round off to two decimal places) is ________.
Answer: (15.00 to 16.00)
52. The ion product of water (pKw) is 14. If a rain water sample has a pH of 5.6, the concentration of OH− in the sample (in 10−9 mol/litre, round off to one decimal place), is _________.
Answer: (3.8 to 4.1)
53. A waste to energy plant burns dry solid waste of composition: Carbon = 35%. Oxygen = 26%, Hydrogen = 10%, Sulphur = 6%, Nitrogen = 3% and Inerts = 20%. Burning rate is 1000 tonnes/d. Oxygen in air by weight is 23%. Assume complete conversion of Carbon to CO2, Hydrogen to H2O Sulphur to SO2 and Nitrogen to NO2.
Given Atomic weights: H = 1, C = 12, N = 14, O = 16, S = 32
The stoichiometric (theoretical) amount of air (in tones/d, round off to the nearest integer) required for complete burning of this waste, is________.
Answer: (6963 to 6967)
54. A sample of water contains an organic compound C8H16O8 at a concentration of 10−3 mol/litre. Given that the atomic weight of C = 12 g/mol, H = 1 g/mol, and O = 16 g/mol, the theoretical oxygen demand of water (in g of O2 per litre, round off to two decimal places), is _______.
Answer: (0.24 to 0.27)
55. A theodolite is set up at station A. The RL of instrument axis is 212.250 m. The angle of elevation to the top of a 4 m long staff, held vertical at station B, is 7°. The horizontal distance between stations A and B is 400 m. Neglecting the errors due to curvature of earth and refraction, the RL (in m, round off to three decimal places) of station B is_________.
1. It is a common criticism that most o the academicians live in their ______, so, they are not aware of the real life challenges.
(A) homes
(B) ivory towers
(C) glass palaces
(D) big flats
Answer: (B)
2. His hunger for reading is insatiable. He reads indiscriminately. He is most certainly a/an _____ reader.
(A) all-round
(B) precocious
(C) voracious
(D) wise
Answer: (C)
3. Select the word that fits the analogy:
Fuse : Fusion :: Use : ______
(A) Usage
(B) User
(C) Uses
(D) Usion
Answer: (A)
4. If, 0, 1, 2, …….. 7, 8, 9 are coded as O, P, Q, …., V, W, X, then 45 will be coded as _______.
(A) TS
(B) ST
(C) SS
(D) SU
Answer: (B)
5. The sum of two positive numbers is 100. After subtracting 5 from each number, t he product of the resulting numbers is 0. One of the original numbers is ______.
(A) 80
(B) 85
(C) 90
(D) 95
Answer: (D)
Q6 – Q10 carry two marks each.
6. The American psychologist Howard Gardner expounds that human intelligence can be subcategorized into multiple kinds, in such a way that individuals differ with respect to their relative competence in each kind. Based on this theory, modern educationists insist on prescribing multi-dimensional curriculum and evaluation parameters that enable development and assessment of multiple intelligences.
Which of the following statements can be inferred from the given text?
(A) Howard Gardner insists that the teaching curriculum and evaluation needs to be multidimensional.
(B) Howard Gardner wants to develop and assess the theory of multiple intelligences.
(C) Modern educationists want to develop and assess the theory of multiple intelligences.
(D) Modern educationists insist that the teaching curriculum and evaluation needs to be multi-dimensional.
Answer: (D)
7. Five friends P, Q, R, S and T went camping. At night, they had to sleep in a row inside the tent. P, Q and T refused to sleep next to R since he snored loudly. P and S wanted to avoid Q as he usually hugged people in sleep.
Assuming everyone was satisfied with the sleeping arrangements, what is the order in which they slept?
(A) RSPTQ
(B) SPRTQ
(C) QRSPT
(D) QTSPR
Answer: (A)
8. Insert seven numbers between 2 and 34, such that resulting sequence including 2 and 34 is an arithmetic progression. The um of these inserted seven numbers is ______.
(A) 120
(B) 124
(C) 126
(D) 130
Answer: (C)
9. The unit’s place in 26591749110016 is ______.
(A) 1
(B) 3
(C) 6
(D) 9
Answer: (A)
10. The total expenditure of a family, on different activities in a month, is shown in the pie-chart. The extra money spent on education as compared to transport (in percent) is _____.
(A) 5
(B) 33.3
(C) 50
(D) 100
Answer: (C)
CE1: Civil Engineering
Q1 – Q25 carry one mark each.
1. In the following partial differential equation, θ is a function of t and z, and D and K are functions of θ
The above equation is
(A) a second order linear equation
(B) a second degree linear equation
(C) a second order non-linear equation
(D) a second degree non-linear equation
Answer: (C)
2. The value of is
(A) 0
(B) 1/4
(C) 1/2
(D) 1
Answer: (B)
3. The true value of ln(2) is 0.69. If the value of ln(2) is obtained by linear interpolation between ln(1) and ln(6), the percentage of absolute error (round of to the nearest integer), is
(A) 35
(B) 48
(C) 69
(D) 84
Answer: (B)
4. The area of an ellipse represented by an equation is
(A) πab/4
(B) πab/2
(C) πab
(D) 4πab/3
Answer: (C)
5. Consider the planar truss shown in the figure (not drawn to the scale)
Neglecting self-weight of the members, the number of zero-force members in the truss under the action of the load P, is
(A) 6
(B) 7
(C) 8
(D) 9
Answer: (C)
6. A reinforcing steel bar, partially embedded in concrete, is subjected to a tensile force P. The figure that appropriately represents the distribution of the magnitude of bond stress (represented as hatched region), along the embedded length of the bar, is
Answer: (C)
7. In a two-dimensional stress analysis, the state of stress at a point P is
The necessary and sufficient condition for existence of the state of pure shear at the point P, is
(A)
(B) τxy = 0
(C) σxx + σyy = 0
(D)
Answer: (C)
8. During the process of hydration of cement, due to increase in Dicalcium Silicate (C2S) content in cement clinker, the heat of hydration
(A) increases
(B) decreases
(C) initially decreases and then increases
(D) does not change
Answer: (B)
9. The Los Angeles test for stone aggregates is used to examine
(A) abrasion resistance
(B) crushing strength
(C) soundness
(D) specific gravity
Answer: (A)
10. Which one of the following statements is NOT correct?
(A) A clay deposit with a liquidity index greater than unity is in a state of plastic consistency.
(B) The cohesion of normally consolidated clay is zero when triaxial test is conducted under consolidated undrained condition.
(C) The ultimate bearing capacity of a strip foundation supported on the surface of sandy soil increases in direct proportion to the width of footing.
(D) In case of a point load, Boussinesq’s equations predicts higher value of vertical stress at a point directly beneath the load as compared to Westergaard’s equation.
Answer: (A)
11. In a soil investigation work at a site, Standard Penetration Test (SPT) was conducted at every 1.5 m interval up to 30 m depth. At 3 m depth, the observed number of hammer blows for three successive 150 mm penetrations were 8, 6 and 9 respectively. The SPT N-value at 3 m depth, is
(A) 23
(B) 17
(C) 15
(D) 14
Answer: (C)
12. Velocity of flow is proportional to the first power of hydraulic gradient in Darcy’s law. This law is applicable to
(A) laminar flow in porous media
(B) transitional flow in porous media
(C) turbulent flow in porous media
(D) laminar as well as turbulent flow in porous media
Answer: (A)
13. A body floating in a liquid is in a stable state of equilibrium if its
(A) metacentre lies above its centre of gravity
(B) metacentre lies below its centre of gravity
(C) metacentre coincides with its centre of gravity
(D) centre of gravity is below its centre of bouyancy
Answer: (A)
14. Uniform flow with velocity U makes an angle θ with the y-axis, as shown in the figure
The velocity potential (ϕ), is
(A) ±U(x sin θ + y cos θ)
(B) ±U(y sin θ − x cos θ)
(C) ±U(x sin θ − y cos θ)
(D) ±U(y sin θ + x cos θ)
Answer: (A)
15. The data an agricultural field for a specific month are given below:
Pan Evaporation = 100 mm
Effective Rainfall = 20 mm (after deducting losses due to runoff and deep percolation)
Crop Coefficient = 0.4
Irrigation Efficiency = 0.5
The amount of irrigation water (in mm) to be applied to the field in that month, is
(A) 0
(B) 20
(C) 40
(D) 80
Answer: (C)
16. During chlorination process, aqueous (aq) chlorine reacts rapidly with water to form Cl−, HOCl, and H+ as shown below
Cl2 (aq) + H2O ⇌ HOCl + Cl− + H+
The most active disinfectant in the chlorination process from amongst the following, is
(A) H+
(B) HOCl
(C) Cl−
(D) H2O
Answer: (B)
17. An amount of 35.67 mg HCl is added to distilled water and the total solution volume is made to one litre. The atomic weights of H and Cl are 1 and 35.5, respectively. Neglecting the dissociation of water, the pH of the solution, is
(A) 3.50
(B) 3.01
(C) 2.50
(D) 2.01
Answer: (B)
18. The probability that a 50 year flood may NOT occur at all during 25 years life of a project (round of to two decimal places), is ______.
Answer: (0.59 to 0.61)
19. A planar elastic structure is subjected to uniformly distributed load, as shown in the figure (not drawn to the scale)
Neglecting self-weight, the maximum bending moment generated in the structure (in kN.m round off to the nearest integer), is _________.
Answer: (95 to 97)
20. In an urban area, a median is provided to separate the opposing streams of traffic. As per IRC:86-1983, the desirable minimum width (in m, expressed as integer) of the median, is _______.
Answer: (5 to 5)
21. A road in a hilly terrain is to be laid at a gradient of 4.5%. A horizontal curve of radius 100 mm is laid at a location on this road. Gradient needs to be eased due to combination of curved horizontal and vertical profiles of the road. As per IRC, the compensated gradient (in %, round off to one decimal place), is _______.
Answer: (4.0 to 4.0)
22. In a drained triaxial compression test, a sample of sand fails at deviator stress of 150 kPa under confining pressure of 50 kPa. The angle of internal friction (in degree, round of to the nearest integer) of the sample, is _______.
Answer: (36 to 38)
23. A fully submerged infinite sandy slope has an inclination of 30° with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 kN/m3 and 38°, respectively. The unit weight of water is 10 kN/m3. Assume that seepage is parallel to the slope. Against shear failure of the slope. the factor of safety (round off to two decimal places) is _______.
Answer: (0.59 to 0.61)
24. A 4 m wide rectangular channel carries 6 m3/s of water. The Manning’s ‘n’ of the open channel is 0.02. Considering g = 9.81 m/s2, the critical velocity of flow (in m/s, round off to two decimal places) in the channel, is _________.
Answer: (2.35 to 2.55)
25. A river has a flow of 1000 million litres per day (MLD), BOD5 of 5 mg/litre and Dissolved Oxygen (DO) level of 8 mg/litre before receiving the wastewater discharge at a location. For the existing environmental conditions, the saturation DO level is 10 mg/litre in the river. Wastewater discharge of 100 MLD with the BOD5 of 200 mg/litre and DO level of 2 mg/litre falls at that location. Assuming complete mixing of wastewater and river water, the immediate DO deficit (in mg/litre round off to two decimal places), is ________.
Answer: (2.45 to 2.65)
Q26 – Q55 carry two marks each.
26. For the Ordinary Differential Equation with initial conditions x(0) = 0 and the solution is
(A) −5e2t + 6e3t
(B) 5e2t + 6e3t
(C) −10e2t + 10e3t
(D) 10e2t + 10e3t
Answer: (C)
27. A continuous function f(x) is defined. If the third derivative at xi is to be computed by using the fourth order central finite-divided-difference scheme (with step length = h), the correct formula is
Answer: (A)
28. Distributed load(s) of 50 kN/m may occupy any position(s) (either continuously or in patches) in the girder PQRST as shown in the figure (not drawn to the scale)
The maximum negative (hogging) bending moment (in kN.m) that occurs at point R is
(A) 22.50
(B) 56.25
(C) 93.75
(D) 150.00
Answer: (B)
29. A rigid weightless platform PQRS shown in the figure (not drawn to the scale) can slide freely in the vertical direction. The platform is held in position by the weightless member OJ and four weightless, frictionless rollers. Points O and J are pin connections. A block of 90 kN rests on the platform as shown in the figure
The magnitude of horizontal component of the reaction (in kN) at pin O, is
(A) 90
(B) 120
(C) 150
(D) 180
Answer: (B)
30. A cantilever beam PQ of uniform flexural rigidity (EI) is subjected to a concentrated moment M at R as shown in the figure
The deflection at the free end Q is
(A) ML2/6EI
(B) ML2/4EI
(C) 3ML2/8EI
(D) 3ML2/4EI
Answer: (C)
31. A dowel bar is placed at a contraction joint. When contraction occurs, the concrete slab cracks at predetermined location(s). Identify the arrangement, which shows the correct placement of dowel bar and the place of occurrence of the contraction crack(s).
Answer: (B)
32. The relationship between traffic flow rate (q) and density (D) is shown in the figure
The shock wave condition is depicted by
(A) flow with respect to point 1 (q1 = qmax)
(B) flow changing from point 2 to point 6 (q2 > q6)
(C) flow changing from point 3 to point 7 (q3 > q7)
(D) flow with respect to point 4 and point 5 (q4 = q5)
Answer: (MTA)
33. The appropriate design length of a clearway is calculated on the basis of ‘Normal Take-off’ condition. Which one of the following options correctly depicts the length of t he clearway? (Note : None of the options are drawn to scale)
Answer: (C)
34. The total stress paths corresponding to different loading conditions, for a soil specimen under the isotropically consolidated stress state (O), are shown below
The correct match between the stress paths and the listed loading conditions, is
(A) OP – I, OQ – II, OR – IV, OS – III
(B) OP – IV, OQ – III, OR – I, OS – II
(C) OP – III, OQ – II, OR – I, OS – IV
(D) OP – I, OQ – III, OR – II, OS – IV
Answer: (B)
35. The soil profile at a suite up to a depth of 10 m is shown in the figure (not drawn to the scale). The soil is preloaded with a uniform surcharge (q) of 70 kN/m2 at the ground level. The water table is at a depth of 3 m below ground level. The soil unit weight of the respective layers is shown in the figure. Consider unit weight of water as 9.81 kN/m3 and assume that the surcharge (q) is applied instantaneously.
Immediately after preloading, the effective stresses (in kPa) a points P and Q, respectively, are
(A) 124 and 204
(B) 36 and 90
(C) 36 and 126
(D) 54 and 95
Answer: (D)
36. Water flows at the rate of 12 m3/s in a 6 m wide rectangular channel. A hydraulic jump is formed in the channel at a point where the upstream depth is 30 cm (just before the jump). Considering acceleration due to gravity as 9.81 m/s2 and density of water as 1000 kg/m3, the energy loss in the jump is
(A) 114.2 kW
(B) 114.2 MW
(C) 141.2 h.p.
(D) 141.2 J/s
Answer: (A)
37. A water supply scheme transports 10 MLD (Million Litres per Day) water through a 450 mm diameter pipeline for a distance of 2.5 km. A chlorine dose of 3.50 mg/litre is applied at the starting point of the pipeline to attain a certain level disinfection at the downstream end. It is decided to increase the flow rate from 10 MLD 13 MLD in the pipeline. Assume exponent for concentration, n = 0.86. With this increased flow, in order to attain the same level of disinfection, the chlorine dose (in mg/litre) to be applied at the starting point should be
(A) 3.95
(B) 4.40
(C) 4.75
(D) 5.55
Answer: (C)
38. An open traverse PQRST is surveyed using theodolite and the consecutive coordinates obtained are given in the table
If the independent coordinates (Northing, Easting) of station P are (400 m, 200 m), the independent coordinates (in m) of station T, are
(A) 194.7, 370.1
(B) 205.3, 429.9
(C) 394.7, 170.1
(D) 405.3, 229.9
Answer: (C)
39. If C represents a line segment between (0, 0, 0) and (1,1, 1) in Cartesian coordinate system, the value (expressed as integer) of the line integral ∫c[(y + z)dx + (x + z)dy + (x + y)dz] is _______.
Answer: (3 to 3)
40. Consider the system of equations
The value of x3 (round off to the nearest integer), is ______.
Answer: (3 to 3)
41. A rigid, uniform, weightless, horizontal bar is connected to three vertical members P, Q and R as shown in the figure (not drawn to the scale). All three members have identical axial stiffness of 10 kN/mm. The lower ends of bars P and R rest on a rigid horizontal surface. When NO load is applied, a gap of 2 mm exists between the lower end of the bar Q and the rigid horizontal surface. When a vertical load W is placed on the horizontal bar in the downward direction, the bar still remains horizontal and gets displaced by 5 mm in the vertically downward direction.
The magnitude of the load W (in kN, round off to the nearest integer), is ________.
Answer: (129 to 131)
42. The flange and web plates of the doubly symmetric built-up section are connected by continuous 10 mm thick fillet welds as shown in the figure (not drawn to the scale). The moment of inertial of the section about its principal axis X-X is 7.73 × 106 mm4. The permissible shear stress in the fillet welds is 100 N/mm2. The design shear strength of the section is governed by the capacity of the fillet welds.
The maximum shear force (in kN, round off to one decimal place) that can be carried by the section, is_______.
Answer: (393.5 to 399.1)
43. The singly reinforced concrete beam section shown in the figure ( not drawn to the scale) is made of M25 grade concrete and Fe500 grade reinforcing steel. The total cross-sectional area of the tension steel is 942 mm2.
As per Limit State Design of IS 456:2000, the design moment capacity (in kN.m, round of to two decimal places) of the beam section, is ________.
Answer: (158.00 to 158.80)
44. A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zeo at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.
Answer: (39 to 41)
45. Traffic volume count has been collected on a 2-lane road section which needs upgradation due to severe traffic flow condition. Maximum service flow rate per lane is observed as 1280 veh/h at level of service ‘C’. The Peak Hour Factor is reported as 0.78125. Historical traffic volume count provides Annual Average Daily Traffic as 12270 veh/day. Directional spilt of the traffic flow is observed to be 60:40. Assuming that traffic stream consists of ‘All Cars’ and all drivers are ‘Regular Commuters’, the number of extra lane(s) (round off to the next higher integer) to be provided, is _______.
Answer: (MTA)
46. A vertical retaining wall of 5 m height has to support soil having unit weight of 18 kN/m3, effective cohesion of 12 kN/m2, and effective friction angle of 30°. As per Rankine’s earth pressure theory and assuming that a tension crack has occurred, the lateral active thrust on the wall per meter length (in kN/m, round off to two decimal places), is_______.
Answer: (21.00 to 23.00)
47. Water flows in the upward direction in a tank through 2.5 m thick sand layer as shown in the figure. The void ratio and specific gravity of sand are 0.58 and 2.7, respectively. The sand is fully saturated. Unit weight of water is 10 kN/m3.
The effective stress (in kPa, round off to two decimal places) at point A, located I am above the base of tank, is _______.
Answer: (8.70 to 9.30)
48. A 10 m thick clay layer is resting over a 3 m thick sand layer and is submerged. A fill of 2 m thick sand with unit weight of 20 kN/m3 is placed above the clay layer to accelerate the rate of consolidation of the clay layer. Coefficient of consolidation of clay is 9 × 10−2 m2/year and coefficient of volume compressibility of clay is 2.2 × 10−4 m2/kN. Assume Taylor’s relation between time factor and average degree of consolidation.
The settlement (in mm, round off to two decimal places) of the clay layer, 10 years after the construction of the fill, is ______.
Answer: (18.40 to 19.50)
49. Three reservoirs P, Q and R are interconnected by pipes as shown in the figure (not drawn to the scale). Piezometric head at the junction S of the pipes is 100 m. Assume acceleration due to gravity as 9.81 m/s2 and density of water as 1000 kg/m3. The length of the pipe from junction S to the inlet of reservoir R is 180 m.
Considering head loss only due to friction (with friction factor of 0.03 for all the pipes), the height of water level in the lowermost reservoir R (in m, round off to one decimal place) with respect to the datum, is ________.
Answer: (97.2 to 97.8)
50. In a homogenous unconfined aquifer of area 3.00 km2, the water table was at an elevation of 102.00 m. After a natural recharge of volume of 0.90 million cubic meter (Mm3), the water table rose to 103.20 m. After this recharge, ground water pumping took place and the water table dropped down to 101.20 m. The volume of ground water pumped after the natural recharge, expressed (in Mm3 and round of to two decimal places), is ________.
Answer: (1.40 to 1.60)
51. A circular water tank of 2 m diameter has circular orifice of diameter 0.1 m at the bottom. Water enters the tank steadily at a flow rate of 20 litre/s and escapes through the orifice. The coefficient of discharge of the orifice is 0.8. Consider the acceleration due to gravity as 9.81 m/s2 and neglect frictional losses. The height of the water level (in m, round off to two decimal places) in the tank at the steady state, is ________.
Answer: (0.50 to 0.54)
52. Surface overflow Rate (SOR) of a primary settling tank (discrete settling) is 20000 litre/m2 per day. Kinematic viscosity of water in the tank is 1.01 × 10−2 cm2/s. Specific gravity of the settling particles is 2.64. Acceleration due to gravity is 9.81 m/s2. The minimum diameter (in μm, round off to one decimal place) of the particles that will be removed with 80% efficiency in the tank, is ______.
Answer: (14.0 to 15.0)
53. A gaseous chemical has a concentration of 41.6 μmol/m3 in air at 1 atm pressure and temperature 293 K. The universal gas constant R is 82.05 × 10−6 (m3 atm)/(mol K). Assuming that ideal gas law is valid, the concentration of the gaseous chemical (in ppm, round off to one decimal place), is _______.
Answer: (0.9 to 1.1)
54. A steam with a flow rate of 5 m3/s is having an ultimate BOD of 0 mg/litre. A wastewater discharge of 0.20 m3/s having BOD5 of 500 mg/litre joins the stream at a location and instantaneously gets mixed up completely. The cross-sectional area of the stream is 40 m2 which remains constant. BOD exertion rate constant is 0.3 per day (logarithm base to e). The BOD (in mg/litre, round off to two decimal places) remaining at 3 km downstream from the mixing location, is _______.
Answer: (49.00 to 50.00)
55. The lengths and bearings of a traverse PQRS are:
The length of line segment SP (in m, round off to two decimal places), is _________.
1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.
(A) with, at
(B) on, in
(C) on, at
(D) to, at
Answer: (C)
2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.
(A) slim
(B) bright
(C) obvious
(D) uncertain
Answer: (B)
3. Select the word that fits the analogy:
Cover : Uncover :: Associate : _______
(A) Unassociate
(B) Inassociate
(C) Missassociate
(D) Dissociate
Answer: (D)
4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.
Which of the following statements can be inferred from the given passage?
(A) Officials declared that the food-grain production target will be met due to good rains.
(B) Officials want the food-grain production target to be met by the November-February period.
(C) Officials feel that the food-grain production target cannot be met due to floods.
(D) Officials hope that the food-grain production target will be met due to a good rabi produce.
Answer: (D)
5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.
(A) n2 – n
(B) n2 + n
(C) 2n2 – n
(D) 2n2 + n
Answer: (B)
Q6-Q10 carry two marks each.
6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.
Which of the following statements can be inferred from the above passage?
(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.
(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.
(C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.
(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.
Answer: (D)
7. P, Q, R, S, T, U, V, and W are seated around a circular table.
(I) S is seated opposite to W.
(II) U is seated at the second place to the right of R.
(III) T is seated at the third place to the left of R.
(IV) V is a neighbor of S.
Which of the following must be true?
(A) P is a neighbor of R.
(B) Q is a neighbor of R.
(C) P is not seated opposite to Q.
(D) R is the left neighbor of S.
Answer: (C)
8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?
(A) 66.6
(B) 75.2
(C) 88.2
(D) 116.5
Answer: (B)
9. For a matrix M = [mij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and mij = −mij. The minimum number of elements required to fully specify the matrix is_______.
(A) 0
(B) 6
(C) 12
(D) 16
Answer: (B)
10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.
(A) 15 : 17
(B) 16 : 17
(C) 17 : 15
(D) 17 : 16
Answer: (B)
BT: Biotechnology
Q1 – Q25 carry one mark each.
1. Protein P becomes functional upon phosphorylation of a serine residue. Replacing this serine with _____ will result in a phophomimic mutant of P.
(A) alanine
(B) aspartic acid
(C) phenylalanine
(D) lysine
Answer: (B)
2. Ras protein is a
(A) trimeric GTPase involved in relaying signal from cell surface to nucleus.
(B) monomeric GTPase involved in relaying signal from cell surface to nucleus.
(C) trimeric GTPase involved in regulation of cytoskeleton.
(D) monomeric GTPase involved in regulation of cytoskeleton.
Answer: (B OR D)
3. Which of the following statements are CORRECT?
[P] Viruses can play a role in causing human cancer
[Q] A tumor suppressor gene can be turned off without any change in its DNA sequence
[R] Alteration in miRNA expression levels contributes to the development of cancer
(A) P and Q only
(B) Q and R only
(C) P and R only
(D) P, Q and R
Answer: (D)
4. Which class of antibody is first made by developing B cells inside bone marrow?
(A) IgG
(B) IgE
(C) IgA
(D) IgM
Answer: (D)
5. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r] regarding mammalian cells.
Assertion [a]: Cells use Ca2+, and not Na+, for cell-to-cell signaling
Reason [r]: In the cytosol, concentration of Na+ is lower than that of Ca2+
(A) Both [a] and [r] are true and [r] is the correct reason for [a].
(B) Both [a] and [r] are true but [r] is not the correct reason for [a].
(C) Both [a] and [r] are false.
(D) [a] is true but [r] is false.
Answer: (D)
6. Vincristine and vinblastine, two commercially important secondary metabolites from Catharanthus roseus, are examples of
(A) alkaloids.
(B) flavonoids.
(C) terpenoids.
(D) steroids.
Answer: (A)
7. DNA synthesized from and RNA template is called
(A) recombinant DNA.
(B) transcript.
(C) T-DNA.
(D) complementary DNA.
Answer: (D)
8. Two monomeric His-tagged proteins of identical molecular weight are present in a solution.pIs of these two proteins are 5.6 and 6.8. Which one of the following techniques can be used to separate them?
(A) Denaturing polyacrylaminde gel electrophoresis
(B) Size-exclusion chromatography
(C) Ion-exchange chromatography
(D) Nickel affinity chromatography
Answer: (C)
9. During a positive-negative selection process, transformed animal cells expressing ________ are killed in presence of ganciclovir in the medium.
(A) pyruvate kinase
(B) viral thymidine kinase
(C) viral serine/threonine kinase
(D) viral tyrosine kinase
Answer: (B)
10. A vector derived from which one of the following viruses is used to high-frequency genomic integration of a transgene in animal cells?
(A) Adenovirus
(B) Adeno-associated virus
(C) Lentivirus
(D) Herpes simplex virus
Answer: (C)
11. Which one of the following statements about Agrobacterium Ti plasmid is CORRECT?
(A) Vir genes are located within the T-DNA segment
(B) Phytohormone biosynthesis genes are located outside the T-DNA segment
(C) Opine catabolism genes are located within the T-DNA segment
(D) Opine biosynthesis genes are located within the T-DNA segment
Answer: (D)
12. Which of the following types of molecules act as biological catalysts?
[P] Protein
[Q] RNA
[R] Phospholipid
(A) P and Q only
(B) P and R only
(C) Q and R only
(D) P, Q and R
Answer: (A)
13. Which one of the following media components is used to maintain pH in mammalian cell culture?
(A) CaCl2
(B) MgSO4
(C) NaCl
(D) NaHCO3
Answer: (D)
14. Which of the following are energy transducing membranes?
[P] Plasma membrane of bacteria
[Q] Inner membrane of chloroplasts
[R] Inner membrane of mitochondria
(A) P and Q only
(B) P and R only
(C) Q and R only
(D) P, Q and R
Answer: (B)
15. Amino acid sequences of cytochrome c and ribulose 5-phosphate epimerase from 40 organsims were chosen and phylogenetic trees were obtained for each of these two protein families.
Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
Assertion [a]: The two trees will not be identical
Reason [r]: The nature and frequency of mutations in the two families are different
(A) Both [a] and [r] are true and [r] is the correct reason for [a].
(B) Both [a] and [r] are true but [r] is not the correct reason for [a].
(C) Both [a] and [r] are false.
(D) [a] is false but [r] is true.
Answer: (A)
16. A microorganism isolated from a salt-rich (salt concentration~2 M) lake was found to posses diglycerol tetraethers, with polyisoprenoid alcohol side chains, as the major lipid component of its cell membrane. The isolated organism is
(A) a planctomycete.
(B) a cyanobacteria.
(C) a unicellular amoeba.
(D) an archaea.
Answer: (D)
17. A function f is as follows:
The function f is continuous function when c is equal to ______ (answer is an integer).
Answer: (15 to 15)
18. Given that Z= X2 + Y2, the value of and Y = 0 is _______(answer is an integer).
Answer: (2 to 2)
19. The elemental composition of dry biomass of a yeast species is CH6O0.4N0.2S0.0024P0.017, The contribution of carbon to the dry biomass is _________% (round off to 2 decimal places).
[Given: atomic weights of H, C, N, O P and S are 1, 12, 14, 16, 31 and 32, respectively]
Answer: (51.01 to 52.99)
20. Solvents A and B are completely immiscible. Solute S is soluble in both these solvents. 100 g of S was added to a container which has 2 kg each of A and B. The solute is 1.5 times more soluble in solvent A than in solvent B. The mixture was agitated thoroughly and allowed to reach equilibrium. Assuming that the solute has completely dissolved, the amount of solute in solvent A phase is ______g.
Answer: (60 to 60)
21. The number of molecules of a nucleotide of molecular weight 300 g/mol present in 10 picomoles is ______ × 102 (round off to 2 decimal places).
Answer: (5.99 to 6.05)
22. To facilitate mass transfer from a gas to a liquid phase, a gas bubble of radius r is introduced into the liquid. The gas bubble then breaks into 8 bubbles of equal radius. Upon this change, the ratio of the interfacial surface area to the gas phase volume for the system changes form 3/r to 3n/r. The value of n is ________.
Answer: (2 to 2)
23. The largest eigenvalue of the matrix is _______.
Answer: (3 to 3)
24. A normal random variable has mean equal to 0, and standard deviation equal to 3. The probability that on a random draw the value of this random variable is greater than 0 is _________ (round off 2 decimal places).
Answer: (0.49 to 0.51)
25. A variable Y is a function of t. Given that Y (t = 0) = 1 and Y(t = 1) = 2, in the interval t = [0, 1] can be approximated as ______.
Answer: (1 to 1)
Q26 – Q55 carry two marks each.
26. A block of ice at 0°C is supplied heat at a constant rate to convert ice to superheated steam. Which one of the following trajectories correctly represents the trend of the temperature of the system with time? Assume that the specific heat of H2O is not a function of temperature.
Answer: (A)
27. The DNA sequence shown below is to be amplified by PCR:
Which one of the following pair of primers can be used for this amplification?
Answer: (B)
28. Which of the following statements about immune response are CORRECT?
[P] T cells are activated by antigen-presenting cells
[Q] Foreign peptides are not presented to helper T cells by Class II MHC proteins
[R] Dendritic cells are referred to as professional antigen-presenting cells
(A) P and R only
(B) P and Q only
(C) Q and R only
(D) P, Q and R
Answer: (A)
29. Which of the following statements are CORRECT about eukaryotic cells cycle?
[P] CDKs can phosphorylate proteins in the absence of cyclins
[Q] CDKs can be inactivated by phosphorylation
[R] Degradation of cyclins is required for cell cycle progression
[S] CDKs are not involved in chromosome condensation
(A) P and R only
(B) P and S only
(C) P, Q and R only
(D) Q and R only
Answer: (D)
30. W, X and Y are the intermediates in a biochemical pathway as shown below:
Mutants auxotrophic for Z are found in four different complementation groups, namely Z1, Z2, Z3 and Z4. The growth of these mutants on media supplemented with W, X, Y, or Z is shown below (Yes: growth observed; No: growth not observed):
What is the order of the four complementation groups in terms of the step they block?
Answer: (B)
31. In tomato plant, red (R) is dominant over yellow (r) for fruit color and purple (P) is dominant over green (p) for stem color. Fruit color and stem color assort independently. The number of progeny plants of different fruit/stem colors obtained from a mating are as follows:
Red fruit, purple stem – 145
Red fruit, green stem – 184
Yellow fruit, purple stem – 66
Yellow fruit, green stem – 47
What are the genotypes of the parent plants in this mating?
(A) RrPp × Rrpp
(B) RrPp × RrPp
(C) RRPP × rrpp
(D) RrPP × Rrpp
Answer: (A)
32. Some of the cytokinins used in plant tissue culture media are given blow:
[P] BAP
[Q] Zeatin
[R] Kinetin
[S] 2iP
Which of these are synthetic analogs?
(A) P and Q only
(B) Q and S only
(C) R and S only
(D) P and R only
Answer: (D)
33. Carl Woese used the gene sequence of which one of the following for phylogenetic taxonomy of prokaryotes?
(A) A ribosomal RNA of large ribosomal subunit
(B) A ribosomal RNA of small ribosomal subunit
(C) A ribosomal protein of large ribosomal subunit
(D) A ribosomal protein of small ribosomal subunit
Answer: (B)
34. A list of pathogens (Group I) and a list of anti-microbial agents (Group II) used to treat their infections are given below. Match the pathogens with the corresponding anti-microbial agents.
(A) P-4, Q-3, R-2, S-5
(B) P-5, Q-2, R-4, S-1
(C) P-2, Q-3, R-4, S-1
(D) P-2, Q-3, R-1, S-5
Answer: (C)
35. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
Assertion [a]: Dam metylase protects E. coli DNA from phage endonucleases
Reason [r]: E. coli dam methylase methylates the adenosine residue in the sequence “GATC”
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is false but [r] is true
Answer: (D)
36. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
Assertion [a]: Embryonic stem cells are suitable for developing knockout mice
Reason [r]: Homologous recombination is more frequent in embryonic stem cells than that in somatic cells
(A) Both [a] and [r] are false
(B) Both [a] and [r] are true, and [r] is the correct reason for [a]
(C) Both [a] and [r] are true, but [r] is not the correct reason for [a]
(D) [a] is true, but [r] is false
Answer: (B)
37. The schematic of a plasmid with a gap in one of the strands is shown below:
Which of the following enzyme(s) is/are required to fill the gap and generate a covalently closed circular plasmid?
[P] DNA ligase
[Q] Alkaline phosphatase
[R] DNA polymerase
[S] Polynucleotide kinase
(A) P only
(B) P, R and S only
(C) P and R only
(D) P, Q and R only
Answer: (B)
38. Match sub-cellular organelles listed in Group I with their features listed in Group II:
(A) P-1, Q-4, R-2, S-3
(B) P-2, Q-3, R-4, S-1
(C) P-3, Q-4, R-2, S-1
(D) P-3, Q-1, R-4, S-2
Answer: (C)
39. Which of the following strategies are used by cells for metabolic regulation?
[P] Phosphorylation-dephosphorylation
[Q] Allostery
[R] Feedback inhibition
(A) P and Q only
(B) P and R only
(C) Q and R only
(D) P, Q and R
Answer: (D)
40. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
Assertion [a]: A zygote and its immediate descendant cells are unspecialized and are called totipotent
Reason [r]: Totipotent cells retain the capacity to differentiate into only a few cell types
(A) Both [a] and [r] are false
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are true and [r] is the correct reason for [a]
(D) [a] is true but [r] is false
Answer: (D)
41. Which of the following statements about gene therapy are CORRECT?
[P] Affected individuals, but not their progeny, can be cured through germline gene therapy
[Q] Affected individuals, as well as their progeny, can be cured through germline gene therapy
[R] Affected individuals, but not their progeny, can be cured through somatic gene therapy
[S] Affected individuals, as well as their progeny, can be cured through somatic gene therapy
(A) P and R only
(B) P and S only
(C) Q and R only
(D) Q and S only
Answer: (C)
42. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
Assertion [a]: A genetically engineered rice that produces beta-carotene in the rice grain is called Golden rice
Reason [r]: Enabling biosynthesis of provitamin A in the rice endosperm gives a characteristic yellow/orange color
(A) Both [a] and [r] are false
(B) Both [a] and [r] and true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are true and [r] is the correct reason for [a]
(D) [a] is true but [r] is false
Answer: (C)
43. The sequence of a 1 Mb long DNA is random. This DNA has all four bases occurring in equal proportion. The number of nucleotides, on average, between two successive EcoRI recognition site GAATTC is______.
Answer: (4096 to 4096)
44. E.Coli was grown in 15N medium for several generations. Cells were then transferred to 14N medium, allowed to grow for 4 generations and DNA was isolated immediately. The proportion of total DNA with intermediate density is ________ (round off to 2 decimal places).
Answer: (0.11 to 0.14)
45. A batch reactor is inoculated with 1 g/L biomass. Under these conditions, cells exhibit a lag phase of 30 min. If the specific growth rate in the log phase is 0.00417 min−1, the time taken for the biomass to increase to 8 g/L is _______ min (round off to 2 decimal places).
Answer: (526.01 to 529.99)
46. The system of linear equations
cx + y = 5
3x + 3y = 6
has no solution when c is equal to _______.
Answer: (1 to 1)
47. The amino acid sequence of a peptide is Phe-Leu-Ile-Met-Ser-Leu. The number of codons that encode the amino acids present in this peptide is given below:
Phe: 2 codons
Leu: 6 codons
Ile: 3 codons
Met: 1 codon
Ser: 4 codons
The number of unique DNA sequences that can encode this peptide is________.
Answer: (864 to 864)
48. Assume that a cell culture was started with five human fibroblast cells. Two cells did not divide even once whereas the other three cells completed three rounds of cell division. At this stage, the total number of kinetochores in all the cells put together is _______.
Answer: (1196 to 1196)
49. Growth of an organism on glucose in a chemostat is characterized by Monod model with specific growth rate = 0.45 h−1 and Ks = 0.5 g/L. Biomass from the substrate is generated as YXS = 0.4 g/g. The chemostat volume is 0.9 L and media is fed at 1 L/h and contains 20 g/L of glucose. At steady state, the concentration of biomass in t he chemostat is _______ g/L.
Answer: (0 to 0)
50. A function f is given as: f(X) = 4X – X2
The function f is maximized when X is equal to _______.
The value of S is ________ (round off to 2 decimal places).
Answer: (2.20 to 2.30)
52. Protein A and protein B form a covalent complex. Gel filtration chromatography of this complex showed a peak corresponding to 200 kDa. SDS-PAGE analysis of this complex, with and without beta-mercaptoethanol, showed a single band corresponding to molecular weight 50 and 25 kDa, respectively. Given that the molecular weight of protein A is 25 kDa, the molecular weight of protein B is ______ kDa.
Answer: (25 to 25)
53. The concentrations of ATP, ADP and inorganic phosphate in a cell are 2.59, 0.73 and 2.72 mM, respectively. Under these conditions, free energy change for the synthesis of ATP at 37°C is _____ kJ/mol (round off to 2 decimal places).
Given: free energy change for ATP hydrolysis under standard condition is −30.5 kJ/mol and R = 8.315 kJ/mol.K
Answer: (48.50 to 49.50 OR 18521.20 to 18521.30)
54. An algorithm was designed to find globins in protein sequence databases. A database which as 78 globin sequences was searched using this algorithm. The algorithm retrieved 72 sequences of which only 65 were globins. The sensitivity of this algorithm is ________% (round off to 2 decimal places).
Answer: (83.30 to 83.40)
55. The mitochondrial electron transfer chain oxidizes NADH with oxygen being the terminal electron acceptor. The redox potentials for the two half-reactions are given below:
The free energy change associated with the transfer of electrons from NADH to O2 is ______ kJ/mol (round off to 2 decimal places).
1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.
(A) with, at
(B) on, in
(C) on, at
(D) to, at
Answer: (C)
2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.
(A) slim
(B) bright
(C) obvious
(D) uncertain
Answer: (B)
3. Select the word that fits the analogy:
Cover : Uncover :: Associate : _______
(A) Unassociate
(B) Inassociate
(C) Missassociate
(D) Dissociate
Answer: (D)
4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.
Which of the following statements can be inferred from the given passage?
(A) Officials declared that the food-grain production target will be met due to good rains.
(B) Officials want the food-grain production target to be met by the November-February period.
(C) Officials feel that the food-grain production target cannot be met due to floods.
(D) Officials hope that the food-grain production target will be met due to a good rabi produce.
Answer: (D)
5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.
(A) n2 – n
(B) n2 + n
(C) 2n2 – n
(D) 2n2 + n
Answer: (B)
Q6-Q10 carry two marks each.
6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.
Which of the following statements can be inferred from the above passage?
(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.
(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.
(C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.
(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.
Answer: (D)
7. P, Q, R, S, T, U, V, and W are seated around a circular table.
(I) S is seated opposite to W.
(II) U is seated at the second place to the right of R.
(III) T is seated at the third place to the left of R.
(IV) V is a neighbor of S.
Which of the following must be true?
(A) P is a neighbor of R.
(B) Q is a neighbor of R.
(C) P is not seated opposite to Q.
(D) R is the left neighbor of S.
Answer: (C)
8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?
(A) 66.6
(B) 75.2
(C) 88.2
(D) 116.5
Answer: (B)
9. For a matrix M = [mij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and mij = −mij. The minimum number of elements required to fully specify the matrix is_______.
(A) 0
(B) 6
(C) 12
(D) 16
Answer: (B)
10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.
(A) 15 : 17
(B) 16 : 17
(C) 17 : 15
(D) 17 : 16
Answer: (B)
BM: Biomedical Engineering
Q1 – Q25 carry one mark each.
1. m1 and m2 are the roots of the characteristic equation of a linear second order physical system. Match the nature of the roots with the natural response of the system.
(A) P-L, Q-M, R-K
(B) P-M, Q-L, R-K
(C) P-L, Q-K, R-M
(D) P-M, Q-K, R-L
Answer: (C)
2. A person is sitting in a chair with feet on the ground. While rising up on his feet, the kinematic motion NOT occurring is
(A) Hip extension
(B) Plantar flexion
(C) Hip flexion
(D) Knee extension
Answer: (C)
3. The equipment that measures elasticity of blood vessel in vivo is
(A) Rheometer
(B) Dimension anlayser
(C) Thermomechanical analyser
(D) Dynamic mechanical analyser
Answer: (B)
4. Biomaterials with shape memory effects are NOT used in
(A) Intracranial aneurysm clips
(B) Arterial blood vessel closure devices
(C) Orthopedic total joint replacements
(D) Orthodontic dental arch wires
Answer: (C)
5. The MRI scanner parameter of long TRep or short TEcho will generate a ________contrast image
(A) Proton Density-weighted
(B) T2-weighted
(C) T1-weighted
(D) T2*-weighted
Answer: (MTA)
6. In diagnostic X-ray imaging, the following is NOT a part of primary EM radiation interaction in soft tissue.
(A) Photoelectric effect
(B) Characteristic radiation production
(C) Compton scattering
(D) Pair-production
Answer: (B OR D)
7. A 5 MHz ultrasound pulse is used to image a tumor at a depth of 2 cm in a soft tissue. It takes time t for the reflected echo from the tumor to come back to the receiver. Instead, if a 2.5 MHz wave is used, how long will it take for the echo from the same tumor to arrive at the receiver?
(A) t/2
(B) t
(C) 2t
(D) 4t
Answer: (B)
8. X(s) is the Laplace transform of a signal x(t).
The Laplace transform of assuming x(0) = 0, is
(A) sX(s)
(B) X(s)/s
(C) DX(s)/ds
(D)
Answer: (A)
9. Which of the following are odd functions?
P: Sin(t)
Q: Cos(t)
R: Sin(t) + Cos(t)
(A) Q and S
(B) P and Q
(C) P and S
(D) R and Q
Answer: (C)
10. State-space model of a system is given as:
The conditions for the system to be controllable are
(A) a = 0, b ≠ 0
(B) a ≠, b = 0
(C) a ≠ = 0, b ≠ 0
(D) a = 0, b = 0
Answer: (C)
11. In microprocessor systems with memory mapped I/O, which of the following is true?
(A) Only I/O devices with internal memory can be interfaced.
(B) I/O devices can be accessed using IN and OUT instructions
(C) Each I/O device can be addressed as a memory location
(D) Arithmetic and logic operations cannot be directly performed with the I/O data
Answer: (C)
12. The number of electrodes used in recording standard 12-lead Electrocardiogram (ECG)
(A) 13
(B) 12
(C) 11
(D) 10
Answer: (D)
13. Which of the following is NOT a part of knee joint?
(A) Patella
(B) Tibia
(C) Femur
(D) Fibula
Answer: (D)
14. During a routine stethoscopic examination at the left midclavicular-5th intercostals space, murmurs were noted between first and second heart sound. The possible abnormality among the following could be
(A) Aortic stenosis
(B) Mitral regurgitation
(C) Mitral stenosis
(D) Aortic regurgitation
Answer: (B)
15. The thin filament of a muscle fiber is comprised of
(A) Troponin, Tropomyosin, Actin
(B) Troponin, Tropomyosin, Titin
(C) Tropomyosin, Titin, Actin
(D) Actin, Mysoin, Troponin
Answer: (A)
16. The value of the integral evaluated over the contour C : |z| = 3/2 is ________
Answer: (-1.1 to -0.9)
17. The eigenvalues of a 3 × 3 non-singular matrix P are 1, 2 and 3. The trace of matrix P−1 (rounded off to two decimal places) is _______
Answer: (1.82 to 1.84)
18. The following recursion relation, when started from a finite positive non-zero value, converges to ______
Answer: (1 to 1)
19. In a nuclear imaging system, Sodium Iodide (NaI) crystals are used to detect gamma rays of 120 keV. The percentage (%) of gamma-rays that will pass through 1 cm of NaI crystal, assuming the Half-Value-Layer (HVL) of NaI as 0.2 cm, is ________ (rounded off to one decimal place).
Answer: (3.0 to 3.2)
20. The distal end of an endoscope is placed at a distance of 1 mm from the gastrointestinal wall. The refractive indices of the fiber core and cladding are 1.5 and 1.45, respectively.
The maximum field of view for the endoscope is _______ degrees (rounded off to one decimal place).
Answer: (44 to 46)
21. Two inductors with the details given below are wound separately on two identical ring type ferromagnetic cores.
The ratio L2/L1 is ______.
Answer: (4 to 4)
22. Two days X and Y having concentrations in the ratio 0.25 in identical cuvettes were subjected to absorption measurements in a spectrophotometer. The estimated ratio of their absorbance is 0.5. The ratio of their molar extinction coefficients is ______.
Answer: (2 to 2)
23. Hydrolysis of one ATP molecule provides an energy of _______ kilo calories (correct up to one decimal place).
Answer: (7.25 to 7.35)
24. An 830 nm laser Doppler flow meter probe is oriented at an angle of 60° to the flow axis. If the average flow velocity is 3 cm/s, the magnitude of Doppler shift frequency (kHz) is ________ (rounded off to one decimal place).
Answer: (35.8 to 36.4)
25. A 100 mA single current pulse from a pulse generator is used for artificial pacing of heart at the right ventricle. If the delivered energy does not exceed the fibrillation threshold of 300 μJ, the safe duration of the pulse that could be applied to the tissue mass having an impedance of 500 Ω is ________ μ
Answer: (60 to 60)
Q26 – Q55 carry two marks each.
26. The resting potential of a mammalian nerve cell is −80 mV. A certain drug administered to the body changes the intracellular K+ concentration from 150 mmol/L to 55 mmol/L. The nearest value of cell membrane potential after the drug administration, assuming that the external equilibrium of K+ does not get changed during the event, is
(Gas constant = 8.315 J/mol/K, core temperature = 37°C and Faraday constant = 96500 C/mol)
(A) −117 mV
(B) −18.71 mV
(C) −53.32 mV
(D) −141.30 mV
Answer: (C)
27. The arrangement of four resistors of equal value in the diaphragm of a physiological pressure measurement catheter is shown below. The applied pressure is observed to cause an increase in length of resistors R2, R4 and an increase in cross sectional area in R1 and R3. The operation results in an equal change in the values of all four resistors. Which among the configuration given below should be used to connect the resistors to form a Wheatstone bridge so that bridge output voltage is proportional to the change in resistance of individual resistors?
(A) I only
(B) II only
(C) Neither I nor II
(D) Both I and II
Answer: (A)
28. For the given input voltage, Vin = 10 sin (2πt) to the functional circuit shown below, the output signal will be
Answer: (D)
29. During a non-invasive measurement of blood pressure, mean arterial pressure was observed to be 100 mm Hg. If systolic pressure is 150 mm Hg, the diastolic pressure would be
(A) 110 mm Hg
(B) 75 mm Hg
(C) 70 mm Hg
(D) 50 mm Hg
Answer: (B)
30. Two loads are connected to AC supply mains as depicted in the figure. One load draws 10 kW whereas the other load of 10 kVA is operated at 0.6 pf lagging. To achieve an overall power factor of 0.9544 lagging, the nearest kVAr rating of the capacitor bank needed to be connected across the supply mains is equal to
(A) 3
(B) 5
(C) 7
(D) 9
Answer: (A)
31. The nearest value of power dissipated in the 3Ω resistance in the circuit is
(A) 3 W
(B) 25/3 W
(C) 12 W
(D) 25/12 W
Answer: (A)
32. A second order low pass filter is being constructed by cascading two first order low pass filters with the following transfer functions
where ω1 and ω2 are the respective 3dB cut off frequencies.
The undamped natural frequency ωc of the resulting second order low pass filter is
(A)
(B)
(C)
(D)
Answer: (A)
33. Match the bridge type with the application given below:
(A) P-L, Q-K, R-N, S-M
(B) P-N, Q-K, R-L, S-M
(C) P-N, Q-L, R-M, S-K
(D) P-L, Q-M, R-N, S-K
Answer: (A)
34. For a non-unity feedback system with the magnitude of steady-state error to a unit step-input is
(A) 0.50
(B) 0.45
(C) 0.25
(D) 0.20
Answer: (D)
35. Match the Boolean expression with its minimal realization
(A) P-K, Q-L, R-N, S-M
(B) P-L, Q-K, R-N, S-M
(C) P-L, Q-N, R-M, S-K
(D) P-M, Q-K, R-L, S-N
Answer: (B)
36. The glomerulus filtration process of kidney is modeled as a flat membrane with pores of radius 1 nm and length of pore 60 nm. The viscosity of the fluid is 0.002 Pa s. The aggregate area of the pores makeup 5% of total surface area of the membrane. The average pressure on the blood side of the membrane is 8000 Pa and on the ultrafiltrate side is 6200 Pa. The total available area of membrane is 1.5 m2. The nearest value of resulting filtration rate in cm3/min is
(A) 0.14
(B) 1.40
(C) 8.43
(D) 84.37
Answer: (C)
37. During resting state, the voltage outside the cell membrane compared to that inside the membrane is _______. Under such conditions, the intracellular and extracellular regions have _______ and ________ concentrations, respectively.
(A) Moe positive, more Potassium [K+], more Sodium [Na+]
(B) More negative, more Potassium [K+], more Sodium [Na+]
(C) More negative, more Sodium [Na+], more Potassium [K+]
(D) More positive, more Sodium [Na+], more Potassium [K+]
Answer: (A)
38. The tensile strength of a degradable suture used for a surgical procedure in the human body is observed to decrease exponentially from its original strength by 40% and 50% after 10 days and 20 days, respectively. The closest approximation of the time taken for the tensile strength to decay to 20% of its original value would be
(A) 35 days
(B) 45 days
(C) 60 days
(D) 70 days
Answer: (D)
39. A 60 kg person is standing on one foot on force plate. The ground reaction force is found to act 40 mm anterior to the ankle joint. The mass center of a foot is 60 mm from the Trochanter Knee Ankle (TKA) line. If the weight of the foot is 0.8 kg, the closest value of magnitude of moment acting on the ankle joint is
(A) 23 Nm
(B) 48 Nm
(C) 235 Nm
(D) 466 Nm
Answer: (A)
40. The temperature of bone cement is increased from 37°C to 87°C during the femoral hip arthroplasty. The cement thickness is noted to be 20 mm. The stress developed due to exothermic reaction of bone cement during the polymerization process and shrinkage of the bone cement, respectively, are
Assume that
(i) bone, cement, and implant are modeled as a set of concentric cylinders
(ii) no direct adhesion takes place between bone and cement
(iii) temperature is uniform
Coefficient of thermal expansion of bone cement = 90 × 10−6/°C
Young’s modulus of bone cement = 3.5 GPa
(A) 15.75 MPa, 90 μm
(B) 15.75 MPa, 110 μm
(C) 6.85 MPa, 110 μm
(D) 6.85 MPa, 90 μm
Answer: (A)
41. A patient is initially imaged in a 1 Tesla MRI scanner and induced voltage is found to be equal to V1. The expression for the magnitude of the received voltage in RF coil is given below.
|V| = 2πγ0VSM0 (Sin α) βr
VS : MR slice volume, M0: Magnitude of resultant magnetic vector at equilibrium,
γ0 : Larmor frequency, α: tip angle, βr : Magnetic field sensitivity of receive coil.
When the patient is shifted to a 3 Tesla MRI scanner that uses the same RF coil and the slice thickness is halved, the magnitude of the induced voltage was found to be equal to V2. The ratio V2/V1 is
(A) 1.5
(B) 3.0
(C) 4.5
(D) 6.0
Answer: (C)
42. A 3 MHz ultrasound transducer transmits a 3-cycle long pulse into a soft tissue at normal incidence to fat and liver interface. The axial resolution (mm) and the amplitude reflection coefficient at fat-liver interface, respectively, are
43. The forward biased current of a silicon (SI) diode is being calculated from the exponential model of the V-I characteristics. If the diode current ID = 1 mA at a voltage drop VD = 0.7 V, the nearest value of ID when VD = 0.8 V is
Assume thermal voltage VT = 25.3 mV for Si diode
(A) 0.133 mA
(B) 2 mA
(C) 52 mA
(D) 90 mA
Answer: (C)
44. A continuous random variable x has a probability density function given by f(x) = e−α|x| (−∞ < x < ∞)
where α is a real constant. The variance of x is _______ (correct up to one decimal place).
Answer: (0.5 to 0.5)
45. The magnitude of the gradient of the function f(x, y) = x2 + y2 at the point (1, 1) is ________ (rounded off to two decimal places).
Answer: (2.8 to 2.9)
46. The value of following double integral is ________ (correct up to three decimal places).
∬R xy dxdy
where R is the first quadrant of the circle with center at the origin and radius of one unit.
Answer: (0.125 to 0.125)
47. A gynaeocologist recorded the blood pressure (BP) of patients as shown in the Table below. Using Regression processes, the diastolic BP of a 38 year old patient (mm Hg) is ______ (rounded off to two decimal places).
Answer: (86.5 to 87.7)
48. A person in standing position first flexes the hip by 50° from the initial Trochanter knee ankle (TKA) line and then flexes knee by 20°. The distance of ankle joint from the initial TKA line is _____ (rounded off to nearest integer).
(i) the distance between hip joint and knee joint is 400 mm
(ii) the distance between knee joint and ankle joint is 300 mm.
Answer: (456 to 457)
49. A chest radiograph of 36 cm × 48 cm is digitized. If we want to preserve details in the image to a spatial resolution of 6 cycles/mm, the approximate image data size in MB for an 8 bit quantization is _______ (rounded off to two decimal places).
Answer: (23.70 to 23.75)
50. An X-ray radiography scenario is shown in the figure. If the number of incident photons (Ni) is equal to 2 × 106 at 50 keV, the number of photons (Nd) that exit the tissue is ______ × 106 (rounded off to two decimal places).
(use linear attenuation coefficient for soft tissue and blood at 50 keV as 0.4 cm−1 and 0.2 cm−1, respectively)
Answer: (0.5 to 0.6)
51. The wavelength of an electron accelerated to a potential of 1V is ________ nm (rounded off to two decimal places).
Mass of electron = 9.11 × 10−31 kg
Planck’s constant, h = 6.63 × 10−34 Js
Charge of electron = 1.6 × 10−19 C
Answer: (1.20 to 1.25)
52. In a permanent magnetic moving coil (PMMC) instrument having following specifications, the angular deflection of the pointer for a coil current of 100 μA will be _______ degrees (rounded off to one decimal place).
Magnetic flux density = 1.5 Tesla
Torsional spring constant = 2 × 10−6 Nm/deg
Cross sectional area of the coil = 2.5 cm2
Number of turns of the coil = 500
Answer: (9.0 to 9.6)
53. Arterial blood extracted from a healthy adult showed an oxygen partial pressure value of 40 mm Hg. The total oxygen content in the arterial blood measured in %V/V is ________ (rounded off to one decimal place).
Given : Solubility of oxygen in blood = 0.003 ml/mm Hg/dL
Hemoglobin oxygen saturation = 95%
Oxygen carrying capacity of Hb = 1.34 ml/g
Arterial blood hemoglobin concentration = 15 g/dL
Answer: (19.2 to 19.4)
54. In the process of measure blood flow from an artery using C-clamp magnetic flow probe, the voltage recorded across diametrically opposite sites of the artery is 3.75 nV. The blood flow rate through the artery is _____ cm3/s (rounded off to two decimal places).
The inner diameter of the C-clamp = 0.5 cm,
The magnetic flux density = 1.5 × 10−5 Wb/m2.
Answer: (0.95 to 0.99)
55. A cell is injected with a current i(t) = u(t) to produce a change in the intracellular membrane voltage v(t). The cell-membrane is modeled as a linear system with impulse response h(t) = Ae−t/τ u(t). The cell membrane voltage output at 5 ms is _______ mV.
1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.
(A) with, at
(B) on, in
(C) on, at
(D) to, at
Answer: (C)
2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.
(A) slim
(B) bright
(C) obvious
(D) uncertain
Answer: (B)
3. Select the word that fits the analogy:
Cover : Uncover :: Associate : _______
(A) Unassociate
(B) Inassociate
(C) Missassociate
(D) Dissociate
Answer: (D)
4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.
Which of the following statements can be inferred from the given passage?
(A) Officials declared that the food-grain production target will be met due to good rains.
(B) Officials want the food-grain production target to be met by the November-February period.
(C) Officials feel that the food-grain production target cannot be met due to floods.
(D) Officials hope that the food-grain production target will be met due to a good rabi produce.
Answer: (D)
5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.
(A) n2 – n
(B) n2 + n
(C) 2n2 – n
(D) 2n2 + n
Answer: (B)
Q6 – Q10 carry two marks each.
6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.
Which of the following statements can be inferred from the above passage?
(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.
(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.
(C) Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.
(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.
Answer: (D)
7. P, Q, R, S, T, U, V, and W are seated around a circular table.
(I) S is seated opposite to W.
(II) U is seated at the second place to the right of R.
(III) T is seated at the third place to the left of R.
(IV) V is a neighbor of S.
Which of the following must be true?
(A) P is a neighbor of R.
(B) Q is a neighbor of R.
(C) P is not seated opposite to Q.
(D) R is the left neighbor of S.
Answer: (C)
8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?
(A) 66.6
(B) 75.2
(C) 88.2
(D) 116.5
Answer: (B)
9. For a matrix M = [mij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and mij = −mij. The minimum number of elements required to fully specify the matrix is_______.
(A) 0
(B) 6
(C) 12
(D) 16
Answer: (B)
10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.
(A) 15 : 17
(B) 16 : 17
(C) 17 : 15
(D) 17 : 16
Answer: (B)
AR: Architecture and Planning
Q1 – Q25 carry one mark each
1. In the architectural style of ancient North Indian Temples, the term ‘Adhisthana’ refers to
(A) Pinnacle
(B) Base Platform
(C) Vestibule
(D) Transept
Answer: (B)
2. Who among the following architects has NOT won the Pritzker Architecture Prize till 2019>
(A) Arata Isozaki
(B) I. M. Pei
(C) B. V. Doshi
(D) Moshe Safdie
Answer: (A OR D)
3. The stone used in the construction of Kailasa temple at Ellora is
(A) Limestone
(B) Marble
(C) Sandstone
(D) Basalt
Answer: (D)
4. Four vertical lines having same thickness appear to be of the same height in perspective as shown in the figure. Which line actually has the maximum height?
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (B)
5. As per URDPFI Guidelines 2015, Government of India, choose the correct hierarchy of plans higher to lower order.
(A) Perspective plan, Development plan, Regional plan, Zonal plan
(B) Perspective plan, Regional plan, Development plan, Zonal plan
(C) Regional plan, Perspective plan, Development plan, Zonal plan
(D) Zonal plan, Development plan, Regional plan, Perspective plan
Answer: (B)
6. Which of the following shapes can be used as an interlocking paver block without adding any other shape?
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (C)
7. In India, the Constitution (Seventy Fourth Amendment) Act, 1992, delegates powers to institutions forming the third tier of government, which are
(A) Municipal Corporation, Municipality and Nagar Panchayat
(B) Development Authority, Municipal Corporation and Municipality
(C) Improvement Trust, Nagar Panchayat and Panchayat
(D) Development Authority, Improvement Trust and Panchayat
Answer: (A)
8. As on 2018, ‘Right to Property’ in India is a
(A) Fundamental Right
(B) Secondary Right
(C) Constitutional Right
(D) Tertiary Right
Answer: (C)
9. ‘Tendon’ is primarily used
(A) as a compression member
(B) to pre-stress concrete
(C) as roof sheathing
(D) to prepare a tender document
Answer: (B)
10. Emergency preparedness for risk reduction does NOT include
(A) rescue
(B) relief distribution
(C) rehabilitation
(D) revision of code
Answer: (D)
11. If Beam : Column :: Transom : X,
which of the following options can replace ‘X’ ?
(A) Balustrade
(B) Sill
(C) Mullion
(D) Ceiling
Answer: (C)
12. The correct chronological order of the given architectural movements is
13. The decay of sound in a large room is indicated in the following figure. The spike within the dashed zone denotes
(A) Flutter echo
(B) Perfect sound diffusion
(C) Echo
(D) Early reflection
Answer: (C)
14. For the same thickness of material layers, relative position of insulation in the wall sections 1 and 2 shown below will have an impact on
(A) Thermal Time Constant
(B) Thermal Conductivity
(C) Thermal Resistivity
(D) Thermal Transmittance
Answer: (A)
15. The solar altitude angle on April 16 at 7 : 00 AM in Kochi is 16°. The same solar altitude angle will occur at the same time in the same year at the same location on
(A) July 21
(B) August 27
(C) September 23
(D) October 21
Answer: (B)
16. In a perspective drawing, the picture Plane is in between the Object and the Observer. If the Observer comes closer straight towards the Picture Plane, without changing the distance between Object and Picture Plane, the perspective image will be
(A) Bigger than the previous image
(B) Smaller than the previous image
(C) Will remain the same as previous image
(D) Will become the mirror image of the previous
Answer: (B)
17. Shyam-Rai temple of Bishnupur in West Bengal, is an example of
(A) Nava-ratna terracotta temple
(B) Stone carved Nagara type temple
(C) Pancha-ratna type terracotta temple
(D) Stone carved Dravidian type temple
Answer: (C)
18. Which one of the following is NOT a land use zone?
(A) Industrial Zone
(B) Agriculture Zone
(C) Heritage Zone
(D) Commercial Zone
Answer: (C)
19. ‘Formulation of GIS based master plan’ is a sub-scheme of
(A) Atal Mission for Rejuvenation and Urban Transformation
(B) Smart Cities Mission
(C) Jawaharlal Nehru National Urban Renewal Mission
(D) Shyama Prasad Mukherji Rurban Mission
Answer: (A)
20. One hectare is equal to
(A) 4000 m2
(B) 4048 m2
(C) 4840 m2
(D) 10000 m2
Answer: (D)
21. One of the sites added to the list of UNESCO World Heritage Sites in 2019 is
(A) Walled City, Ahmedabad
(B) Walled City, Jaipur
(C) Chandigarh
(D) Fatehpur Sikri
Answer: (B)
22. In the given contour map, the angle at ‘A’ (in degrees, rounded off to two decimal places) is ________
Answer: (18.2 to 18.5)
23. A 1.2 m high window is located on a south facing wall. The solar azimuth angle is equal to the wall azimuth angle and the solar altitude angle is 60°. The minimum depth (in metres, rounded off to two decimal places) of overhand required to completely shade the window is_______
(Assume that the overhang is located at the lintel level of the window)
Answer: (0.68 to 0.70)
24. In the given figure, the area of the shaded portion is_________
Answer: (8 to 8)
25. Average density of a highway is 25 vehicles per km. Average volume of the vehicles on the highway is 520 vehicles per hour. The mean speed (in km/hour, rounded off to one decimal place) is _________
Answer: (20.8 to 20.8)
Q26 – Q55 Carry two marks each.
26. Match the terminologies of Munsell colour wheel in Group I with their corresponding descriptions in Group II
(A) P-2, Q-4, R-5, S-1
(B) P-4, Q-2, R-5, S-3
(C) P-4, Q-2, R-3, S-1
(D) P-2, Q-4, R-1, S-3
Answer: (B)
27. Match the plant forms in Group I with the botanical names in Group II, as per ‘A Handbook of Landscape’, CPWD 2013, Government of India
(A) P-1, Q-5, R-2, S-3
(B) P-3, Q-4, R-2, S-1
(C) P-3, Q-5, R-4, S-1
(D) P-1, Q-3, R-4, S-5
Answer: (C)
28. Match the images of gardens in Group I with their names in Group II
(A) P-5, Q-3, R-1, S-4
(B) P-3, Q-4, R-1, S-2
(C) P-1, Q-4, R-3, S-2
(D) P-3, Q-2, R-4, S-5
Answer: (B)
29. Match the Architects in Group I with their projects in Group II
(A) P-3, Q-4, R-1, S-2
(B) P-2, Q-5, R-4, S-1
(C) P-4, Q-3, R-1, S-2
(D) P-3, Q-4, R-5, S-2
Answer: (A)
30. Match the graphical representations in Group I with corresponding elements in Group II
(A) P-1, Q-2, R-3, S-5
(B) P-4, Q-1, R-3, S-2
(C) P-2, Q-3, R-4, S-5
(D) P-2, Q-1, R-4, S-5
Answer: (D)
31. Based on the psychrometric chart given below, match the vector in Group I with the respective process in Group II
(A) P-4, Q-1, R-5, S-2
(B) P-4, Q-3, R-1, S-5
(C) P-5, Q-3, R-4, S-1
(D) P-3, Q-1, R-5, S-2
Answer: (A)
32. Match the software tools in Group I with their primary applications in Group II
(A) P-2, Q-5, R-4, S-3
(B) P-4, Q-1, R-2, S-3
(C) P-4, Q-5, R-1, S-3
(D) P-2, Q-4, R-5, S-1
Answer: (A)
33. Match the structural form in Group I with their corresponding illustration in Group II
(A) P-2, Q-4, R-5, S-1
(B) P-2, Q-4, R-1, S-5
(C) P-5, Q-4, R-2, S-1
(D) P-4, Q-1, R-5, S-2
Answer: (A)
34. Match the books in Group I with the corresponding authors in Group II
(A) P-3, Q-2, R-1, S-4
(B) P-4, Q-1, R-5, S-3
(C) P-3, Q-1, R-5, S-4
(D) P-4, Q-2, R-1, S-3
Answer: (B)
35. Match the name of tactile paving in Group I with their patterns in Group II
(A) P-4, Q-2, R-3, S-1
(B) P-3, Q-5, R-4, S-1
(C) P-3, Q-2, R-4, S-1
(D) P-2, Q-5, R-1, S-4
Answer: (C)
36. Match the name of architects in Group I with the buildings designed by them in Group II
(A) P-3, Q-1, R-4, S-2
(B) P-2, Q-5, R-1, S-3
(C) P-2, Q-1, R-4, S-5
(D) P-4, Q-5, R-1, S-3
Answer: (B)
37. Match the terms in Group I with the parameters in Group II
(A) P-2, Q-5, R-4, S-1
(B) P-3, Q-2, R-1, S-4
(C) P-2, Q-3, R-4, S-5
(D) P-3, Q-4, R-5, S-1
Answer: (A)
38. Match the structural system in Group I with their potential causes of failure in Group II
(A) P-3, Q-4, R-1, S-2
(B) P-1, Q-3, R-5, S-2
(C) P-2, Q-4, R-1, S-3
(D) P-3, Q-5, R-4, S-1
Answer: (A)
39. Match the brick masonry bond type in Group I with the corresponding illustration in Group II
(A) P-2, Q-1, R-4, S-5
(B) P-4, Q-1, R-2, S-3
(C) P-2, Q-5, R-1, S-3
(D) P-4, Q-1, R-2, S-5
Answer: (D)
40. Mach the characteristics in Group I with the type of settlements in Group Ii as given in URDPFI Guidelines 2015, Government of India
(A) P-4, Q-3, R-1, S-5
(B) P-3, Q-5, R-1, S-4
(C) P-3, Q-5, R-2, S-4
(D) P-3, Q-4, R-1, S-2
Answer: (D)
41. A population of 2500 persons requires a minimum area of 3000 m2 for primary schools. For the population in four different sectors given in the table below, the Sector having maximum shortage of school area per person is_______
Answer: (3 to 3)
42. Number of married couples in a household along with number of rooms (for a household) are given in the table. Assuming each married couple needs one separate room, the total number of additional rooms required for them is ________
Answer: (5214 to 5214)
43. In a residential complex , the central play area is to be converted as a detention pond for storm water management. For a 24 hour rainfall event of 100 mm, 100% storm water of central play area and 70% storm water run-off from rest of the complex is to be held at detention pond. Area distribution in the residential complex is given in the table.
Answer: (760 to 760)
44. In the plot shown below, ‘S1’ and ‘S2’ are two non-directional point sources, having a sound intensity level of 95 dB and 60 dB, respectively, at a distance of 1 m from each point source. Considering free field conditions, the effective sound intensity level at the receiver location ‘R’ (in dB, rounded off to two decimal places) is _________
Answer: (75.00 to 79.00)
45. A room measures 5m × 10m × 3m (L×B×H). Consider the following conditions,
Total solar radiation incident on the root surface = 800 W/m2
Outdoor air temperature = 40°C
Outside film coefficient of the root surface = 18 W/m2
The outdoor mean radiant temperature is equal to outdoor air temperature
The minimum reduction required in solar absorptance of the roof (rounded off to two decimal places) to achieve a 20° reduction in sol-air temperature is _______
Answer: (0.43 to 0.47)
46. The activity duration, early start, early finish, late start and late finish of the three activities ‘P’, ‘Q’ and ‘R’ are shown in the following figure. The independent float of activity ‘Q’ is ________
Answer: (1 to 1)
47. A square based regular pyramid has all sides equal to 10 units. Its height (in the same units, rounded off to two decimal places) is ________
Answer: (7.00 to 7.10)
48. A parking area measuring 52m ×67 m is approached through a driveway as shown in the given illustration. The parking is designed at an angle of 30° with the parking by of 2.5m × 5m.
The number of cars that can be parked in the designated parking area considering no car overshoots the length of the parking area is _______
Answer: (9 to 10)
49. Plan and section of an isolated foundation is given below. The volume of concrete up to Ground Level (GL) (in m3, rounded off to two decimal places) is ______
Answer: (3.10 to 3.40)
50. Top floor of a 25 story building is using a flush valve system with a minimum fixture pressure of 1.0 kg/cm2. If static pressure increases by 0.3 kg/cm2 per metre length and friction loss is zero, then height of bottom of the water tank from the top fixture (in metres, rounded off to two decimal places) is ________
Answer: (3.30 to 3.40)
51. In a single phase alternate current circuit, an electric lamp is rated 100 watts. If 220 volts is impressed on it and the power factor is 0.85, the energy (in watt hour, rounded off to one decimal place) delivered in an hour is ______
Answer: (100 to 100)
52. A simply supported RCC beam of cross section 0.4 m ×6 m covers a span of 8 m. It is subjected to a uniformly distributed load of 30 kN/m. If the unit weight of concrete is 24 kN/m3, the tensile stress (in N/mm2, rounded off to two decimal places) at the bottom of the beam at mid-span is_______
Answer: (11.80 to 12.00)
53. A basement wall resists lateral pressure exerted by soil and water. The soil pressure amounts to 4.5 kN/m2 for every metre of depth below Ground Level (GL). The subsoil water level is 1.0 m below GL and hydrostatic pressure of water is 9.8 kN/m2 for every metre of depth below GL. The total lateral pressure (in kN/m2, rounded off to one decimal place) exerted on the wall 2 m below GL is _______
Answer: (14.3 to 18.8)
54. Assuming that the population growth trend given in the table will continue, the population (in persons) for the year 2031 will be_________
Answer: (484315 to 484316)
55. A developer would like to select a residential plot of 3000 m2 for group housing in a city. Different options with varying development controls are given. In every group housing plot, 15% of the Floor Area Ratio (FAR) over and above the maximum permissible FAR has to be utilized for Economically Weaker Section (EWS) units. The maximum built-up area (in m2) available from the options given below is_________
1. The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die ______ diseases like cardio vascular disease, cancer, etc.
(A) in, of
(B) from, of
(C) during, from
(D) from, from
Answer: (A)
2. He was not only accused of theft ______ of conspiracy.
(A) rather
(B) but also
(C) but even
(D) rather than
Answer: (B)
3. Select the word that fits the analogy:
Explicit : Implicit : : Express: _______
(A) Impress
(B) Repress
(C) Compress
(D) Suppress
Answer: (B)
4. The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements is English lasting 15 seconds, as opposed to informal 5 second messages in French.
The French-speaking couple were upset at ______.
(A) the in-flight announcements being made in English.
(B) the English announcements being clearer than the French ones.
(C) the English announcements being longer than the French ones.
(D) equal importance being given to English and French.
Answer: (C)
5. A superadditive function f (∙) satisfies the following property
f(x1 + x2) ≥ f(x1) + f(x2)
Which of the following functions is a superadditive function for x > 1?
(A) ex
(B) √x
(C) 1/x
(D) e−x
Answer: (A)
Q6 – Q10 carry two marks each.
6. The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.
Which one of the following sequences shows the correct precedence as per the given passage?
(A) East Asian crisis → subprime lending crisis → banking crisis global financial crisis.
(B) Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.
(C) Banking crisis → subprime lending crisis → global financial crisis → East Asian crisis.
(D) Global financial crisis → East Asian crisis → Banking crisis → subprime lending crisis.
Answer: (A)
7. It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.
(A) 0°
(B) 7.5°
(C) 15°
(D) 22.5°
Answer: (B)
8. A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is ______.
(A) πa2 – a2
(B) πa2 – √2a2
(C) πa2 – 2a2
(D) πa2 – 3a2
Answer: (C)
9. a, b, c are real numbers. The quadratic equation ax2 – bx + c = 0 has equal roots, which is β, then
(A) β = b/a
(B) β2 = ac
(C) β3 = bc/(2a2)
(D) b2 ≠ 4ac
Answer: (C)
10. The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is ______ .
(A) 8 : 23
(B) 23 : 8
(C) 23 : 31
(D) 31 : 23
Answer: (B)
AG: Agricultural Engineering
Q1 – Q25 carry one mark each.
1. The function f(x) = x4 – 4x3 + 6x2 – 4x + 1 has a
(A) Maxima at x = 0
(B) Minima at x = 0
(C) Maxima at x = 1
(D) Minima at x = 1
Answer: (D)
2. A linear system of equations has n unknowns. The ranks of the coefficient matrix and the augmented matrix of the linear system of equations are r1 and r2, respectively. The condition for the equations to be consist with a unique solution is
(A) r1 ≠ r2 < n
(B) r1 = r2 = n
(C) r1 = r2 < n
(D) r1 ≠ r2 > n
Answer: (B)
3. General solution to the ordinary differential equation, is
(A) C1e−x + C2e−2x + C3e−3x
(B) C1e−x + C2e−2x + C3e3x
(C) C1e−x + C2e2x + C3e3x
(D) C1ex + C2e2x + C3e3x
Answer: (D)
4. In a tractor steering system, the angle made by the kingpin axis projected on the longitudinal plane of the tractor with the vertical axis is known as
(A) Kingpin inclination
(B) Caster angle
(C) Camber angle
(D) Steering angle
Answer: (B)
5. A tractor operated 9-row precision planter has 16 cells on the metering plates. The speed ratio of the metering plates to the ground rive wheel is 1:2 and the rolling diameter of the ground drive wheel is 40 cm. Assuming no skid, the plant to plant spacing in rows in mm is
(A) 39
(B) 50
(C) 157
(D) 314
Answer: (C)
6. A self-propelled wheel does not have
(A) Wheel torque
(B) Tractive power
(C) Rolling resistance
(D) Drawbar pull
Answer: (D)
7. Match the following items between Column I and Column II with the most appropriate combinations:
(A) P-3, Q-2, R-1, S-4
(B) P-2, Q-3, R-1, S-4
(C) P-2, Q-3, R-4, S-1
(D) P-3, Q-2, R-4, S-1
Answer: (C)
8. From the performance evaluation of drippers, the discharge exponent value and the coefficient of variation were obtained as 0.5 and 0.04, respectively. The drippers are categorized as
(A) Pressure compensating drippers of excellent quality
(B) Turbulent flow-tortuous path orifice type drippers of good quality
(C) Turbulent flow-tortuous path orifice type drippers of marginal quality
(D) Laminar flow drippers of excellent quality
Answer: (B)
9. In a basin, rainfall is recorded by five automatic weather stations A, B, C, D and E with respective average annual rainfall of 1020, 810, 675, 940 and 780 mm. In a particular year, the station A was non-operational and the remaining stations B, C, D and E recorded annual rainfall of 890, 725, 980 and 850 mm, respectively. The estimated rainfall at the station A in that particular year in mm is
(A) 758
(B) 878
(C) 1038
(D) 1098
Answer: (D)
10. A field crop is irrigated when the available soil water reduces to 60%. The moisture content at field capacity and wilting point are 32% and 12%, respectively. The bulk density of the soil is 1.5 g cm−3. The field water application efficiency is 75% and the crop root zone depth is 50 cm. The gross depth of irrigation required to bring soil moisture content to field capacity in cm is
(A) 6
(B) 8
(C) 9
(D) 12
Answer: (B)
11. A cold storage takes 5 hours to bring down the temperature of 100 metric tons of potato from 35°C to 8° The specific heat capacity of potato is 3.1 kJ kg−1 °C−1. The coefficient of performance (COP) and the latent heat of vapourisation of the refrigerant (R-22) at an evaporation temperature of −10°C are 3.66 and 230 kJ kg−1, respectively. Neglecting respiration heat load of potato, and assuming no power loss, the values of refrigerant flow rate and the power input to the compressor are
(A) 121.3 kg min−1 and 127.1 kW
(B) 124.7 kg min−1 and 121.3 kW
(C) 127.1 kg min−1 and 121.3 kW
(D) 124.7 kg min−1 and 127.1 kW
Answer: (A)
12. Hydrothermal treatment of paddy makes
(A) Shelling more difficult
(B) Polishing of parboiled rice easier
(C) Higher retention of vitamins and minerals
(D) Kernel soft, resulting in faster cooking
Answer: (C)
13. Both particle formation and drying process are carried out by
(A) Flash dryer
(B) Fluidized bed dryer
(C) Pneumatic conveyor dryer
(D) Spray dryer
Answer: (D)
14. If one of the two Eigenvalues of a matrix is 4.236, then the other Eigenvalu (round off to 3 decimal places) is ________.
Answer: (-0.237 to -0.235)
15.
Answer: (2 to 2)
16. At the maximum power output of a solar panel, the voltage and current are 18 V and 5.56 V, respectively. If the open circuit voltage and short circuit current of the same solar panel are 21.6 V and 6.11 A, respectively, the fill factor of the panel (round off to 2 decimal places) is ________.
Answer: (0.75 to 0.77)
17. The sound pressure level on the operator’s seat of a tractor is 80 dB. If the reference sound pressure is 2 × 10−5 N m−2, the root mean square (RMS) sound pressure in N m−2 (round off to 2 decimal places) is_______.
Answer: (0.19 to 0.21)
18. A towed pneumatic wheel with an unloaded radius of 330 mm covers a distance of 9.9 m in 5 revolutions without any skid. Assuming the rolling radius to be same as the static loaded radius of the wheel, the deflection of the wheel in mm (round off to 1 decimal place) is ________.
Answer: (14.7 to 15.1)
19. The grain to straw ratio of 500 kg feed material is 3.2. The blown grain loss, separation loss and cleaning efficiency of thresher are 0.05%, 0.5% and 99.1%, respectively. Considering 100% threshing efficiency, grain recovery at the main grain outlet in kg (round off to 2 decimal places) is _________.
Answer: (298.30 to 298.40)
20. A tubewell has a discharge of 40 m3 h−1 and operates daily for 20 h during irrigation season. The irrigation interval is 20 days and depth of irrigation is 8 cm. The command area of tubewell in ha is______.
Answer: (20 to 20)
21. The drainage coefficient of a watershed of 720 ha area is 1.2 cm. The design discharge of the drain in m3s−1 is _______.
Answer: (1 to 1)
22. The following data were used for a watershed experiencing soil erosion problem: Rainfall Erosivity Index = 280 MJ mm ha−1 h−1 year−1, Soil Erodibility Index = 0.38 ton ha h MJ−1 mm−1, Slope length = 200 m, Average slope of the land = 8%, Slope steepness factor = 0.85, Cropping management factor = 0.35, and Conservation practice factor = 0.60
If the slope length is reduced to half, percentage reduction in soil loss (round off to 2 decimal places) is _______.
Answer: (29.10 to 29.50)
23. Fresh tomato juice containing 6% (w/w) total solids enters in a single effect evaporator at a feed rate of 500 kg h−1 to concentrate up to 36% (w/w) solids. In this process, the rate of water removal in kg h−1 (round off to 1 decimal place) is ________.
Answer: (416.0 to 418.0)
24. Heat gain is occurring through a composite cold storage wall, made of brick and polyurethane foam insulation (thickness and thermal conductivity values are given below). If the exposed surfaces of brick and insulation are at 45°C and 10°C, respectively, the temperature at the interface of brick and insulation in °C (round off to 1 decimal place) is ________.
Answer: (41.4 to 41.6)
25. A milk processing plant pasteurize a batch of 12500 L whole milk to inactivate the pathogen Coxiella burnetii, (decimal reduction time of 14 seconds at 72°C) prior to packing in 500 milliliter pouches. The initial count of the noted organism is 10 per millimeter. For this batch pasteurization process at 72°C, resulting in no survivor in any of the packages, the process F-value in seconds is ______.
Answer: (126 to 126)
Q26 – Q55 carry two marks each.
26. A particle moves along the curve where t is the time. The velocity component of the particle in the direction at time t = 2 is
(A) 122/√14
(B) 122
(C) 168/√14
(D) 168
Answer: (c)
27. Let a function f(t) = 4 cos 2t + 6 e−8t. The Laplace transform of the given function f(t), is
(A)
(B)
(C)
(D)
Answer: (*)
28. In an irrigation channel of uniform section, water passes through a 90° triangular weir measuring 36 m head over the crest. After traveling certain distance in the same channel, water passes through 1.0 m long rectangular weir. There is no loss of water in between two weirs. Using Francis’ formula, the head over the crest of rectangular weir in cm is
(A) 22.1
(B) 18.4
(C) 15.0
(D) 11.8
Answer: (C)
29. Two ends of a differential mercury manometer are connected at two points on a pipe carrying oil. The manometer shows difference in mercury level of 20 cm. The specific gravity of oil of mercury are 0.8 and 13.6, respectively. The density of water is 1000 kg m−3 at 4 °C and acceleration due to gravity (g) is 9.814 m s−2. At the same two points in pipe, the difference of pressure in Nm−2 is
(A) 25.11
(B) 251.14
(C) 25113.60
(D) 251136.00
Answer: (C)
30. Math the following items between Column I and Column II with the most appropriate combinations:
(A) P-4, Q-5, R-6, S-3, T-1, U-2
(B) P-5, Q-4, R-6, S-3, T-2, U-1
(C) P-4, Q-5, R-3, S-6, T-2, U-1
(D) P-4, Q-5, R-6, S-3, T-2, U-1
Answer: (D)
31. A retaining wall of 5 m height retains cohesionless dry soil having density 1.9 Mg m−3 and angle of internal friction of 28°. The surface of the backfill soil is horizontal. The active and passive earth pressures per meter length of the wall in kN are ________ and _________, respectively. [Take g = 9.81 ms−2]
(A) 84.11, 645.38
(B) 645.38, 84.11
(C) 142.12, 381.63
(D) 381.63, 142.12
Answer: (A)
32. A 40 cm diameter tubewell is constructed in a 10 m thick confined aquifer having hydraulic conductivity of 25 m day−1. The peizometric surface is observed to be 40 m high from the impervious stratum at the radius of influence of 500 m. The drawdown in the tubewell is 30 m. If the thickness of aquifer is doubled and diameter of tubewell is reduced to half, keeping all other parameters and conditions same, the change in discharge from the well is [Take π = 3.14]
(A) Increased by 83.72%
(B) Decreased by 83.72%
(C) Increased by 82.28%
(D) Decreased by 82.28%
Answer: (A)
33. Choose the correct combination of process (Column I) performed by corresponding machine component(s) (Column II)
(A) P-4, Q-1, R-3, S-2
(B) P-4, Q-3, R-1, S-2
(C) P-1, Q-4, R-3, S-2
(D) P-2, Q-1, R-4, S-3
Answer: (B)
34. Saturated steam at 121°C is used to sterilize pineapple juice by direct steam injection. The initial temperature of the juice is 80°C and after sterilization, the blend of diluted juice exits the sterilizer at 95° The enthalpy values of steam and condensate water are given in Table below. Specific heat capacity of the juice is 3.9 kJ kg−1 °C−1. Assuming no energy loss to the surroundings in the process of sterilization, the ratio of juice sterilized to steam utilized is
(A) 34.79
(B) 37.94
(C) 39.47
(D) 43.97
Answer: (C)
35. Hot refined oil at 120°C enters a concentric tube-in-tube heat exchanger (HE) at the rate of 20 kg min−1. The oil is cooled by water entering at a temperature of 30°C from the other end of the HE at the rate of 50 kg min−1. Specific heat capacities of oil and water are 1.9 and 4.2 kJ kg−1 °C−1, respectively. The effectiveness of the HE may be taken as 0.7. Assuming no heat loss to the surrounding under steady-state condition, the exit temperature of water for the HE in °C is
(A) 39.9
(B) 41.4
(C) 57.7
(D) 63.0
Answer: (B)
36. Taking six intervals, each of π/12 and using Simpson’s one-third rule, the value of the definite integral (round off to 3 decimal places) is ________.
Answer: (1.186 to 1.189)
37. Two playing cards are drawn at random, but in succession from a pack of red cards (26 in number) without replacement. The probability of drawing a king first, followed by drawing a queen is P × 10−3. The value of P (round off to 3 decimal places) is________.
Answer: (6.100 to 6.200)
38. A hydraulic sprayer when operating at a speed of 10 km h−1 and working pressure of 420 kPa covers a width of 4.5 m. The power requirement and efficiency of the pump are 0.75 kW and 70%, respectively. Out of total pump discharge, 10% is bypassed for agitation purpose. The working pressure is increased to 500 kPa. Assuming no change in the width of coverage, the application rate of the sprayer in L ha−1 (round of to 1 decimal place) is _______.
Answer: (981.5 to 982.5)
39. A tractor PTO operated rotary disc mower has 4 rotating discs and the width of cut of each disc is 60 cm without any overlap. The specific power losses to air stubble and gear-train friction is 2.5 kW per meter of cutting width. The specific cutting energy requirement is 2.0 kJ m−2. If the machine is operated at a forward speed of 6 km h−1, the PTO power requirement in kW (round off to 2 decimal places) is _________.
Answer: (13.90 to 14.10)
40. A water pumping system is driven by a horizontal axis multi-bladed wind turbine at a power coefficient (Cp) of 0.4. The total pumping head and discharge are 20 m and 15 L s−1, respectively. The mean wind velocity is 8 ms−1 and the pump efficiency is 70%. The density of air and water are 1.2 and 1000 kg m−3, respectively. If the transmission efficiency from wind turbine to the pump is 90%, the required diameter of the wind turbine in m (round of to 2 decimal places) is __________.
Answer: (6.92 to 6.98)
41. A two-wheel drive tractor with a total weight of 25 kN has a wheelbase of 2.2 m and its centre of gravity lies 0.7 m ahead of the centre of rear axle. A steady horizontal pull is applied at a drawbar hitch height of 0.5 m on a concrete surface such that the weight on front axle becomes 20% of static weight of the tractor. The coefficient of net traction (round off to 2 decimal places) is _______.
Answer: (0.64 to 0.66)
42. The cooling system of a tractor fitted with diesel engine rejects 0.58 kW of heat per kW of brake power. It requires 0.16 L s−1 of water per kW of heat rejection from the engine to maintain a temperature drop of 6°C of water as it moves from the top of radiator to its bottom. If the engine develops 45 kW brake power, the required water flow rate in the radiator in Ls−1 (round off to 2 decimal place) is ________.
Answer: (4.16 to 4.18)
43. A V-belt drive transmits 10 kW power at a belt velocity of 8 ms−1. The angle of contact on the smaller pulley is 170° and groove angle of the pulley is 38°. The coefficient of friction between the pulley and the belt is 0.28 and the maximum permissible stress of the belt is limited to 4 MPa. Neglecting centrifugal effect of the belt, the minimum cross-sectional area of the V-belt in mm2 (round of to 1 decimal place) is ________.
Answer: (337.0 to 340.0)
44. A chaff cutter is operated by an electric motor running at 1140 rpm. The speed reduction from motor to the main shaft of the cutting units is 4:1. The feed rollers of 10 cm diameter each are driven by the main shaft through a suitable gear drive with a speed reduction o 15 : 1. If the chaff cutter has to knives, the theoretical length of cut chaff in mm (round of to 2 decimal places) is _________.
Answer: (10.40 to 10.60)
45. A tractor drawn right-hand offset disk harrow experiences longitudinal and side soil reactions in the front gang as 3.0 kN and 2.5 kN, respectively as compared to 3.5 kN and 4.0 kN in the rear gang. The longitudinal distance of centers of front and rear gangs are located at 2.5 m and 4.0 m, respectively behind the tractor hitch point. The required amount of offset of the disk harrow in m (round off to 2 decimal places) is ________.
Answer: (1.45 to 1.55)
46. A diesel engine when operates with biodiesel blend B20 (20% biodiesel and 80% diesel by volume) develops a brake power of 10 kW with a brake specific fuel consumption of 0.26 kg kW−1 h−1. If the density of biodiesel is 880 kg m−3 and that of diesel is 850 kg m−3, the amount of biodiesel required to run the engine for 3 hours in L (round off to 2 decimal places) is ________.
Answer: (1.80 to 1.84)
47. Area enclosed by different contours of a pond is given in the following Table. Using trapezoidal formula, the total estimated capacity of pond in m3 is _________.
Answer: (4860 to 4860)
48. At a speed of 1800 rpm, a centrifugal pump discharges 50 Ls−1 at its best point of efficiency for a total head of 25 m. The specific speed of the pump in rpm (round off to 2 decimal places) is ________.
Answer: (35.90 to 36.10)
49. The Curve Number (CN) of a watershed of 40 ha area under given hydrologic soil group, land use and management practices, and Antecedent Moisture Condition (AMC)-II is 80. The initial abstraction is 20% of maximum retention. For the rainfall event of 40 mm, the direct runoff in mm (round off to 2 decimal places) is ________.
Answer: (8.10 to 8.30)
50. The underside beam of a railway bridge, marked as permanent Bench Mark (BM) with Reduced Level (RL) of 85.168 m, is taken as reference for leveling operation. The Back Sight (BS) on the staff held vertically inverted to the BM is 3.645 m. For the Sight (FS) of 1.523 m at a point in the construction site, the RL or elevation in m is _______
Answer: (80 to 80)
51. Air-water vapour mixture at 30°C DBT and 40% RH is heated to 65°C DBT and 30°C WBT and is used as drying medium under the constant rate period drying of spinach leaves. Specific heat capacities of dry air and pure water vapour are 1.005 and 1.88 kJ kg−1 °C−1, respectively. Using the properties given in Table below, the value of absolute humidity in kg water vapour per kg dry air (round off to 3 decimal places) for the dryer exit air at DBT of 45°C is ________.
Answer: (0.017 to 0.020)
52. Tray type paddy separator is employed to separate paddy from a binary mixture of paddy and brown rice at a feed rate of 1200 kg h−1. Mass fractions of paddy in feed, separated paddy and brown rice steams are 0.2, 0.75 and 0.02, respectively. The amount of paddy in separated paddy steam in kg h−1 (round off to 2 decimal places) is ________.
Answer: (221.00 to 223.00)
53. A cylindrical silo with 3.0 diameter and height to diameter ratio of 5 : 1 is filled with 60 metric ton wheat grains having bulk density of 725 kg m−3. The coefficient of friction between grain and silo wall is 0.42 and the ratio of lateral pressure to vertical pressure is 0.5. The vertical pressure at the bottom of silo in kPa (round off to 2 decimal places) is _________. [use 1 kgf = 9.81 N]
Answer: (23.50 to 25.50)
54. A bucket elevator for lifting parboiled paddy (bulk density = 840 kg m−3) is operated at a linear speed of 2 ms−1. The width of the bucket is 25.4 cm and its cross section is making a subtending angle of 75° at the centre of a circle having 12.7 cm radius. the space between two adjacent buckets on the elevator belt is 40 cm. If the buckets are filled to 80% of their volumetric capacity, the lifting capacity of elevator in kg min−1 (round off to 2 decimal places) is _________.
Answer: (538.00 to 542.00)
55. A contact plate freezer extracts thermal energy from a 24 mm thick slab of boneless meat containing 85% (w/w) water. Initially the slab is at the freezing point of meat, that is 272.5 K and corresponding latent heat of freezing is 335 kJ kg−1 The plate temperature of the freezer is assumed steady at 247.5 K. Bulk density of the slab is 750 kg m−3. The thermal conductivity value for frozen meat is 1.5 W m−1 K−1. The minimum duration required for complete freezing of the slab in seconds is __________.
1. The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die ______ diseases like cardio vascular disease, cancer, etc.
(A) in, of
(B) from, of
(C) during, from
(D) from, from
Answer: (A)
2. He was not only accused of theft ______ of conspiracy.
(A) rather
(B) but also
(C) but even
(D) rather than
Answer: (B)
3. Select the word that fits the analogy:
Explicit : Implicit : : Express: _______
(A) Impress
(B) Repress
(C) Compress
(D) Suppress
Answer: (B)
4. The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements is English lasting 15 seconds, as opposed to informal 5 second messages in French.
The French-speaking couple were upset at ______.
(A) the in-flight announcements being made in English.
(B) the English announcements being clearer than the French ones.
(C) the English announcements being longer than the French ones.
(D) equal importance being given to English and French.
Answer: (C)
5. A superadditive function f (∙) satisfies the following property
f(x1 + x2) ≥ f(x1) + f(x2)
Which of the following functions is a superadditive function for x > 1?
(A) ex
(B) √x
(C) 1/x
(D) e−x
Answer: (A)
Q6 – Q10 carry two marks each.
6. The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.
Which one of the following sequences shows the correct precedence as per the given passage?
(A) East Asian crisis → subprime lending crisis → banking crisis global financial crisis.
(B) Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.
(C) Banking crisis → subprime lending crisis → global financial crisis → East Asian crisis.
(D) Global financial crisis → East Asian crisis → Banking crisis → subprime lending crisis.
Answer: (A)
7. It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.
(A) 0°
(B) 7.5°
(C) 15°
(D) 22.5°
Answer: (B)
8. A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is ______.
(A) πa2 – a2
(B) πa2 – √2a2
(C) πa2 – 2a2
(D) πa2 – 3a2
Answer: (C)
9. a, b, c are real numbers. The quadratic equation ax2 – bx + c = 0 has equal roots, which is β, then
(A) β = b/a
(B) β2 = ac
(C) β3 = bc/(2a2)
(D) b2 ≠ 4ac
Answer: (C)
10. The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is ______ .
(A) 8 : 23
(B) 23 : 8
(C) 23 : 31
(D) 31 : 23
Answer: (B)
AE : Aerospace Engineering
Q1 – Q25 Carry one mark each.
1. for f(x) = |x|, with df/dx denoting the derivative, the mean value theorem is not applicable because
(A) f(x) is not continuous at x = 0
(B) f(x) = 0 at x = 0
(C) df/dx is not defined at x = 0
(D) df/dx = 0 at x = 0
Answer: (C)
2. For the function and σ and μ are constants, the maximum occurs at
(A) x = σ
(B) x = σ√2π
(C) x = 2σ2
(D) x = μ
Answer: (D)
3. y = Aemx + Be−mx, where A, B and m are constants, is a solution of
(A)
(B)
(C)
(D)
Answer: (A)
4. Which of the following statements is true about the effect of increase in temperature on dynamic viscosity of water and air, at room temperature?
(A) It increases for both water and air.
(B) It increases for water and decreases for air.
(C) It decreases for water and increases for air.
(D) It decreases for both water and air.
Answer: (C)
5. Given access to the complete geometry, surface pressure and shear stress distribution over a body placed in a uniform flow, one can estimate
(A) the moment coefficient, and the force on the body.
(B) the force coefficient, and the force on the body.
(C) the moment coefficient, and the moment on the body.
(D) the force and the moment on the body.
Answer: (D)
6. A pair of infinitely long, counter-rotating line vortices of the same circulation strength Γ are situated a distance h apart in a fluid, as shown in the figure. The vortices will
(A) rotate counter-clockwise about the midpoint with the tangential velocity at the line vortex equal to
(B) rotate counter-clockwise about the midpoint with the tangential velocity at the line vortex equal to
(C) translate along +y direction with velocity at the line vortex equal to
(D) translate along +y direction with velocity at the line vortex equal to
Answer: (C)
7. The streamlines of a steady two dimensional flow through a channel of height 0.2 m are plotted in the figure, where Ψ is the stream function in m2/s. The volumetric flow rate per unit depth is
(A) 1.0 m2/s
(B) 2.0 m2/s
(C) 0.5 m2/s
(D) 0.1 m2/s
Answer: (B)
8. Which of the following options can result in an increase in the Mach number of a supersonic flow in a duct?
(A) Increasing the length of the duct
(B) Adding heat to the flow
(C) Removing heat from the flow
(D) Inserting a convergent-divergent section with the same cross-sectional area at its inlet and exit planes
Answer: (C)
9. Which one of the following conditions needs to be satisfied for ϕ = Ax4 + By4 + Cxy3 to be considered as an Airy’s stress function?
(A) A – B = 0
(B) A + B = 0
(C) A – C = 0
(D) A + C = 0
Answer: (B)
10. Consider the plane strain filed given by εxx = Ay2 + x, εyy = Ax2 + y, γxy = B x y + y . The relation between A and B needed for this strain field to satisfy the compatibility condition is
(A) B = A
(B) B = 2A
(C) B = 3A
(D) B = 4A
Answer: (D)
11. For hyperbolic trajectory of a satellite of mass m having velocity V at a distance r from the center of earth (G: gravitational constant, M: mass of earth), which one of the following relations is true?
(A)
(B)
(C)
(D)
Answer: (A)
12. For conventional airplanes, which one of the following is true regarding roll control derivative and yaw control derivative where δr is rudder deflection?
(A)
(B)
(C)
(D)
Answer: (A)
13. The ratio of exit stagnation pressure to inlet stagnation pressure across the rotating impeller of a centrifugal compressor, operating with a closed exit, is
(A) 0
(B) 1
(C) > 1
(D) 0.5
Answer: (C)
14. Which one of the following is a hypergolic propellant combination used in rocket engines?
15. In aircraft engine thermodynamic cycle analysis, perfectly expanded flow in the nozzle means that the static pressure in the flow at the nozzle exit is equal to
(A) the stagnation pressure at the engine inlet.
(B) the stagnation pressure at the nozzle exit.
(C) the ambient pressure at the nozzle exit.
(D) the static pressure at the nozzle inlet.
Answer: (C)
16. Three long and slender aluminum bars of identical length are subjected to an axial tensile force. These bars have circular, triangular and rectangular cross sections. with same cross sectional area. If they yield at Fcircle, Ftriangle and Frectangle, respectively, which one of the following is true?
(A) Fcircle > Ftriangle > Frectangle
(B) Fcircle < Ftriangle < Frectangle
(C) Ftriangle > Fcircle > Frectangle
(D) Fcircle = Ftriangle = Frectangle
Answer: (D)
17. The positive high angle-of-attack condition is obtained in a steady pull-out maneuver at the largest permissible angle-of-attack of the wing. Under this condition, at which of the following regions of the wing does the maximum tension occur?
(A) I
(B) II
(C) III
(D) IV
Answer: (C)
18. The natural frequency of the first mode of rectangular cross section contilever aluminum beam is ω rad/s. If the material and cross-section remain the same, but the length of the beam is doubled, the first mode frequency will become
(A)
(B) 4ω rad/s
(C)
(D) 16ω rad/s
Answer: (A)
19. Given the sum of squares of eigenvalues of A is
(A) tan2θ
(B) 1
(C) sin2θ
(D) cos2θ
Answer: (B)
20. Burnout velocity of a space vehicle in a circular orbit at an angle 5 degrees above the local horizon around earth is 13.5 km/s. Tangential velocity of the space vehicle in the orbit is ________ km/s (round off to two decimal places).
Answer: (13.42 to 13.47)
21. Velocity of an airplane in the body fixed axes is given as [100 – 10 20]m/s. The sideslip angle is ______ degrees (round off to two decimal places).
Answer: (-5.62 to -5.57)
22. The similarity solution for the diffusion equation, is u(x, t) = u(η), where similarity variable, _______ (round off to one decimal places).
Answer: (1.9 to 2.1)
23. Air enters the rotor of an axial compressor stage with no pre-whirl (Cθ = 0) and exits the rotor with whirl velocity, Cθ = 150 m/s. The velocity of rotor vanes, U is 200 m/s. Assuming Cp = 1005 J/(kg K), the stagnation temperature rise across the rotor is _______ K (round off to one decimal places).
Answer: (29.8 to 30.0)
24. A thin walled beam of constant thickness shown in the figure is subjected to a torque of 3.2 kNm. If the shear modulus is 25 GPa, the angle of twist per unit length is _____rad/m ((round off to three decimal places).
Answer: (0.009 to 0.011)
25. An airplane of mass 5000 kg is flying at a constant speed of 360 km/h at the bottom of a vertical circle with a radius of 400 m, as shown in the figure. Assuming that the acceleration due to gravity is 9.7 m/s2, the load factor experienced at the center of gravity of the airplane is _______(round off to two decimal places).
Answer: (3.50 to 3.60)
Q26 – Q55 carry two marks each.
26. The equation where c is a constant, represents a family of
(A) exponential curves
(B) parabolas
(C) circles
(D) hyperbolas
Answer: (C)
27. A wedge shaped airfoil is placed in a supersonic flow as shown in the figure (not to scale). The corners of the wedge are at x = XA, x = XB, x = XC, respectively.
Which one of the following represents the correct static pressure profiles along y = YI and y = YII ?
Answer: (D)
28. The value of Poisson’s ratio at which the shear modulus of an isotropic material is equal to the bulk modulus is
(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/8
Answer: (D)
29. A load P is applied to the free end of a stepped cantilever beam as shown in the figure. The Young’s modulus of the material is E, and the moments of inertia of the two sections of length 2 m and 2 m are I and 3I, respectively. Ignoring transverse shear and stress concentration effects, the deflection at the point where the load is applied at the free end of the cantilever is
(A) 23/243EI
(B) I/3EI
(C) 43/3EI
(D) 23/3EI
Answer: (C)
30. The three dimensional strain-stress relation for an isotropic material, written in a general matrix form, is
A, B and C are compliances which depend on the elastic properties of the material. Which one of the following is correct?
(A)
(B)
(C)
(D)
Answer: (D)
31. For three different airplanes A, B and C, the yawing moment coefficient (Cn) was measured in a wind-tunnel for three settings of sideslip angle β and tabulated as
Which one of the following statements is true regarding directional static stability of the airplanes A, B and C?
(A) All three airplanes A, B and C are stable.
(B) Only airplane C is stable, while both A and B are unstable.
(C) Airplane C is unstable, A and B are stable with A being more stable than B.
(D) Airplane C is unstable, A and B are both stable with A less stable than B.
Answer: (C)
32. A closed curve is expressed in parametric form as x = a cos θ and y = b sin θ, where a = 7 m and b = 5 m. Approximating π = 22/7, which of the following is the area enclosed by the curve?
(A) 110 m2
(B) 74 m2
(C) 35 m2
(D) 144 m2
Answer: (A)
33. An axial compressor is designed to operate at a rotor speed of 15000 rpm and an inlet stagnation temperature of 300 K. During compressor testing, the inlet stagnation temperature of the compressor measured was 280 K. What should be the rotor speed for the compressor to develop the same performance characteristics during this test as in the design condition?
(A) 14000 rpm
(B) 14491 rpm
(C) 15526 rpm
(D) 16071 rpm
Answer: (B)
34. For the state of stress shown in the figure, which one of the following represents the correct free body diagram showing the maximum shear stress and the associated normal stresses?
Answer: (B)
35. In the equation AX = B, where A is an orthogonal matrix, the sum of the unknowns, x + y +z = ______ (round off to one decimal place).
Answer: (0.9 to 1.1)
36. If is evaluated numerically using trapezoidal rule with four intervals, the difference between the numerically evaluated value and the analytical value of the integral is equal to ________ (round off to three decimal places).
Answer: (0.010 to 0.012)
37. The table shows the lift characteristics of an airfoil at low speeds. The maximum lift coefficient occurs at 16 degrees.
Using Prandtl-Glauert rule, the lift coefficient for the airfoil at the angle of attack of 6 degrees free stream Mach number of 0.6 is _______(round off to two decimal places).
Answer: (0.92 to 0.94)
38. A low speed uniform flow U0 is incident on an airfoil of chord c. In the figure, the velocity profile some distance downstream of the airfoil is idealized as shown for section B. The static pressure at sections A and B is the same. The drag coefficient of the airfoil is ______(round off to three decimal places).
Answer: (0.009 to 0.011)
39. An oblique shock is inclined at an angle of 35 degrees to the upstream flow of velocity 517.56 m/s. The deflection of the flow due to this shock is 5.75 degrees and the temperature downstream is 182.46 K. Assume the gas constant R = 287 J/(Kg K), specific heat ratio γ = 1.4, and specific heat at constant pressure Cp = 1005 J/(Kg K). Using conservation relations, the Mach number of the upstream flow can be obtained as ______(round off to ne decimal place).
Answer: (1.9 to 2.1)
40. The thickness of a laminar boundary layer (δ) over a flat plate is, where x is measured from the leading edge along the length of the plate. The velocity profile within the boundary layer is idealized as varying linearly with y. For freestream velocity of 3 m/s and kinematic viscosity of 1.5 × 10−5 m2/s, the displacement thickness at 0.5 m fro the leading edge is _______ mm (round off to two decimal places).
Answer: (4.00 to 4.20)
41. A wing of 15 m span with elliptic lift distribution is generating a lift of 80 kN at a speed of 90 m/s. The density of surrounding air is 1.2 kg/m3 . the induced angle of attack at this condition is ______ degrees (round off to two decimal places).
Answer: (1.29 to 1.38)
42. A solid circular shaft, made of ductile material with yield stress σY = 280 MPa, is subjected to a torque of 10 kNm. Using the Tresca failure theory, the smallest radius of the shaft to avoid failure is _______ cm (round off to two decimal places).
Answer: (3.55 to 3.58)
43. The ratio of tangential velocities of a planet at the perihelion and the aphelion from the sun is 1.0339. Assuming that the planet’s orbit around the sun is planar and elliptic, the value of eccentricity of the orbit is _________(round off to three decimal places).
Answer: (0.016 to 0.018)
44. The eigenvalues for phugoid mode of a general aviation airplane at a stable cruise flight condition at low angle of attack are λ1, 2 = −02 ± 0.25. If the acceleration due to gravity is 9.8 m/s2, the equilibrium speed of the airplane is ________m/s (round off to two decimal places).
Answer: (55.20 to 55.33)
45. For a general aviation airplane with tail efficiency η = 0.95, horizontal tail volume ratio VH = 0.453, downwash angle slope dε/dα = 0.35, wing lift curve slope horizontal tail lift curve slope shift in neutral point location as a percentage of mean aerodynamic chord is ______(round off to two decimal places).
Answer: (25.60 to 25.70)
46. A single engine, propeller driven, general aviation airplane is flying in cruise at sea-level condition (density of air at sea-level is 1.225 kg/m3) with speed to cover maximum range. For drag coefficient CD = 0.025 + 0.049 CL2 and wing loading W/S = 9844 N/m2, the speed of the airplane is ______m/s (round off to one decimal place).
Answer: (149.0 to 151.0)
47. The design flight Mach number of an ideal ramjet engine is 2.8. The stagnation temperature of air at the exit of the combustor is 2400 K. Assuming the specific heat ratio of 1.4 and gas constant of 287 J/(kg K), the velocity of air at the exit of the engine is _______ m/s (round off to one decimal place).
Answer: (1712.0 to 1719.0)
48. The operating conditions of an aircraft engine combustor are as follows.
The rat of total enthalpy of air entering the combustor = 28.94 MJ/s
The rate of total enthalpy of air leaving the combustor = 115.42 MJ/s.
Mass flow rate of air = 32 kg/s.
Air to fuel mass ratio = 15.6.
Lower heating value of the fuel = 46 MJ/kg.
The efficiency of the combustor is _______% (round off to two decimal places.)
Answer: (91 to 93)
49. The figure shows the T-S diagram for an axial turbine stage.
Assuming specific heat ratio of 1.33 for the hot gas, the isentropic efficiency of the turbine stage is ______% (round off to two decimal places).
Answer: (87 to 89)
50. A rocket engine has a sea level specific impulse of 210 s and a nozzle throat area of 0.005 m2. While testing at sea level conditions, the characteristic velocity and pressure for the thrust chamber are 1900 m/s and 50 bar, respectively. Assume the acceleration due to gravity to be 9.8 m/s2. The thrust produced by the rocket engine is _______kN (round off to one decimal place).
Answer: (27.0 to 27.2)
51. A critically damped single degree of freedom spring-mass-damper system used in a door closing mechanism becomes overdamped due to softening of the spring with extended use. If the new damping ratio (ξnew) for overdamped condition is 1.2, the ratio of the original spring stiffness to the new spring stiffness (korg/knew), assuming that the other parameters remain unchanged, is _______(round off to two decimal places).
Answer: (1.43 to 1.45)
52. The two masses of the two degree of freedom system shown in the figure are given initial displacement of 2 cm (x1) and 1.24 cm (x2). The system starts to vibrate in the first mode. The first mode shape of this system is ϕ1 = [1 a]T, where a = _______(round off to two decimal places).
Answer: (0.61 to 0.63)
53. As shown in the figure, a beam of length 1 m is rigidly supported at one end and simply supported at the other. Under the action of a uniformly distributed load of 10 N/m, the magnitude of the normal reaction force at the simply supported end is _______N (round off to two decimal places).
Answer: (3.74 to 3.76)
54. An airplane of mass 4000 kg and wing reference area 25 m2 flying at sea level has a maximum lift coefficient of 1.65. Assume density of air as 1.225 kg/m3 and acceleration due to gravity as 9.8 m/s2. Using a factor of safety of 1.25 to account for additional unsteady lift during a sudden pull-up, the speed at which the airplane reaches a load factor of 3.2 is _________m/s (round off to two decimal places).
Answer: (62.95 to 63.08)
55. A Pitot tube mounted on the wing tip of an airplane flying at an altitude of 3 k measures a pressure of 0.72 bar, and the outside air temperature is 268.66 K. Take the sea level condition as, pressure = 1.01 bar, temperature = 288.16 K, and density = 1.225 kg/m3. The acceleration due to gravity is 9.8 m/s2 and the gas constant is 287 J/(kg K). Assuming standard atmosphere, the equivalent airspeed for this airplane is _____m/s (round off to two decimal place).
1. Once the team of analysts identify the problem, we _____ in a better position to comment on the issue.
Which one of the following choices CANNOT fill the given blank?
(A) will be
(B) were to be
(C) are going to be
(D) might be
Answer: (B)
2. A final examination is the _______ of a series of evaluations that a student has to go through.
(A) culmination
(B) consultation
(C) desperation
(D) insinuation
Answer: (A)
3. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = _____. .
(A) JDE
(B) JED
(C) JDC
(D) JCD
Answer: (B)
4. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?
(A) 6
(B) 7
(C) 8
(D) 9.5
Answer: (Marks to All)
5. Are there enough seats here? There are _______people here than I expected.
(A) many
(B) most
(C) least
(D) more
Answer: (D)
Q.6 – Q. 10 carry two marks each.
6. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is______.
(A) 37.50
(B) 35.70
(C) 25.00
(D) 10.00
Answer: (A)
7. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is_____.
(A) 13.50
(B) 14.5
(C) 15.50
(D) 16.50
Answer: (B)
8. While teaching a creative writing class in India, I was surprised at receiving stories from the students that were all set in distant places: in the American West with cowboys and in Manhattan penthouses with clinking ice cubes. This was, till an eminent Caribbean writer gave the writers in the once-colonised countries the confidence to see the shabby lives around them as worthy of being “told”.
The writer of this passage is surprised by the creative writing assignments of his students, because ______ .
(A) Some of the students had written stories set in foreign places
(B) None of the students had written stories set in India
(C) None of the students had written about ice cubes and cowboys
(D) Some of the students had written about ice cubes and cowboys
Answer: (B)
9. Mola is a digital platform for taxis in a city. It offers three types of rides – Pool, Mini and Prime. The Table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of revenue contributed by Prime to the total revenues of Mola, for the entire duration?
(A) 16.24
(B) 23.97
(C) 25.8
(D) 38.74
Answer: (B)
10. X is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, X is almost forcing its customers towards its loyalty membership. If its loyalty membership continues to grow at its current rate, within the next eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
(A) Most households that subscribe to X’s loyalty membership discontinue watching cable television
(B) Non-members prefer to watch cable television
(C) Cable television operators don’t subscribe to X’s loyalty membership
1. Once the team of analysts identify the problem, we _____ in a better position to comment on the issue.
Which one of the following choices CANNOT fill the given blank?
(A) will be
(B) were to be
(C) are going to be
(D) might be
Answer: (B)
2. A final examination is the _______ of a series of evaluations that a student has to go through.
(A) culmination
(B) consultation
(C) desperation
(D) insinuation
Answer: (A)
3. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = _____. .
(A) JDE
(B) JED
(C) JDC
(D) JCD
Answer: (B)
4. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?
(A) 6
(B) 7
(C) 8
(D) 9.5
Answer: (Marks to All)
5. Are there enough seats here? There are _______people here than I expected.
(A) many
(B) most
(C) least
(D) more
Answer: (D)
Q.6 – Q. 10 carry two marks each.
6. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is______.
(A) 37.50
(B) 35.70
(C) 25.00
(D) 10.00
Answer: (A)
7. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is_____.
(A) 13.50
(B) 14.5
(C) 15.50
(D) 16.50
Answer: (B)
8. While teaching a creative writing class in India, I was surprised at receiving stories from the students that were all set in distant places: in the American West with cowboys and in Manhattan penthouses with clinking ice cubes. This was, till an eminent Caribbean writer gave the writers in the once-colonised countries the confidence to see the shabby lives around them as worthy of being “told”.
The writer of this passage is surprised by the creative writing assignments of his students, because ______ .
(A) Some of the students had written stories set in foreign places
(B) None of the students had written stories set in India
(C) None of the students had written about ice cubes and cowboys
(D) Some of the students had written about ice cubes and cowboys
Answer: (B)
9. Mola is a digital platform for taxis in a city. It offers three types of rides – Pool, Mini and Prime. The Table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of revenue contributed by Prime to the total revenues of Mola, for the entire duration?
(A) 16.24
(B) 23.97
(C) 25.8
(D) 38.74
Answer: (B)
10. X is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, X is almost forcing its customers towards its loyalty membership. If its loyalty membership continues to grow at its current rate, within the next eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
(A) Most households that subscribe to X’s loyalty membership discontinue watching cable television
(B) Non-members prefer to watch cable television
(C) Cable television operators don’t subscribe to X’s loyalty membership
(D) The X is cancelling accounts of non-members
Answer: (A)
Engineering Sciences
Engineering Mathematics XE-A
XE-A: Q. 1 – Q. 7 carry one mark each & Q. 8 – Q. 11 carry two marks each.
1. Let 𝑋 be the Poisson random variable with parameter 𝜆 = 1. Then, the probability
(2 ≤ 𝑋 ≤ 4) equals
(A) 19/24e
(B) 17/24e
(C) 13/24e
(D) 11/24e
Answer: (B)
2. For the series which of the following statements is NOT correct?
(A) The series converges at 𝑥 = −3
(B) The series converges at 𝑥 = −1
(C) The series converges at 𝑥 = 0
(D) The series converges at 𝑥 = 1
Answer: (D)
3. Let is the complex conjugate of 𝑧. Then, it is differentiable on
(A) |𝑧| > 1
(B) |𝑧| < 1
(C) |𝑧| = 1
(D) the entire complex plane ℂ
Answer: (C)
4. If the transformation (𝑥, 𝑡) = 𝑒𝑥𝑣(𝑥, 𝑡) reduces the partial differential equation then f(x) equals
(A) −𝑒−𝑥
(B) 𝑒−𝑥
(C) −2𝑒−𝑥
(D) 2𝑒−𝑥
Answer: (A)
5. The value of 𝛼 for which the system of equations
𝑥 − 𝑦 − 3𝑧 = 3
2𝑥 + = 0
−2𝑦 − 7 = 𝛼
has a solution is ______.
Answer: (6 to 6)
6. The value of the line integral where 𝛾 is the circle 𝑥2 + 𝑦2 = 1 oriented counter clockwise, is ______.
Answer: (3 to 3)
7. Let 𝑦1(𝑥) and 𝑦2(𝑥) be two linearly independent solutions of the differential equation is ______.
Answer: (0 to 0)
8. If is the matrix where 𝒗1, 𝒗2 and 𝒗3 are linearly independent eigenvectors of the matrix 𝑄, then the sum of the absolute values of all the elements of the matrix 𝑃−1𝑄𝑃 is
(A) 6
(B) 10
(C) 14
(D) 22
Answer: (B)
9. If (𝑥) = 𝑎𝑥3 + 𝑏𝑥2 + 𝑐𝑥 + 𝑑 is the polynomial obtained by Lagrange interpolation satisfying 𝑃(0) = −8, 𝑃(1) = −7, 𝑃(2) = −6 and 𝑃(4) = 20, then the value of 𝑎 − 𝑏 + 𝑐 is
(A) 1
(B) 3
(C) 5
(D) 7
Answer: (D)
10. The number of critical points of the function (𝑥, 𝑦) = 𝑥3 + 3𝑥𝑦2 − 15𝑥 − 12𝑦 at which there is neither maximum nor minimum is_____.
Answer: (2 to 2)
11. Let and 𝛾 is the circle |𝑧| = 2 oriented counter clockwise. Then, the value of 𝐼 rounded off to one decimal place is _______.
Answer: (6.0 to 6.2)
XE : B Fluid Mechanics
XE -B: Q. 1 – Q. 9 carry one mark each
1. For stable equilibrium of a floating body, which one of the following statements is correct?
(A) Centre of gravity must be located below the centre of buoyancy.
(B) Centre of buoyancy must be located below the centre of gravity.
(C) Metacentre must be located below the centre of gravity.
(D) Centre of gravity must be located below the metacentre.
Answer: (D)
2. If 𝑢 and 𝑣 are the velocity components in the x- and y-directions respectively, the z-component of vorticity 𝜔𝑧 at a point in a flow field is
Answer: (B)
3. In which one of the following devices the difference between static and total pressure is used to determine the flow velocity?
(A) Piezometer
(B) Pitot static tube
(C) Orificemeter
(D) Venturimeter
Answer: (B)
4. A golf ball is dimpled to make the flow turbulent and consequently to reduce the drag. Turbulent flow reduces the drag on the golf ball because
(A) skin friction coefficient is lower in a turbulent flow.
(B) skin friction coefficient is higher in a turbulent flow.
(C) turbulent flow has a lower tendency to separate.
(D) turbulent flow has a higher tendency to separate.
Answer: (C)
5. For a steady laminar incompressible boundary layer flow over a sharp-edged flat plate at zero incidence,
(A) the edge of the boundary layer is a streamline.
(B) the edge of the boundary layer is a pathline.
(C) the skin friction coefficient decreases as the distance from the leading edge increases.
(D) the skin friction coefficient remains constant all along the plate.
Answer: (C)
6. The power input 𝑃 to a centrifugal pump is a function of the volume flow rate 𝑄, impeller diameter 𝐷, rotational speed Ω, fluid density 𝜌, dynamic viscosity 𝜇, and surface roughness 𝜖. To carry out a dimensional analysis using Buckingham’s 𝜋 theorem, which one of the following sets can be taken as the set of repeating variables?
(A) 𝑄, Ω, 𝐷
(B) 𝑄, 𝜖, 𝐷
(C) 𝜖, 𝐷, 𝜌
(D) 𝐷, 𝜌, Ω
Answer: (D)
7. Consider the two-dimensional laminar flow of water (𝜇 = 0.001 N.s/m2) between two infinitely long parallel plates 0.1 m apart as shown in the figure below. The velocity profile at any location is given by (𝑦) = 100(0.1𝑦 − 𝑦2) m/s where y is in m. The magnitude of shear stress (in N/m2, rounded off to 2 decimal places) acting on the bottom plate is ______
Answer: (0.01 to 0.01)
8. The maximum velocity in a fully developed laminar incompressible flow through a circular pipe of constant cross-sectional area is 6 m/s. The average velocity (in m/s) of the flow is ______
Answer: (3 to 3)
9. The theoretical discharge for the flow through an orificemeter is 40 m3/s. If the measured discharge in an experiment is 32 m3/s, then the discharge coefficient (rounded off to one decimal place) is _______
Answer: (0.8 to 0.8)
XE – B: Q. 10 – Q. 22 carry two marks each.
10. Consider the flow between two infinitely long parallel plates of large width separated by a distance 2H. The upper plate is moving with a constant velocity U while the lower plate is stationary. The volumetric flow rate per unit width of the plate is
(A) 0.25 𝑈𝐻
(B) 0.5 𝑈𝐻
(C) 𝑈𝐻
(D) 2 𝑈𝐻
Answer: (C)
11. The velocity field in Cartesian coordinates in a two-dimensional steady incompressible flow of a fluid with density 𝜌 is 𝐕 = 𝑥𝐢 − 𝑦𝐣. Assuming no body and line forces, the magnitude of pressure gradient ∇𝑝 at point (1,1) is
(A) √2 𝜌
(B) 𝜌
(C) 𝜌/√2
(D) 𝜌/2
Answer: (A)
12. A two-dimensio nal velocity field in Cartesian coordinates is defined by 𝐕 = 𝑦𝐢 − 𝑥𝐣. This flow is
(A) compressible and rotational
(B) compressible and irrotational
(C) incompressible and rotational
(D) incompressible and irrotational
Answer: (C)
13. Assertion [a]: The streamlines in a free vortex flow are concentric circles.
Reasoning [r]: There exists only radial component for the velocity field in a free vortex flow.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) [a] is true but [r] is false
(D) [a] is false but [r] is true
Answer: (C)
14. The velocity components in Cartesian coordinates in a two-dimensional incompressible flow are = 𝑒𝑦 cos(𝑥) and 𝑣 = 𝑒𝑦 sin(𝑥). The magnitude of total acceleration at the point (−1,1) is
(A) 0
(B) 1
(C) 𝑒
(D) 𝑒2
Answer: (D)
15. For steady laminar flow at zero incidence over a flat plate, the component of velocity parallel to the plate in the boundary layer is given by 𝑢(𝑦) = 𝑎 + 𝑏𝑦 + 𝑐𝑦2, where 𝑦 is the distance measured normal to the flat plate. If 𝜇 is the coefficient of dynamic viscosity, 𝑈 is the velocity parallel to the wall at the edge of the boundary layer and 𝛿 is the boundary layer thickness, the wall shear stress is given by
(A) 𝜇𝑈/𝛿
(B) 2𝜇𝑈/𝛿
(C) 2(𝑈/𝛿)2
(D) 3𝜇𝑈/𝛿
Answer: (B)
16. A fluid with constant density of 1 kg/m3 flows past a semi-cylindrical structure with a freestream velocity of 2 m/s as shown in the figure below. The difference in static pressure between points P and Q is 10 N/m2. If the gravitational acceleration g is 10 m/s2 and the flow is assumed to be potential, what is the radius r (in m) of the semi-cylindrical structure?
(A) 1
(B) 0.8
(C) 0.6
(D) 0.4
Answer: (D)
17. The mercury manometer shown in the figure below is connected to a water pipe at one end while the other end is open to the atmosphere. The density of water is 1000 kg/m3, the specific gravity of mercury is 13.6 and the gravitational acceleration g is 10 m/s2. The gauge pressure 𝑝 (in kN/m2, rounded off to 2 decimal places) in the water pipe is______
Answer: (33.25 to 33.75)
18. Water (𝜌 = 1000 kg/m3, 𝜇 = 0.001 N.s/m2) flows through a smooth circular pipe of radius 0.05 m. If the flow Reynolds number is 1000, then the pressure drop (in N/m2, rounded off to 2 decimal places) over a length of 5 m will be ________
Answer: (0.15 to 0.17)
19. A uniform flow with a velocity of 2 m/s in the x-direction approaches a line source placed on the x-axis at a distance of 0.1 m from the origin. If the origin is the stagnation point in the resulting flow, the strength of the source (in m2/s, rounded off to 2 decimal places) is ______
Answer: (1.25 to 1.27 OR 0.20 to 0.20)
20. In a steady incompressible flow of a fluid past a smooth stationary sphere, the drag force 𝐹 depends on the flow velocity 𝑈, diameter 𝐷, and the dynamic viscosity 𝜇 and density 𝜌 of the fluid. Experiments are conducted on the same sphere at the same flow velocity using two different fluids. The density of the second fluid is two times that of the first fluid. The dynamic viscosity of the second fluid is 𝑛 times that of the first fluid. If the non-dimensional force 𝐹/(𝜌𝑈2𝐷2) remains the same in both the experiments, the value of 𝑛 is_______
Answer: (2 to 2)
21. An incompressible fluid flows past a flat plate as shown in the figure below with a uniform inlet velocity profile 𝑢 = 𝑈 and a parabolic exit velocity profile 𝑢 = 𝑈(2𝜂 − 𝜂2), where 𝑢 is the component of velocity parallel to the wall, 𝑦 is the normal distance from the plate and 𝜂 = 𝑦/𝛿. If the volume flow rate across the top surface of the control volume (CV) is 𝑄 = 𝑝𝑈𝛿 per unit width (perpendicular to the x-y plane) of the plate, the value of 𝑝 (rounded off to 2 decimal places) is _______
Answer: (0.32 to 0.34)
22. A jet engine is to be tested on a thrust stand as shown in the figure below. The conditions prevailing in a typical test are as follows: Axial intake air velocity = 100 m/s; axial exhaust gas velocity = 250 m/s; intake cross-sectional area = 1 m2; intake static pressure = −22 kPa (gauge); exhaust static pressure = 0 kPa (gauge); mass flow rate through the engine = 100 kg/s. The anchoring force (in kN) in axial direction on the thrust stand is_______
Answer: (37 to 37)
XE C : Materials Science
XE (C): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.
1. On decreasing the objective aperture size in an optical microscope
(A) the spherical aberration increases
(B) the depth of field increases
(C) the diffraction-limited resolution increases
(D) the astigmatism increases
Answer: (B)
2. Pilling-Bedworth ratios for oxides of some metals are given in the table.
Based on the criterion of Pilling-Bedworth ratio alone, which one of the following metals will be most protected from high temperature oxidation?
(A) Li
(B) Ce
(C) Ta
(D) W
Answer: (B)
3. In NaCl, the substitution of a Na+ ion by a Ca2+ ion would most probably lead to
(A) the formation of a Na+ vacancy
(B) the creation of a Cl‾ interstitial
(C) the formation of a Cl‾ vacancy
(D) the formation of a Na+ and Cl‾ vacancy pair
Answer: (A)
4. Which one of the following is time-independent?
(A) Elastic def ormation
(B) Anelastic deformation
(C) Viscoelast ic deformation
(D) Creep deformation
Answer: (A)
5. Copper is diffused into aluminium at 400 °C for 100 hours to obtain a certain concentration at a given depth. In another experiment conducted at 500°C, to achieve the same concentration of copper at the same depth, the time required in hours is
(Given: Diffusion coefficients of copper in aluminium at 400 °C and 500 °C are 5 × 10 −14 m2 s−1 and 6 × 10−13 m2 s−1, respectively)
(A) 7.33
(B) 8.33
(C) 9.33
(D) 10.33
Answer: (B)
6. If carbon (C) in iron (Fe) is 6 percent by weight, then its atomic percent is approximately
(Given: atomic weight C = 12, Fe = 56)
(A) 13
(B) 23
(C) 30
(D) 50
Answer: (B)
7. GaAs has advantage over silicon when used in intergrated circuits at low power because it has
(A) larger band gap
(B) more than one element
(C) higher electron mobility
(D) higher hole mobility
Answer: (C)
8. Glass transition temperature of a polymer can be determined by
(A) Thermo-gravimetric analysis
(B) Raman spectroscopy
(C) NMR spectroscopy
(D) Differential scanning calorimetry
Answer: (D)
9. The maximum wavelength of radiation to which Germanium (Ge) is opaque will be
(Given: energy gap of Ge = 0.67 eV, Planck’s constant h = 6.63 × 10−34 J s, velocity of light c = 3×108 m s−1 and 1 eV = 1.6×10−19 J )
(A) 0.8 µm
(B) 1.8 µm
(C) 2.8 µm
(D) 4.8 µm
Answer: (B)
10. An alternating copolymer has number-averaged molecular weight of 105 g mol−1 anddegree of polymerization of 2210. If one of the repeat units is ethylene, the other one is
(Given: atomic weight of H = 1, C = 12, F = 19 and Cl = 35.5)
(A) −CH2−CH(CH3)−
(B) −CH2−CHCl−
(C) −CF2−CF2−
(D) −CH2−CH(C6H5)−
Answer: (B)
11. Match the sintering processes in column I with the most suitable products in column II.
(A) P-4; Q-1; R-2; S-3
(B) P-3; Q-2; R-1; S-4
(C) P-3; Q-2; R-4; S-1
(D) P-2; Q-3; R-1; S-4
Answer: (B)
12. Which one of the following conditions will NOT favour the separation of impurities in zone refining process?
(A) Increase in the gap between solidus and liquidus lines
(B) Increase in the solubility of impurities in solid as compared to that in liquid phase
(C) Agitation of melt
(D) Low cooling rate of melt
Answer: (B)
13. A monochromatic X-ray beam of wavelength 0.154 nm is incident on a cubic crystal having lattice parameter a = 0.245 nm. The diffraction angle (2θ) for the first order reflection from a set of planes represented by the schematic plane below is _____degrees. (round off to 1 decimal place)
Answer: (100.0 to 102.0)
14. Nickel corrodes at 298 K in a solution of 0.06 M nickel chloride having pH 4. Assuming complete dissociation of nickel chloride, the partial pressure of hydrogen required to stop the corrosion of nickel is ______ atm. (round off to the nearest integer)
(Given: Standard reduction potential of nickel = ̶ 0.25 V, Faraday’s constant = 96500 C mol−1, Universal gas constant = 8.314 J K−1mol−1)
Answer: (45 to 52)
15. The potential energy, U(r), of a pair of atoms spaced at a distance r in a solid is given by
The equilibrium distance between the atom pair is ______nm.
(round off to 2 decimal places)
(Given: Constants A = 6×10−20 J nm3, B = 2.1×10−22 J nm7)
Answer: (0.28 to 0.32)
16. Tensile true stress – true strain curve for plastic region of an alloy is given by
𝜎 (MPa) = 600 𝜀𝑛.
When true strain is 0.05, the true stress is 350 MPa. For the same alloy, when engineering strain is 0.12 then the engineering stress is______ MPa. (round off to the nearest integer)
Answer: (360 to 364)
17. Box-S has 2 white and 4 black balls and box-T has 5 white and 3 black balls. A ball is drawn at random, from the box-S and put in box-T. Subsequently, the probability of drawing a white ball from box-T is ________. (round off to 2 decimal places)
Answer: (0.58 to 0.61)
18. The zero point energy of an electron in a box of 0.2 nm width is _____ eV.
(round off to 1 decimal place)
(Given: Planck’s constant = 6.63×10−34 J s, electron mass = 9.11×10−31 kg and 1 eV = 1.6×10−19 J )
Answer: (9.2 to 9.6)
19. The de Broglie wavelength of an electron accelerated across a 300 kV potential in an electron microscope is _______ ×10−12 m. Ignore relativistic effects.
(round off to 2 decimal places)
(Given: Planck’s constant = 6.63×10−34 J s, electron rest mass = 9.11×10−31 kg, electron charge = 1.6×10−19 C)
Answer: (2.10 to 2.35)
20. A stress of 17 MPa is applied to a polymer serving as a fastener in a complex assembly. At constant strain the stress drops to 16.6 MPa after 100 hours. The stress on the polymer must remain above 14.5 MPa in order for the assembly to function properly. The expected life of the assembly is ______ hours. (round off to the nearest integer)
Answer: (666 to 670)
21. A piezoelectric material has a Young’s modulus of 72 GPa. The stress required to changethe polarization from 640 to 645 C m m−3 is _____ MPa. (round off to the nearest integer)
Answer: (560 to 565)
22. An iron bar magnet having coercivity of 7000 A m−1 is to be demagnetized. The bar is introduced fully inside a 0.25 m long solenoid having 150 turns of wire. The electric current required to generate the necessary magnetic field is ________ A.
(round off to 1 decimal place)
Answer: (11.0 to 12.5)
XE – D : Solid Mechanics
XE -D: Q. 1 – Q. 9 carry one mark each
1. For a pinned-pinned slender column of length L, with uniform circular cross section, and with second moment of cross sectional area I, the critical buckling load is Pcr. For a similar column, made of same material, having length 2L and second moment of cross sectional area 4I, the critical buckling load is
(A) 4Pcr
(B) 2Pcr
(C) Pcr
(D) 0.5Pcr
Answer: (C)
2. Two rods P and Q of uniform circular cross section are made of same material and are subjected to identical uniaxial tensile load. The length of rod P is twice the length of rod Q and the diameter of rod P is also twice the diameter of rod Q. The ratio of elastic strain energy stored in rod P to that stored in rod Q is
(A) 4:1
(B) 2:1
(C) 1:1
(D) 1:2
Answer: (D)
3. The frame comprises members ABC, CD, and BEDF. This frame is fixed at A, and the connections between the three members are pins. Load P is applied at F. Which of the following statements is TRUE?
(A) ABC and CD are two-force members
(B) CD is the only two-force member
(C) BEDF and CD are two-force members
(D) ABC is the only two-force member
Answer: (B)
4. When two spheres moving in a horizontal plane collide obliquely, which one of the following statements is ALWAYS TRUE?
(A) Energy of the two-sphere system is conserved
(B) Linear momentum of the two-sphere system is conserved along the normal to the plane of impact
(C) Linear momentum of each individual sphere is conserved along the normal to the plane of impact
(D) Linear momentum of each individual sphere is NOT conserved along the horizontal tangent to the plane of impact
Answer: (B)
5. In a bending moment diagram of a simply supported beam, discontinuity in the bending moment occurs
(A) at the point of application of a couple
(B) at the point of application of a concentrated force
(C) at a point where the cross section of the beam changes abruptly
(D) at a point where shear force is zero
Answer: (A)
6. For a solid circular shaft fixed at one end and a torque applied at the other end, which one of the following is TRUE?
(A) Every cross section of the shaft is subjected to the same internal torque
(B) The internal torque gradually increases from one end of the shaft to the other end
(C) Every cross section of the shaft is subjected to the same bending moment
(D) No cross section of the shaft rotates relative to another cross section
Answer: (A)
7. Flexural stress occurs in a straight beam when
(A) it is subjected to pure torsion
(B) it is subjected to axial loads
(C) it is subjected to transverse loads
(D) it is subjected to combined axial and torsional loads
Answer: (C)
8. The bending moment at a point in a beam changes its sign. Which one of the following is ALWAYS TRUE?
(A) The slope of the beam changes its sign at that point
(B) The deflection of the beam changes its sign at that point
(C) The shear force of the beam changes its sign at that point
(D) The curvature of the beam changes its sign at that point
Answer: (D)
9. The state of stress at a point in a body under plane stress condition is given as 𝜎 = 5 MPa, 𝜎𝑦 = ̶ 1 MPa and 𝜏𝑥𝑦 = 4 MPa. If one of the principal stresses at that point is 7 MPa, thenthe other non-zero principal stress (in MPa) is _______
Answer: (-3.0 to -3.0)
XE -D: Q. 10 – Q. 22 carry two marks each.
10. A massless rod of length L having a concentrated mass m attached at its mid-point is held at rest between the smooth ground and the smooth wall when it makes an acute angle 𝜃0 with the ground as shown. The rod is then released. The acceleration due to gravity is 𝑔. At an instant when the angle between the rod and ground is θ, the velocity of the mass m is
Answer: (B)
11. A cantilever beam of constant cross section is subjected to a positive moment M and a positive axial force F as shown. The normal stress due to the axial force F is 200 MPa and the maximum compressive stress due to the moment M is 100 MPa. If the point A is located on the top surface and the point B is located on the centroidal axis of the beam, the stress elements at these points are (with stresses shown in MPa)
(A)
(B)
(C)
(D)
Answer: (A)
12. The block of mass m = 10 kg is held in place along the incline by the force F applied via a pulley arrangement as shown. The coefficient of static friction between the block and incline is 0.65. The range of F (in N) for which the block will remain at rest is (use acceleration due to gravity 𝑔 = 10 m/s2)
(A) 6.3 to 106.30
(B) 0 to 106.30
(C) 0 to 53.15
(D) 53.15 to 106.30
Answer: (C)
13. The frame shown comprises members ABC, BE, BF, and DEF. It is pin supported at A and D. Members BE and BF are pin connected to ABC and DEF. The vertical load P is applied at C. The force in the member BF is
(A) compressive P
(B) tensile P
(C) compressive 2P
(D) tensile 2P
Answer: (D)
14. A simply supported beam is subjected to a concentrated force P = 48000 N at the mid-span as shown. The flexural rigidity of the beam is EI = 11 × 106 N-m2. The curvature of the beam between points Q and R is given as κ = (𝑃𝑥⁄2𝐸𝐼). The magnitude of deflection (in mm) of the beam at 𝑥 = 0.5 m is
(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
Answer: (A)
15. The shear force (V) diagram for a cantilever beam under certain loads applied at points B and C is shown. The magnitude of applied force at B (FB), and the magnitude of applied force at C (FC), are
(A) FB = 500 N FC = 300 N
(B) FB = 200 N FC = 300 N
(C) FB = 300 N FC = 200 N
(D) FB = 300 N FC = 500 N
Answer: (A)
16. A bar of length 1 m, having a uniform area of cross section 1000 mm2, is fixed at one end and subjected to a uniaxial tensile load of 200 kN at the other end. Along with the tensile load, the rod also experiences a uniform temperature rise ΔT = 100 °C. The material of the rod has a Young’s modulus E = 200 GPa and coefficient of thermal expansion α = 1×10 ̶ 5/ °C. The elongation of the rod (in mm) is ______
Answer: (2.0 to 2.0)
17. A solid rod, with uniform circular cross section, of length 1000 mm and diameter 100 mm is subjected to a uniaxial tensile load. As a result, the increase in length of the rod is observed to be 1 mm while the reduction in diameter of the rod is observed to be 0.03 mm. If the Young’s modulus of the material of the rod is 260 GPa, the shear modulus (in GPa) of the material of the rod is _______
Answer: (100 to 100)
18. A spherical pressure vessel has inner diameter of 4 m and wall thickness of 10 mm. It is made of a steel having tensile yield strength of 200 MPa. Neglecting radial stress and using the maximum shear stress theory, the maximum value of gauge pressure (in MPa) that the wall of the pressure vessel can withstand is _____ (rounded off to two decimal places)
Answer: (1.90 to 21.0)
19. Two solid shafts P and Q made of same material transmit equal torque. Shaft P has a uniform circular cross section of area A and shaft Q has a uniform circular cross section of area 4A. If the maximum torsional shear stress developed in shaft P is 160 MPa, the maximum torsional shear stress developed (in MPa) in shaft Q is _______
Answer: (19.0 to 21.0)
20. The slotted arm AB rotates in the horizontal plane about point A at a constant angular speed 𝜔 = 10 rad/sec. The particle P is released from rest, in the frictionless slot, at a distance of 2 m from end A. The magnitude of the velocity of the particle (in m/s) just before it hits end B is ______ (rounded off to two decimal places)
Answer: (52.00 to 54.00)
21. The uniform pendulum rod, having mass 10 kg and length 𝐿 = 5 m, is attached to a viscous damper having damping coefficient c. Use acceleration due to gravity 𝑔 = 10 m/s2. The least value of c (in N-s/m) such that small motions of the pendulum rod decay without oscillations is ______
Answer: (102.0 to 106.0)
22. A beam having a constant solid rectangular cross section is subjected to pure bending. The longitudinal strain at a point A on the cross section is 3.0 × 10−5. If the Young’s modulus of the material of the beam is 200 GPa, the maximum tensile stress (in MPa) is ______
Answer: (10.0 to 10.0)
XE-E
XE-E: Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each. Notations used:
cp: Specific heat at constant pressure; cv: Specific heat at constant volume; h: Specific enthalpy; s: Specific entropy; v: Specific volume; P: Pressure; V: Volume; T: Temperature; R: Gas constant; Ru : Universal Gas constant
1. One kg of an ideal gas (molecular weight = X) occupies a certain volume V at temperature T and pressure 𝑃1. Four kgs of another ideal gas (molecular weight = 2X) is added to the first gas keeping the volume V and temperature T same as before. The final pressure is
(A) 2 𝑃1
(B) 3 𝑃1
(C) 4 𝑃1
(D) 5 𝑃1
Answer: (B)
2. Which of the following is an intensive thermodynamic property?
(A) Enthalpy
(B) Internal energy
(C) Entropy
(D) Pressure
Answer: (D)
3. A thermodynamic process for a substance is represented as a constant pressure process on a P-V diagram, and a constant temperature process on a T-V diagram. Which of the following statements is TRUE?
(A) The substance is an ideal gas.
(B) The substance is a van der Waals gas.
(C) The substance undergoes a phase change.
(D) Such a process is not possible.
Answer: (C)
4. Addition of a reheat process to a simple Rankine cycle will always
(A) increase both efficiency and work output of the cycle.
(B) increase efficiency but not necessarily work output of the cycle.
(C) increase work output but not necessarily efficiency of the cycle.
(D) decrease both efficiency and work output of the cycle.
Answer: (C)
5. A Carnot cycle implemented using an ideal gas in a piston-cylinder system will have
(A) work transfer in two parts of the cycle and heat transfer in the other two parts of the cycle.
(B) work transfer in all four parts of the cycle and heat transfer in two parts of the cycle.
(C) work transfer in two parts of the cycle and heat transfer in all four parts of the cycle.
(D) work transfer in all four parts of the cycle and heat transfer in all four parts of the cycle.
Answer: (B)
6. The “degrees of freedom” for a pure substance at its triple point is
(A) 3
(B) 2
(C) 1
(D) 0
Answer: (D)
7. The differential of the Gibbs function (g) for a simple compressible system can be represented as 𝑑𝑔 = 𝑣 𝑑𝑃 − 𝑠 𝑑𝑇. Using the appropriate Maxwell relation derived from the above equation, the quantity, for an ideal gas is
(A) R/T
(B) R/P
(C) P/R
(D) T/R
Answer: (B)
8. A Carnot engine receives 2000 kJ heat from a source at 1200 K and rejects 500 kJ heat to sink. The sink temperature (K) is ______.
Answer: (300 to 300)
9. A closed vessel contains a pure substance with 0.1 m3 of saturated liquid and 0.9 m3 of saturated vapor. The specific volume of the liquid and vapor phases are 0.000843 m3/kg and 0.02671 m3/kg respectively. The percentage of vapor in the mixture on mass basis (rounded off to two decimal places) is _____.
Answer: (22.00 to 22.30)
10. A gas obeys the van der Waals equation of state where a and b are van der Waals constants. The compressibility factor in the limit of high specific volume (𝑏 ≪ 𝑣) is
Answer: (A)
11. Consider the thermodynamic relation, For a certain gas, if the isobaric thermal expansion coefficient, (where T is the temperature measured in K), then the value of is,
(A) 0
(B) 1
(C) 2
(D) 𝑣/T
Answer: (A)
12. A piston-cylinder system has an initial volume of 0.1 m3 and contains an ideal gas ( 𝑣 = 0.74 kJ/kg.K, 𝑅 = 0.288 kJ/kg.K) at 1.5 bar and 298 K. The piston is moved to compress the gas until the pressure and temperature reach 10 bar and 423 K respectively. During this process, 20 kJ of work is done on the gas. The magnitude of heat transfer (kJ) during this process is
(A) 134.8
(B) 36.2
(C) 8.2
(D) 3.8
Answer: (D)
13. A reversible cyclic device absorbs 400 kJ/s heat from a reservoir maintained at 265 K and rejects heat to another reservoir at 298 K. The magnitude of the rate of work done (kW) by the device is
(A) 849.81
(B) 449.81
(C) 355.70
(D) 49.81
Answer: (D)
14. In a reversible process, an ideal gas (cp = 1.04 kJ/kg.K, R = 0.297 kJ/kg.K) at 293 K, is compressed in a cylinder from 100 kPa to 500 kPa. During this compression process, the relation between pressure and volume is expressed as, 𝑃𝑣1.3 = constant.
In the following options, mark the closest value for the entropy change per kilogram (J/kg.K).
(A) −91
(B) 91
(C) −864
(D) 864
Answer: (A)
15. The sublimation pressure of water vapor at 233 K is 13 Pa. Assume the water vapor to behave as an ideal gas (R = 0.46 kJ/kg.K), and the latent heat of sublimation is 2840 kJ/kg. The sublimation pressure of water vapor at 213 K, (rounded off to 2 decimal places), is _______ Pa.
Answer: (1.05 to 1.15)
16. In a heating and humidification process, dry air (d.a) with relative humidity of 10% at ambient temperature of 10°C, is mixed with superheated steam at temperature ‘T’. The resultant mixture is at 25°C with relative humidity of 50%. The total pressure before and after the process remains the same at 102 kPa. The saturated pressure of water vapor (v) at 10°C and 25°C are 1.2281 kPa, and 3.1698 kPa, respectively. The specific humidity in grams of water vapour per kg of dry air, can be calculated using where 𝑝𝑣 and 𝑝𝑑.𝑎 are the partial pressures of water vapour and dry air respectively. The quantity of steam in grams (rounded off to 2 decimal places) added per kg of dry air is _______
Answer: (8.50 to 9.50)
17. In a vapor compression system, a refrigerant leaves the evaporator and enters the compressor in saturated vapor condition at 0°C. The specific enthalpies of the saturated liquid and the saturated vapor at 0°C are 50 kJ/kg and 250 kJ/kg, respectively. The refrigerant leaves the compressor with a specific enthalpy of 300 kJ/kg. From the exit of the condenser, the refrigerant is throttled to the evaporator pressure. If the coefficient of performance (COP) of the refrigerator is 2.8 then the dryness fraction of the refrigerant entering the evaporator is_________.
Answer: (0.3 to 0.3)
18. Hot air, assumed as an ideal gas (cp = 1000 J/kg.K, γ = 1.4) enters a gas turbine at 10 bar, 1000 K and leaves at a pressure of 5 bar. Subsequently it expands in a nozzle to a pressure of 1 bar. Assume both these processes to be reversible and adiabatic. If the inlet velocity of the air to the nozzle is negligible, the final velocity (m/s, rounded off to 1 decimal place) of air at the exit of the nozzle is _______.
Answer: (770.0 to 785.0)
19.
The “T-s diagram” for a thermodynamic process is shown in the figure. The heat transferred (kJ/kg) during the reversible process 1-3 is ______ .
Answer: (255 to 255)
20. In a simple Rankine cycle, superheated steam enters the turbine at 100 bar, 500°C (h = 3375.1 kJ/kg, s = 6.5995 kJ/kg.K) at a rate of 1000 kg/s. It expands isentropically in the turbine to the condenser pressure. The temperature in the condenser is 30°C (hf = 125.74 kJ/kg, sf = 0.4368 kJ/kg.K, hg = 2555.6 kJ/kg, sg = 8.4520 kJ/kg.K). Saturated water from the condenser is pumped back to the boiler. Neglecting the pump work, the efficiency (in percentage, rounded off to 1 decimal) of the cycle is ________.
Answer: (41.0 to 43.5)
21. A rigid, adiabatic container has two parts (A) and (B) separated by a piston. Initially, part (A) is filled with 1 kg of an ideal gas (cv = 750 J/kg.K, R = 500 J/kg.K) at 1 bar, 600 K. The part (B) is filled with 1 kg of the same ideal gas at 2 bar, 400 K. The piston is now removed. In the final state, the pressure (bar, rounded off to two decimal places) will be ________ .
Answer: (1.25 to 1.25)
22. In a steady flow process, superheated steam at 70 bar and 450°C, is throttled to 30 bar in an insulated valve, at a rate of 2 kg/s. The changes in the kinetic energy and potential energy during the process are assumed to be zero. The rate of entropy generation (kJ/s.K rounded off to three decimal places) during the throttling process is _____.
The thermodynamic property data for superheated steam at 70 bar and 450°C:
h = 3288.3 kJ/kg, s = 6.6353 kJ/kg.K
The thermodynamic property data for superheated steam at 30 bar are given in the following table.
Answer: (0.700 to 0.750)
XE-F: Polymer Science and Engineering
XE-A: Q. 1 – Q. 7 carry one mark each & Q. 8 – Q. 11 carry two marks each. XE (B to H): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.
1. The functionality of allyl alcohol (CH2=CH-CH2OH) for condensation reaction with terephthalic acid is
(A) 0
(B) 1
(C) 2
(D) 3
Answer: (B)
2. Which of the following polymers can be synthesized by ring opening polymerization?
(A) Poly(vinyl alcohol)
(B) Nylon 66
(C) Poly(ethylene terephthalate)
(D) Poly(ε-caprolactone)
Answer: (D)
3. The weather resistant polymer among the following is
(A) natural rubber
(B) styrene butadiene rubber
(C) nitrile rubber
(D) silicone rubber
Answer: (D)
4. If a combination of sodium and naphthalene is used to initiate polymerization of styrene, then the most likely mechanism of polymerization is
(A) free radical
(B) cationic
(C) anionic
(D) olefin metathesis
Answer: (C)
5. Hypalon is the trade name for
(A) chlorosulfonated polyethylene
(B) chlorinated polyethylene
(C) ultra high molecular weight polyethylene
(D) cross-linked polyethylene
Answer: (A)
6. The copolymer(s) among high density polyethylene (HDPE), low density polyethylene (LDPE) and linear low density polyethylene (LLDPE) is/are
(A) LDPE only
(B) LLDPE only
(C) LDPE and LLDPE
(D) HDPE and LDPE
Answer: (B)
7. The polymer which lacks the ability to exhibit tacticity among the following is
(A) polypropylene
(B) polystyrene
(C) polyisobutylene
(D) poly(methyl methacrylate)
Answer: (C)
8. The correct order of glass transition temperature (Tg) for the polymers listed below is
(PC = polyca polycarbonate; PET = poly(ethylene terephthalate); PE = polyethylene; PP = polypropylene)
(A) PC > PE T > PP > PE
(B) PC > PET > PE > PP
(C) PET > P C > PE > PP
(D) PET > PC > PP > PE
Answer: (A)
9. Polystyrene coffee cup can be most economically manufactured by
(A) thermoforming
(B) injection molding
(C) compression molding
(D) blow molding
Answer: (A)
10. Match the following rubber additives to their function:
(A) P-4, Q-1, R-3, S-2
(B) P-3, Q-1, R-4, S-2
(C) P-3, Q-2, R-4, S-1
(D) P-4, Q-2, R-3, S-1
Answer: (B)
11. Match the following polymers with their characteristic infrared (IR) stretching frequency:
(A) P-2, Q-3, R-1, S-4
(B) P-2, Q-1, R-4, S-3
(C) P-4, Q-2, R-3, S-1
(D) P-4, Q-1, R-2, S-3
Answer: (D)
12. Match the following products to the most suitable polymer for their manufacture:
(A) P-3, Q-2, R-1, S-4
(B) P-3, Q-4, R-2, S-1
(C) P-4, Q-3, R-1, S-2
(D) P-2, Q-3, R-1, S-4
Answer: (B)
13. The order of limiting oxygen index for the following polymers is (polypropylene = PP; PTFE=polytetrafluoroethylene; PVC=poly(vinyl chloride)
(A) PP < PTFE < Nylon 6 < PVC
(B) PP < PVC < Nylon 6 < PTFE
(C) PP < Nylon 6 < PVC < PTFE
(D) PP < Nylon 6 < PTFE < PVC
Answer: (C)
14. Match the following plastic additives to their function:
(A) P-3, Q-1, R-2, S-4
(B) P-3, Q-4, R-1, S-2
(C) P-4, Q-3, R-2, S-1
(D) P-4, Q-3, R-1, S-2
Answer: (D)
15. Match the material classification in Column A with the appropriate one in Column B: (PS=polystyrene, PPO=polyphenylene oxide, PDMS=poly(dimethyl siloxane), PP=polypropylene, PE=polyethylene, PP-g-MA= maleic anhydride grafted PP)
(A) P-3, Q-4, R-2, S-1
(B) P-4, Q-3, R-2, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-4, Q-3, R-1, S-2
Answer: (A)
16. A linear amorphous polymer has a Tg of +10 °C. At 28 °C, it has a melt viscosity of 4 × 108 poise. The viscosity of the polymer at its Tg is _____ × 1013 poise (round off to one decimal place).
Answer: (1.2 to 1.4)
17. A polypropylene (PP) bar with a 10 mm × 10 mm square section is 225 mm long. The modulus of PP bar is 861 MN m−2. It is pinned at both ends and an axial compressive load of 140 N is applied. The strain due to the applied load experienced by the PP bar is ______% (round off to two decimal places).
Answer: (0.15 to 0.17)
18. In a unidirectional carbon fibre/vinyl ester composite, the ratio of the moduli of the carbon fibre to that of vinyl ester is 35 and the fibres take up 50% of the cross-section. The percentage of applied force taken up by the fibres is ______% (round off to one decimal place).
Answer: (97.0 to 97.5)
19. A 3 mm thick layer of softened poly(methyl methacrylate) at 190 °C is sandwiched between two flat parallel plates. A shear stress of 100 kPa is applied to the softened polymer. Assuming the softened polymer as a Newtonian fluid with an apparent viscosity of 3.9 × 104 Pa s, the relative sliding velocity between the two plates is _____ mm s−1 (round off to one decimal place).
Answer: (7.6 to 7.8)
20. For AIBN initiated polymerization of styrene, if both the monomer and initiator concentration are doubled, then the rate of polymerization increases by a factor of ______ (round off to two decimal places).
Answer: (2.80 to 2.84)
21. If 49 moles of hexamethylene diamine is reacted with 50 moles of adipic acid to prepare Nylon 66, then the number average molecular weight, of the resulting polymer at 99.5% conversion (ignoring contribution from end groups) is _____ g mol−1 (round off to 2 decimal places).
Answer: (7497.72 to 7517.72)
22. A single screw extruder is to be used to manufacture a nylon rod of 0.5 cm diameter at a production rate of 2.5 cm s−1. The density of solid nylon and nylon melt are 1.140 g cm-3 and 0.790 g cm−3, respectively. The melt flow rate through the die is____ cm3 s−1 (round off to two decimal places).
Answer: (0.69 to 0.73)
XE-G: Food Technology
Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.
1. Colloidal stability of milk casein is because of the highly hydrated carbohydrate residues in______.
(A) αs1 casein
(B) αs2 casein
(C) β casein
(D) κ casein
Answer: (D)
2. Rice bran is stabilized prior to oil extraction to protect it from the activity of ______.
(A) Polyphenol oxidase
(B) Peroxidase
(C) Lipase
(D) Lipoxygenase
Answer: (C)
3. Sticking of powder to wall of the chamber during spray drying of fruit juice is due to _____.
(A) Low glass transition temperature of the compounds in juice
(B) High glass transition temperature of the compounds in juice
(C) Improper processing parameters of spray dryer
(D) Presence of gums in feed material
Answer: (A)
4. Thearubigins and theaflavins in black tea are formed by the oxidation and dimerization of ______.
(A) Quercetin
(B) Catechins
(C) Gallic acid
(D) Kaempferol
Answer: (B)
5. Ratio of Schmidt number to Lewis number is ______.
(A) Prandtl number
(B) Reynolds number
(C) Nusselt number
(D) Sherwood number
Answer: (A)
6. ‘Red dog’ is one of the byproducts during milling of .
(A) Corn
(B) Rice
(C) Ragi
(D) Wheat
Answer: (D)
7. An ice cream mix of 870 g L−1 has been used to prepare ice cream which yielded a finished product of 490 g L−1. The per cent over run is _______(round off to 1 decimal place).
Answer: (77.4 to 77.6)
8. Impeller in a fruit juice mixing tank is rotating at 200 rpm with a Reynolds number >104. Density of juice is 1045 kg m−3. If diameter of the impeller is doubled and other conditions remained constant, the power requirement of mixing will increase by a factor of ______.
Answer: (32 to 32)
9. Paddy consisting of 20% husk has been milled to remove 6% bran during polishing. Assuming no other losses, yield (per cent) of polished rice from the paddy is _____ (round off to 1 decimal place).
Answer: (74.8 to 75.6)
10. Match the following laws in Column I with corresponding phenomenon in Column II.
(A) P-2, Q-3, R-4, S-1
(B) P-3, Q-2, R-4, S-1
(C) P-3, Q-1, R-4, S-2
(D) P-4, Q-3, R-2, S-1
Answer: (A)
11. Match the mold in Column I with its asexual/sexual spore shown in Column II.
(A) P-3, Q-1, R-4, S-2
(B) P-1, Q-4, R-3, S-2
(C) P-4, Q-3, R-1, S-2
(D) P-4, Q-1, R-2, S-3
Answer: (A)
12. Match the foods given in Column I with their specific usage given in Column II.
(A) P-2, Q-4, R-1, S-3
(B) P-4, Q-1, R-2, S-3
(C) P-2, Q-3, R-1, S-4
(D) P-1, Q-4, R-1, S-3
Answer: (A)
13. Match the bioactive compounds in Column I with their botanical source given in Column II.
(A) P-2, Q-4, R-1, S-3
(B) P-3, Q-4, R-1, S-2
(C) P-4, Q-1, R-2, S-3
(D) P-4, Q-3, R-2, S-1
Answer: (B)
14. Match the following microbial species in Column I with related disease caused by them as listed in Column II.
(A) P-1, Q-3, R-4, S-2
(B) P-2, Q-3, R-4, S-1
(C) P-3, Q-1, R-4, S-2
(D) P-3, Q-4, R-1, S-2
Answer: (D)
15. Buffalo milk having density of 1030 kg m−3 is homogenized with a pressure of 30 MPa. Given, acceleration due to gravity as 9.81 m s−2 and assuming no pressure loss, the velocity (m s−1) of the milk flowing through the homogenizer valve will be _____ (round off to 2 decimal places).
Answer: (240.00 to 242.00)
16. Potato slices have been dehydrated from an initial solid content of 12% to a final solid content of 94%. If the peeling and other losses are to the tune of 10%, final yield (per cent) of the dried chips per ton of fresh potato taken is ______ (round off to 2 decimal places).
Answer: (11.45 to 11.55)
17. A mixed fruit beverage with 12 °Brix having specific heat of 4298 J kg−1 K−1 is being heated from 30 °C to 95 °C for pasteurization at a flow rate of 1000 L h−1 in a tubular heat exchanger. Steam at 100 °C is used as heating medium which is converted into condensate at 100 °C. If the density of beverage is 1075 kg m−3 and the latent heat of steam at the given temperature is 2257 kJ kg−1, the mass flow rate of steam (kg min−1) is ______(round off to 2 decimal places).
Answer: (2.16 to 2.25)
18. Fruit juice was cooled in a tubular heat exchanger from 50 °C to 7 °C using water at 2 °C, which gets heated to 5 °C. Assume, Pr = 0.72, Re = 20000 and thermal conductivity = 0.6W m-1 °C−1 and no viscous effect. If pipe diameter was 10 cm, the convective heat transfer coefficient (W m-2 °C−1) is _____ (round off to 1 decimal place).
Answer: (339.1 to 342.9)
19. Room air is at 40 °C with 60% relative humidity. Saturated vapour pressure of water at 40 °C is 7.375 kPa. Volume of humid air (m3 per kg of dry air) is ______ (round off to 3 decimal places).
Answer: (0.924 to 0.930)
20. A shallow-bed horizontal belt type solvent extractor is operating on 0.3 mm thick soybean flakes with 0.5 m bed depth and a forward speed of 0.8 m min−1 with miscella flux rate of 0.25 m min−1. If porosity of the flakes is 60%, the distance between washing nozzle and miscella collecting receptacle (cm) is _____ (round off to 1 decimal place).
Answer: (95.0 to 100.0)
21. An extruded snack food is packed in a barrier film having water vapour transmission rate of 0.02 mL m−2 day−1. Pack surface area is 0.0012 m2 per gram of dry food solids, EMC of the food is 6% (d.b.), initial moisture content is 2% (d.b.), critical moisture content is 5% (d.b.) and slope of moisture sorption isotherm is 3.4% (d.b.) per unit water activity (aw). Sealed pack is stored at 30 °C. Assume that the vapor pressure of pure water at 30 °C is 31.7 torr. Time required for the food to reach the critical moisture content (days) is______ (round off to 1 decimal place).
Answer: (58.1 to 62.9)
22. Freezing of 100 mm spherical meat ball with 60% moisture at 35 °C is being done in an air blast freezer maintained at −45 °C. Given, latent heat of fusion for water is 333.2 kJ kg−1, thermal conductivity of meat is 1.5 W m−1 °C−1, convective heat transfer coefficient is 40 W m-2 °C−1, density of frozen meat is 980 kg m-3 and initial freezing temperature of meat ball is −10 °C. Using Plank’s equation, freezing time (h) is ______ (round off to 2 decimal places).
Answer: (1.06 to 1.09)
XE-H: Atmospheric and Oceanic Sciences
XE-A: Q. 1 – Q. 7 carry one mark each & Q. 8 – Q. 11 carry two marks each. XE (B to H): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each. XL-P: Q. 1 – Q. 5 carry one mark each & Q. 6 – Q. 15 carry two marks each XL (Q to U):Q. 1 – Q. 10 carry one mark each & Q. 11 – Q. 20 carry two marks each.
1. In the equatorial belt, the Madden-Julian Oscillation (MJO) propagates
(A) northward
(B) southward
(C) eastward
(D) westward
Answer: (C)
2. Potential temperature increases with height in an atmosphere, Upon adiabatic vertical displacement, a parcel of dry air is
(A) stable
(B) absolutely unstable
(C) neutral
(D) conditionally unstable
Answer: (A)
3. Oxygen minimum zones in the ocean are formed in the layers where
(A) Photosynthesis is dominant
(B) Sunlight is maximum
(C) Decomposition of organic matter is dominant
(D) Iron availability is maximum
Answer: (C)
4. Water level in an estuary rises and falls in response to tidal forces. Assume that the only tidal period in an estuary is 12 hours. The speed of the ebb current in that estuary would be maximum
(A) At high tide
(B) At low tide
(C) About 3 hours after high tide
(D) About 6 hours after low tide
Answer: (C)
5. The most abundant ions in seawater are
(A) Sodium and chloride ions
(B) Magnesium and chloride ions
(C) Calcium and chloride ions
(D) Magnesium and sulphide ions
Answer: (A)
6. Which among the following statements is true with respect to the axis of the Indian monsoon trough
(A) Relative vorticity is cyclonic at 850 hPa
(B) Relative vorticity is anticyclonic at 850 hPa
(C) It shifts to the south during break monsoon
(D) It moves to the head Bay of Bengal when a monsoon depression is present over the Indian subcontinent
Answer: (A)
7. A student considered the following possibilities regarding trade wind inversion:
(P) Zonal component of wind is westerly
(Q) Zonal component of wind is easterly
(R) Meridional component of wind is poleward
(S) Meridional component of wind is equatorward
The only combination of correct statements is
(A) P,S
(B) Q,S
(C) Q,R
(D) P,R
Answer: (B)
8. Which of the following statements about thermal wind is NOT correct:
(A) Flow is in geostrophic balance
(B) Horizontal temperature gradient is non-zero
(C) Wind speed varies with height
(D) Flow is quasi-geostrophic
Answer: (D)
9. A numerical weather forecasting model follows sigma (σ) coordinate system in the vertical. ions A and B, the surface pressure is 1000 hPa and 500 hPa respectively. The values to pressure at A and B (in that order) for σ = 0.5 are:
(A) 2000 hPa, 1000 hPa
(B) 500 hPa, 250 hPa
(C) 999.5 hPa, 499.5 hPa
(D) 500 hPa, 0 hPa
Answer: (B)
10. At a given temperature and pressure, equilibrium vapor pressure over the surface of a rain droplet compared to that over a flat surface of pure water is
(A) Always less
(B) Always more
(C) Always equal
(D) Can be less, equal to or more depending on the size and chemical composition of the cloud condensation nuclei, and droplet radius
Answer: (D)
11. Velocity field in a geophysical flow is given by u = -5x, v = 4y, w = 0 where u, v, w are zonal, meridional and vertical components of velocity, and x and y refer to eastward and northward distance. Which among the following statements is NOT true for the flow at 45oN:
(A) Flow is incompressible
(B) Relative vorticity is zero
(C) Potential vorticity is positive
(D) Flow is compressible
Answer: (A)
12. The distance between Mars and Earth is 0.52 times the distance between Sun and Earth. If the solar constant on Earth is 1370 W m−2, then the solar constant on Mars is _____ W m−2. (Round off to one decimal place.)
Answer: (592.8 to 593.2)
13. Ideal gas equation for dry air is expressed as p = ρd Rd T, where p is pressure, ρd is density, T is temperature and Rd is gas constant. If CO2 concentration in Earth’s atmosphere quadruples due to fossil fuel burning, then the new gas constant is _______J kg−1 K−1. (Round off to two decimal places.)
Take the universal gas constant (R*) = 8.314 J K−1 mole−1, molecular weight of CO2 = 44, and present value of Rd = 287 J kg−1 K−1, present concentration of CO2 = 500 mg kg−1.
Answer: (286.40 to 287.30)
14. On a calm evening under a clear sky, the lowest 20 m of the atmosphere is continuously losing energy at a rate of 10 W m−2 due to radiative cooling. Sensible and latent heat flux exchange with the ground is zero. If air temperature and dew point depression at 6 p.m. are 25oC and 8oC, respectively, the probability of fog formation at midnight is ____%. (Round off to the nearest integer.)
Take Cp = 1005 J kg−1 K−1, density of air = 1.15 kg m−3
Answer: (99 to 100)
15. The dynamical core of a general circulation model uses 256 spherical harmonic waves to cover the globe in east-west direction. If two grids of the model exactly resolve the shortest of those waves, then the grid spacing at the equator is _____km. (Round off to one decimal place.)
Take radius of the earth (RE) = 6400 km.
Answer: (78.4 to 78.6)
16. It rains 10 cm in a day over an ocean with a mixed layer depth of 5 m and initial salinity 30 g kg−1. The rain water uniformly mixes with the existing mixed layer water. The finalsalinity after the rain is _____ g kg−1. (Round off to one decimal place.)
Answer: (29.3 to 29.5)
17. A moist air parcel is lifted adiabatically to 800 hPa level. Initial temperature and pressure of the parcel are 300 K and 1010 hPa, and the partial pressure of water vapor is 10 hPa. The partial pressure of the water vapor at the new location is _____ hPa. (Round off to one decimal place.)
Take saturation vapor pressure of water at temperature T as
𝑒s(𝑇) = 𝐴𝑒−𝐵/T
where A = 2.53 × 109 hPa, B = 5420 K, gas constant (R) = 287 J kg−1 K−1, and Cp = 1005 J kg−1 K−1.
Answer: (7.8 to 8.1)
18. In steady state, global mean precipitation P is equal to global mean evaporation E from the surface of the earth. If P is 2.8 mm day-1, then global mean surface latent heat flux is ____ W m−2. (Round off to the nearest integer).
Take latent heat of evaporation of water as 2.5 × 106 J kg−1.
Answer: (75 to 85)
19. A column of seawater from surface to 1000 m depth is initially at rest at the equator. The column is moved to 30oN with no change in column depth. In the absence of friction, the vertical component of relative vorticity of the water in the column at 30oN is _______ ×10−5 s−1. (Round off to one decimal place.)
Answer: (-7.6 to -7.0)
20. Consider two north-south (i.e. meridional) sections A and B in the ocean, separated by 100 km; section B is to the east of section A (as shown in figure below). The steady northward wind stress at A and B are 0.1 N/m2 and 0.2 N/m2, respectively; zonal wind stress is zero everywhere. Density of seawater is 1000 kg m−3. At 30°N, the vertical velocity at the base of the Ekman layer is _______ meters per day. (Round off to one decimal place.)
Answer: (1.1 to 1.3)
21. A tsunami is a long gravity wave, i.e. its wavelength is much larger than the depth of the ocean. A tsunami moves from point A to point B (see figure below); water depth at A is 2000 m, and water depth at B is 500 m. Assume no frictional losses. By energy conservation, Cg <E> is constant, where Cg is group speed and <E> is the total (potential plus kinetic) energy density of the wave field. If the amplitude of the tsunami at point A is 1 m, its amplitude at B is ________m. (Round off to two decimal places.)
Answer: (1.30 to 1.50)
22. At mid-latitudes, long Rossby waves obey the dispersion relation σ = −βk / L−2, where σ is frequency, k is zonal wavenumber, β is rate of change of Coriolis parameter with northward distance (units m−1 s−1), and L is Rossby radius. If L = 100 km, the speed of the long Rossby wave at 45oN is ________ m s−1. (Round off to two decimal places.)
1. Once the team of analysts identify the problem, we _____ in a better position to comment on the issue.
Which one of the following choices CANNOT fill the given blank?
(A) will be
(B) were to be
(C) are going to be
(D) might be
Answer: (B)
2. A final examination is the _______ of a series of evaluations that a student has to go through.
(A) culmination
(B) consultation
(C) desperation
(D) insinuation
Answer: (A)
3. If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = _____. .
(A) JDE
(B) JED
(C) JDC
(D) JCD
Answer: (B)
4. The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?
(A) 6
(B) 7
(C) 8
(D) 9.5
Answer: (Marks to All)
5. Are there enough seats here? There are _______people here than I expected.
(A) many
(B) most
(C) least
(D) more
Answer: (D)
Q.6 – Q. 10 carry two marks each.
6. Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is______.
(A) 37.50
(B) 35.70
(C) 25.00
(D) 10.00
Answer: (A)
7. Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is_____.
(A) 13.50
(B) 14.5
(C) 15.50
(D) 16.50
Answer: (B)
8. While teaching a creative writing class in India, I was surprised at receiving stories from the students that were all set in distant places: in the American West with cowboys and in Manhattan penthouses with clinking ice cubes. This was, till an eminent Caribbean writer gave the writers in the once-colonised countries the confidence to see the shabby lives around them as worthy of being “told”.
The writer of this passage is surprised by the creative writing assignments of his students, because ______ .
(A) Some of the students had written stories set in foreign places
(B) None of the students had written stories set in India
(C) None of the students had written about ice cubes and cowboys
(D) Some of the students had written about ice cubes and cowboys
Answer: (B)
9. Mola is a digital platform for taxis in a city. It offers three types of rides – Pool, Mini and Prime. The Table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of revenue contributed by Prime to the total revenues of Mola, for the entire duration?
(A) 16.24
(B) 23.97
(C) 25.8
(D) 38.74
Answer: (B)
10. X is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, X is almost forcing its customers towards its loyalty membership. If its loyalty membership continues to grow at its current rate, within the next eight years more households will be watching X than cable television.
Which one of the following statements can be inferred from the above paragraph?
(A) Most households that subscribe to X’s loyalty membership discontinue watching cable television
(B) Non-members prefer to watch cable television
(C) Cable television operators don’t subscribe to X’s loyalty membership
(D) The X is cancelling accounts of non-members
Answer: (A)
Textile Engineering and Fibre Science
Q.1 – Q. 25 carry one mark each.
1. The value of is
(A) – 1/2
(B) 0
(C) 1/2
(D) 1
Answer: (C)
2. For 𝑥 in [0, 𝜋], the maximum value of (sin 𝑥 + cos 𝑥) is
(A) 1/√2
(B) 1
(C) √2
(D) 2
Answer: (C)
3. The eigenvalues of the matrix are
(A) −1, 1, 3
(B) −3, 2, −2
(C) 3, 2, −1
(D) 3, 2, 1
Answer: (A)
4. Acrylic fibre is made from at least 85% by weight of
(A) Acrylic acid
(B) Acrylonitrile
(C) Acrylamide
(D) Methyl methacrylate
Answer: (B)
5. The pair of natural fibres, belonging to the category of seed fibre, is
(A) Cotton and Sisal
(B) Kenaf and Kapok
(C) Cotton and Kenaf
(D) Cotton and Kapok
Answer: (D)
6. The term ‘half-lap’ is associated with
(A) Card
(B) Drawframe
(C) Comber
(D) Roving frame
Answer: (C)
7. In a modern card, the highest angular velocity (rpm) is found in
(A) Feed roller
(B) Taker-in
(C) Cylinder
(D) Doffer
Answer: (B)
8. For multifilament yarns, optimum add-on (%) of size is in the range
(A) 0-0.5
(B) 4-8
(C) 20-25
(D) 30-35
Answer: (B)
9. The movements of guide bars in warp knitting are
(A) Swinging and shaking
(B) Shaking and shogging
(C) Shogging and twisting
(D) Swinging and shogging
Answer: (D)
10. Among the following options, the thickest Classimat fault is
(A) B3
(B) D1
(C) G
(D) H2
Answer: (A)
11. Work factor of a perfectly elastic yarn is
(A) 0
(B) 0.5
(C) 1
(D) 2
Answer: (B)
12. Barium Activity Number (BAN) of a cotton fabric was found to be 150. The fabric must have undergone
(A) Desizing only
(B) Desizing and scouring only
(C) Desizing and bleaching only
(D) Desizing, scouring and mercerization
Answer: (D)
13. The gum present in the raw mulberry silk fibre is
(A) Sericin
(B) Fibroin
(C) Keratin
(D) Casein
Answer: (A)
14. The value of 𝑘 for which the matrix does not have an inverse is______.
Answer: ()
[/bg_collapse6 to 6]
15. If a continuous random variable has the following probability density function then the value of 𝑘 is ______.
Answer: (4 to 4)
16. A blend of nylon 6 and polyester fibres when dissolved in formic acid at room temperature leaves a bone dry residue of 40% by weight. The weight fraction of polyester in the blend (rounded off to 1 decimal place) is _______.
Answer: (0.4 to 0.4)
17. Molecular weight of the repeat unit of poly (ethylene terephthalate) is _______.
Answer: (192.0 to 192.5)
18. Six carded slivers of 4 ktex each are drawn to produce a sliver of 5 ktex. The draft required (rounded off to 1 decimal place) is ________.
Answer: (4.7 to 4.9)
19. The ratio of yarn tensile modulus to fibre tensile modulus, where the surface fibres are inclined at a twist angle of 25°, (rounded off to 2 decimal places) is ______.
Answer: (0.81 to 0.83)
20. If the linear density (tex) of a yarn is doubled, then percentage increase in tightness factorof single jersey knitted fabric (rounded off to 1 decimal place) is ______.
Answer: (40.0 to 43.0)
21. A square plain jammed fabric has yarns with circular cross-section. If the yarn diameter is0.02 cm, then number of ends per cm (rounded off to 1 decimal place) is _______.
Answer: (24.0 to 34.0)
22. If the moisture content of a fibre is 10%, its moisture regain (%) (rounded off to 2 decimalplaces) is _______.
Answer: (11.00 to 11.20)
23. The 2.5% span length and uniformity ratio of a particular variety of cotton fibre are 30 mm and 45%, respectively. The 50% span length (mm) of the fibre (rounded off to 1 decimal place) is ______.
Answer: (13.0 to 14.0)
24. A wool fabric is to be dyed with an acid dye to a shade of 4% on the weight of fabric (owf).The material to liquor ratio is 1:40 and the exhaustion is 100%. The concentration (gpl) of the dye in the initial dye bath is ________.
Answer: (1 to 1)
25. A cellulosic fabric has been treated with boric acid to impart flame retardancy. The wet expression is 100%. The molecular weight of boric acid is 62 and the atomic mass of boron is 11. Assume that no chemical reaction takes place between boric acid and the fibre. If 2.2 % boron has been added on the weight of fabric (owf), then the add-on of boric acid on fabric (% owf) (rounded off to 1 decimal place) is __________.
Answer: (12.2 to 12.6)
Q.26 – Q. 55 carry two marks each.
26. One of the points which lies on the solution curve of the following differential equation
2𝑥𝑦 𝑑𝑥 + (𝑥2 + 𝑦2) 𝑑𝑦 = 0
with the initial condition 𝑦(1) = 1 is
(A) (−1, 1)
(B) (0, 0)
(C) (0, 1)
(D) (2, 1)
Answer: (A)
27. Let 𝑋 be a binomial random variable with mean 1 and variance 3/4. The probability that 𝑋 takes the value 3 is
(A) 3/64
(B) 3/16
(C) 27/64
(D) ¾
Answer: (A)
28. Match the process steps in viscose fibre manufacture listed in Group I with the corresponding chemicals given in Group II. The correct option is
(A) P-4, Q-3, R-2, S-1
(B) P-4, Q-3, R-1, S-2
(C) P-3, Q-4, R-1, S-2
(D) P-2, Q-3, R-1, S-4
Answer: (B)
29. The correct combination of techniques to determine the crystallinity in fibres is
(A) TGA and DSC
(B) Birefringence and DSC
(C) X-ray diffraction and Density measurement
(D) Birefringence and X-ray diffraction
Answer: (C)
30. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]
[a]: Kevlar fibre has high strength and high modulus.
[r] : It has high orientation and low crystallinity.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Answer: (D)
31. An opening roller in blowroom with 100 cm length, 38 cm diameter and 2 teeth per cm2 is rotating at an angular velocity of 400 rpm to deliver fibre tufts at a production rate of 500 kg/h. The intensity of opening (fibre mass in mg per tooth) of the opening roller approximately is
(A) 0.44
(B) 0.87
(C) 1.74
(D) 2.74
Answer: (B)
32. A drawframe with a 3 over 3 drafting arrangement, having an eccentric bottom middle roller of 28 mm diameter, is used to produce a sliver. The back zone and front zone drafts are 1.7 and 3.5, respectively. The sliver is further given a draft of 200 to produce a yarn. The wavelength (m) of the periodic fault in the yarn approximately is
(A) 17.6
(B) 29.9
(C) 61.6
(D) 104.7
Answer: (C)
33. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]
[a] : The short term mass irregularity of rotor yarn is less than that of ring yarn.
[r] : Rotor yarn has belt or wrapper fibres, but ring yarn does not.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Answer: (B)
34. Match the looms listed in Group I with the corresponding components given in Group II. The correct option is
(A) P-1, Q-3, R-4, S-2
(B) P-3, Q-2, R-1, S-4
(C) P-3, Q-2, R-4, S-1
(D) P-1, Q-2, R-3, S-4
Answer: (C)
35. The punch density of a needle-punched nonwoven fabric is 50 punches/cm2. If the stroke frequency of needle bed is doubled and the fabric delivery speed is halved, then the punch density (punches/cm2) would be
(A) 25
(B) 50
(C) 100
(D) 200
Answer: (D)
36. In air-jet weaving, the correct combination of parameters, on which drag force on weft yarn depends, is
(P) Weave pattern
(Q) Density of air
(R) Weft yarn diameter
(S) Picks per cm
(A) P and Q
(B) Q and R
(C) R and S
(D) P and S
Answer: (B)
37. The correct combination of reasons, which leads to decrease in tear strength of a woven fabric, is
(P) Increase in yarn to yarn friction
(Q) Decrease in yarn to yarn friction
(R) Increase in fabric sett
(S) Decrease in fabric sett
(A) P and R
(B) P and S
(C) Q and R
(D) Q and S
Answer: (A)
38. Match the instruments listed in Group I with the corresponding operating principles given in Group II. The correct option is
(A) P-4, Q-3, R-1, S-2
(B) P-4, Q-2, R-3, S-1
(C) P-1, Q-3, R-2, S-4
(D) P-4, Q-3, R-2, S-1
Answer: (D)
39. The set containing oxidative bleaching agents only is
(P) Sodium hydrosulphite
(Q) Thiourea dioxide
(R) Sodium hypochlorite
(S) Hydrogen peroxide
(A) P and Q
(B) Q and R
(C) R and S
(D) P and S
Answer: (C)
40. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]
[a] : Synthetic thickeners used in pigment printing are neutralized before printing.
[r] : Without neutralization, the viscosity required for printing would not be achieved.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Answer: (A)
41. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]
[a] : The equilibrium dye uptake by a fibre decreases with increasing dyeing temperature.
[r] : Dyeing is an endothermic process.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Answer: (D)
42. The value of the integral obtained using Simpson’s 1/3 rule (rounded off to 2 decimal places) is_________.
Answer: (0.24 to 0.28)
43. Let The value of λ for which the vector is ______.
Answer: (3 to 3)
44. In melt spinning, the diameter of monofilament at the spinneret exit is 0.3 mm and at thetake-up point is 0.15 mm. Assuming that there is no change in density of filament, the spin- draw ratio is ________.
Answer: (4 to4)
45. The experimentally determined density of a fibre is 1.31 g/cc. If the density of the void free fibre is 1.35 g/cc, then the void volume fraction (%) of the fibre sample (rounded off to 2 decimal places) is ________.
Answer: (2.60 to 3.00)
46. The spindle speed of a ring frame, producing a yarn of 25 tex, is 25000 rpm and the rate of delivery is 25 m/min. The twist multiplier (m−1∙ tex0.5) of the yarn is _______.
Answer: (5000 to 5000)
47. If the value of twist retraction of a yarn is 0.2, then the value of twist contraction (rounded off to 2 decimal places) is ________.
Answer: (1.24 to 1.26)
48. A yarn is passing through an additive type tensioner. The mass of dead weight on disc is 50 g and the coefficient of friction between yarn and disc is 0.3. If the input tension is 50 gf, then the output tension (gf) is __________.
Answer: (79 to 81)
49. In a shuttle loom, if the loom speed (picks per minute) is increased by 20%, then the percentage increase in picking power required per meter of fabric is _______.
Answer: (41 to 45)
50. A sample of 150 cotton fibres is tested for maturity. The number of normal and thin-walled fibres are 105 and 30, respectively. The rest are dead fibres. The maturity ratio is _______.
Answer: (1 to 1)
51. In a vibroscope, the fundamental resonant frequency of fibre X is twice that of fibre Y. Keeping the test length and tensioning weight the same, if the linear density of fibre Y is 10 denier, then the linear density (denier) of fibre X (rounded off to 1 decimal place) is______.
Answer: (2.5 to 2.5)
52. The 95% confidence limits of mean yarn tenacity (cN/tex) based on 100 test samples is 30 ± 1.5. The number of test samples required to obtain 95% confidence limits of 30 ± 0.5 is ________.
Answer: (900 to 900)
53. A 180 denier polyester multifilament yarn, a 60 Ne cotton yarn and a 50 Nm (metric count) polyester/wool yarn are twisted together. The resultant linear density (tex) of the 3-ply yarn, neglecting twist contraction, (rounded off to 2 decimal places) is______.
Answer: (49.50 to 50.00)
54. A polyester fabric is dyed with a disperse dye till equilibrium is reached. If the concentration of the dye in the spent dyebath is 0.05 gpl and the partition coefficient is 1000 ml/g, then amount of dye in the fibre (g/100 g) is ________.
Answer: (5 to 5)
55. A wet polyester fabric has areal density of 160 g/m2. The initial temperature of the wet fabric is 20°C. After it is completely dried on a cylinder dryer, its areal density drops to 100 g/m2.
Consider,
•Specific heat of polyester as 2.0 J/g °C
•Specific heat of water as 4.2 J/g °C
•Latent heat of evaporation of water as 2260 kJ/kg
Assuming that there is no heat loss, the energy (kJ) required to dry 1 m2 of the fabric (rounded off to 2 decimal places) is _______.
which of the following statements is NOT correct?
is the complex conjugate of 𝑧. Then, it is differentiable on
then f(x) equals
where 𝛾 is the circle 𝑥2 + 𝑦2 = 1 oriented counter clockwise, is ______.
is ______.
is the matrix where 𝒗1, 𝒗2 and 𝒗3 are linearly independent eigenvectors of the matrix 𝑄, then the sum of the absolute values of all the elements of the matrix 𝑃−1𝑄𝑃 is
and 𝛾 is the circle |𝑧| = 2 oriented counter clockwise. Then, the value of 𝐼 rounded off to one decimal place is _______.
for an ideal gas is
where a and b are van der Waals constants. The compressibility factor 
in the limit of high specific volume (𝑏 ≪ 𝑣) is
For a certain gas, if the isobaric thermal expansion coefficient, 
(where T is the temperature measured in K), then the value of 
is,
where 𝑝𝑣 and 𝑝𝑑.𝑎 are the partial pressures of water vapour and dry air respectively. The quantity of steam in grams (rounded off to 2 decimal places) added per kg of dry air is _______
of the resulting polymer at 99.5% conversion (ignoring contribution from end groups) is _____ g mol−1 (round off to 2 decimal places).
is
are
does not have an inverse is______.
then the value of 𝑘 is ______.
obtained using Simpson’s 1/3 rule (rounded off to 2 decimal places) is_________.
The value of λ for which the vector 
is ______.