JEE Main Session 2 March 18th Shift 2 Question Paper with Answer Key

Physics

Section-A

1. The decay of a proton to neutron is:

(a)  Not possible as proton mass is less than the neutron mass

(b)  Always possible as it is associated only with β+ decay

(c)  Possible only inside the nucleus

(d) Not possible but neutron to proton conversion is possible

Answer: (d)

2. An object of mass m1 collides with another object of mass m2, which is at rest. After the collision, the objects move at equal speeds in opposite directions. The ratio of the masses m2: m1 is:

(a)  2 : 1

(b)  1 : 1

(c)  1 : 2

(d) 3 : 1

Answer: (d)

3. A plane electromagnetic wave propagating along y-direction can have the following pair of electric field  and magnetic field components.

(a)  Ex, Bz or Ez, Bx

(b)  Ey, Bx or Ex, By

(c)  Ex, By or Ey, Bx

(d) Ey, By or Ez, Bz

Answer: (a)

4. A solid cylinder of mass m is wrapped with an inextensible light string and is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is :

[The coefficient of static friction, μs, is 0.4]

(a)   

(b)  0

(c)  mg/5

(d) 5 mg

Answer: (c)

5. An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S1 and that of the other part is S2. Given that S1 > S2. If the piston is removed then the total entropy of the system will be:

(a)  S1 + S2

(b)  S1 – S2

(c)  S1 × S2

(d) S1/S2

Answer: (a)

6. The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is :

(a)   

(b)    

(c)  Infinite

(d)  

Answer: (a)

7. For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where λ is the ratio of specific heats) :

(a)   

(b)  

(c)   

(d)   

Answer: (a)

8. The correct relation between α (ratio of collector current to emitter current) and β (ratio of collector current to base current) of a transistor is :

(a)    

(b)    

(c)   

(d)  

Answer: (a)

9. In a series LCR circuit, the inductive reactance (XL) is 10 Ω and the capacitive reactance (XC) is 4 Ω. The resistance (R) in the circuit is 6 Ω. Find the power factor of the circuit.

(a)  1/√2

(b)  √3/2

(c)  1/2

(d) 1/2√2

Answer: (a)

10. A proton and an α-particle, having kinetic energies Kp and Kα respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that α-particle is 2: 1. The ratio of KP: Kα is :

(a)  1 : 8

(b)  1 : 4

(c)  8 : 1

(d) 4 : 1

Answer: (d)

11. The function of time representing a simple harmonic motion with a period of π/ω is :

(a)  cos(ωt) + cos(2ωt) + cos(3ωt)

(b)   

(c)  sin2 (ωt)

(d) sin (ωt) + cos (ωt)

Answer: (b)

12. Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :

(a)   

(b)   

(c)   

(d)   

Answer: (d)

13. The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is The magnitude of the areal velocity of the planet is :

(a)  L/M

(b)  2L/M

(c)  L/2M

(d) 4L/M

Answer: (c)

14. The velocity – displacement graph of a particle is shown in the figure.

The acceleration – displacement graph of the same particle is represented by:

Answer: (d)

15. Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in the figure.

The refractive indices of the material of the prism for red, green and blue wavelengths are 1.27, 1.42 and 1.49 respectively. The colour of the ray(s) emerging out of the face PR is:

(a)  Blue

(b)  Green

(c)  Red

(d) Blue and Green

Answer: (c)

16. Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is 32 g/mol; R=8.3 JK1 mol1)

(a)    

(b)    

(c)   

(d)   

Answer: (c)

17. A particle of mass m moves in a circular orbit under the central potential field, U(r) = −C/r, where C is a positive constant. The correct radius – velocity graph of the particle’s motion is :

Answer: (a)

18. Which of the following statements are correct ?

(A) Electric monopoles do not exist whereas magnetic monopoles exist.

(B) Magnetic field lines due to a solenoid at its ends and outside cannot be completely straight and confined.

(C) Magnetic field lines are completely confined within a toroid.

(D) Magnetic field lines inside a bar magnet are not parallel.

(E) χ = —1 is the condition for a perfect diamagnetic material, where χ is its magnetic susceptibility.

Choose the correct answer from the options given below :

(a)  (B) and (C) only

(b)  (B) and (D) only

(c)  (C) and (E) only

(d) (A) and (B) only

Answer: (c)

19. The speed of electrons in a scanning electron microscope is 1×107 ms1. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of:

(a)  1/√1837

(b)  √1837

(c)  1837

(d) 1/1837

Answer: (c)

20. If the angular velocity of earth’s spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately :

[Take g = 10 ms2, the radius of earth, R = 6400 × 103 m, Take π = 3.14]

(a)  60 minutes

(b)  does not change

(c)  84 minutes

(d) 1200 minutes

Answer: (c)

Section-B

21. Two wires of same length and thickness having specific resistances 6 Ω cm and 3 Ω cm respectively are connected in parallel. The effective resistivity is ρ Ω cm. The value of ρ, to the nearest integer, is _________.

Answer: (4)

22. A ball of mass 4 kg, moving with a velocity of 10 ms1, collides with a spring of length 8 m and force constant 100 Nm1. The length of the compressed spring is x m. The value of x, to the nearest integer, is _______

Answer: (6)

23. Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance x cm from A. The galvanometer shows zero deflection.

The value of x, to the nearest integer, is ___________

Answer: (48)

24. Consider a water tank as shown in the figure. It’s cross-sectional area is 0.4 m2. The tank has an opening B near the bottom whose cross-sectional area is 1 cm2. A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v ms1. The value of v, to the nearest integer, is …………

[Take value of g to be 10 ms2]

Answer: (3)

25. The typical output characteristics curve for a transistor working in the common emitter configuration is shown in the figure.

The estimated current gain from the figure is …………..

Answer: (200)

26. The radius of a sphere is measured to be (7.50 ± 0.85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest integer x, is …………

Answer: (34)

27. The projectile motion of a particle of mass 5 g is shown in the figure.

The initial velocity of the particle is 5√2 ms1 and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points A and B is X × 102 kgms1. The value of X, to the nearest integer, is …………………..

Answer: (5)

28. An infinite number of point charges, each carrying 1 μC charge, are placed along the y-axis at y = 1m, 2m, 4m, 8m ………… The total force on a 1 C point charge, placed at the origin, is X × 103 The value of X, to the nearest integer, is ………

Answer: (12)

29. A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at.

(i) Ground level

(ii) a height of 5 m

The increase in antenna range in case (ii) relative to case (i) is n%. The value of n, to the nearest integer, is

Answer: (50)

30. A galaxy is moving away from the earth at a speed of 286 km/s. The shift in the wavelength of a redline at 630 nm is X × 1010 The value of X, to the nearest integer, is [Take the value of speed of light c, as 3 × 108 ms1]

Answer: (6)

Chemistry

Section-A

1. Consider the below-given reaction, the product ‘X’ and ‘Y’ respectively are:

Answer: (b)

2. The charges on the colloidal CdS sol. and TiO2 are, respectively

(a)  positive and negative

(b)  negative and negative

(c)  negative and positive

(d) positive and positive

Answer: (c)

3. The oxide that shows a magnetic property is:

(a)  SiO2

(b)  Na2O

(c)  Mn3O4

(d) MgO

Answer: (c)

4. Given below are two statements:

Statement I: Bohr’s theory accounts for the stability and line spectrum of Li+ ion.

Statement II: Bohr’s theory was unable to explain the splitting of spectral lines in the presence of a magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below:

(a)  Both statement I and statement II are true

(b)  Statement I is true but statement II is false

(c)  Statement I is false but statement II is true

(d) Both statement I and statement II are false

Answer: (c)

5. Match List-I with List-II:

List-I                                 List-II

(a) Mercury                       (i) Vapour phase refining

(b) Copper                         (ii) Distillation Refining

(c) Silicon                          (iii) Electrolytic Refining

(d) Nickel                          (iv) Zone Refining

Choose the most appropriate answer from the option given below:

(a)  (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)

(b)  (a)-(ii), (b)-(iv), (c)-(iii),(d)-(ii)

(c)  (a)-(i), (b)-(iv), (c)-(ii), (d)-(iii)

(d) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)

Answer: (d)

6. Match List-I with List-II:

List-I                                             List-II

(Class of Chemicals)                    (Example)

(a) Antifertility drug                     (i) Meprobamate

(b) Antibiotic                                (ii) Alitame

(c) Tranquilizer                           (iii) Norethindrone

(d) Artificial Sweetener               (iv) Salvarsan

Choose the most appropriate answer from the option given below:

(a)  (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

(b)  (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)

(c)  (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

(d) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

Answer: (d)

7. Main Products formed during a reaction of 1-methoxy naphthalene with hydroiodic acid are:

Answer: (d)

8. Consider the given reaction, percentage yield of:

(a)  A > C > B

(b)  B > C > A

(c)  C > B > A

(d) C > A > B

Answer: (c)

9. An organic compound “A” on treatment with benzene sulphonyl chloride gives compound B. B is soluble in dil. NaOH solution. Compound A is:

(a)  C6H5–N–(CH3)2

(b)  C6H5–NHCH2CH3

(c)   

(d) C6H5−CH2NHCH3

Answer: (c)

10. The first ionization energy of magnesium is smaller as a compound to that of elements X and Y but higher than that of Z. The elements X, Y and Z, respectively are:

(a)  argon, lithium and sodium

(b)  chlorine, lithium and sodium

(c)  neon, sodium and chlorine

(d) argon, chlorine and sodium

Answer: (d)

11. In the following molecule:

The hybridisation of Carbon a, b and c respectively are:

(a)  sp3, sp2, sp2

(b)  sp3, sp2, sp

(c)  sp3, sp, sp

(d) sp3, sp, sp2

Answer: (a)

12. In the reaction of hypobromite with amide, the carbonyl carbon is lost as:

(a)  HCO3

(b)  CO32

(c)  CO2

(d) CO

Answer: (b)

13. The oxidation states of nitrogen in NO, NO2, N2O and NO3 are in the order of

(a)  NO2 > NO3 > NO > N2O

(b)  N2O > NO2 > NO > NO3

(c)  NO3 > NO2 > NO > N2O

(d) NO > NO2 > NO3 > N2O

Answer: (c)

14. Match List-I and List-II:

List-I                                 List-II

(a) Be                                (i) treatment of cancer

(b) Mg                               (ii) extraction of metals

(c) Ca                                (iii) incendiary bombs and signals

(d) Ra                                (iv) windows of X-ray tubes

                                          (v) bearings for motor engines

Choose the most appropriate answer from the option given below:

(a)  (a)-(iii), (b)-(iv), (c)-(ii), (d)-(v)

(b)  (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)

(c)  (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

(d) (a)-(iii), (b)-(iv), (c)-(v), (d)-(ii)

Answer: (c)

15. Deficiency of vitamin K causes:

(a)  Cheilosis

(b)  Increase in blood clotting time

(c)  Increase in the fragility of RBCs

(d) Decrease in blood clotting time

Answer: (b)

16. Given below are two statements:

Statement I: C2H5OH and AgCN both can generate nucleophiles.

Statement II: KCN and AgCN both will generate nitrile nucleophiles with all reaction conditions.

Choose the most appropriate option:

(a)  Statement I is false but statement II is true

(b)  Statement I is true but statement II is false

(c)  Both statement I and statement II are false

(d) Both statement I and statement II are true

Answer: (b)

17. Given below are two statements:

Statement I: Non-biodegradable wastes are generated by thermal power plants.

Statement II: Biodegradable detergents lead to eutrophication.

In the light of the above statements, choose the most appropriate answer from the options given below.

(a)  Statement I is false but statement II is true

(b)  Statement I is true but statement II is false

(c)  Both statement I and statement II are false

(d) Both statement I and statement II are true

Answer: (b)

18. A hard substance melts at high temperature and is an insulator in both solid and in molten state. This solid is most likely to be a/an:

(a)  Metallic solid

(b)  Covalent solid

(c)  Ionic solid

(d) Molecular solid

Answer: (b)

19. The secondary valency and the number of hydrogen bonded water molecule(s) in CuSO4.5H2O, respectively, are:

(a)  6 and 4

(b)  4 and 1

(c)  5 and 1

(d) 6 and 5

Answer: (b)

20.In a basic medium, H2O2 exhibits which of the following reactions?

(A) Mn2+ → Mn4+

(B) I2 → I

(C) PbS → PbSO4

(a)  (A), (C) only

(b)  (A) only

(c)  (B) only

(d) (A), (B) only

Answer: (d)

Section-B

21. The solubility of CdSO4 in water is 8.0 × 10–4 mol L–1. Its solubility in 0.01 M H2SO4 solution is ______ × 10–6 mol L–1. (Round off to the Nearest Integer).

(Assume that solubility is much less than 0.01 M)

Answer: (64)

22. The molar conductivities at infinite dilution of barium chloride, sulphuric acid and hydrochloric acid are 280, 860 and 426 S cm2 mol–1 The molar conductivity at infinite dilution of barium sulphate is _____ S cm2 mol–1. (Round off to the Nearest Integer).

Answer: (288)

23. A reaction has a half life of 1 min. The time required for 99.9% completion of the reaction is _____ min. (Round off to the nearest integer) [ Use ln2 = 0.69, ln10 = 2.3]

Answer: (10)

24. The equilibrium constant KC for this reaction is ______ × 10–2. (Round off to the Nearest Integer).

[Use : R = 8.3 J mol–1 K–1, ln 10 = 2.3

log102 = 0.30, 1 atm = 1 bar]

[antilog (– 0.3) = 0.501]

Answer: (2)

25. Consider the below reaction where 6.1 g of benzoic acid is used to get 7.8 g of m-bromo benzoic acid.

The percentage yield of the product is _____

(Round off to the nearest integer)

[Given : Atomic masses : C : 12.0 u, H : 1.0 u, O : 16.0 u, Br : 80.0 u]

Answer: (78)

26. A solute A dimerizes in water. The boiling point of a 2 molal solution of A is 100.52ºC. The percentage association of A is ______. (Round off to the nearest integer.)

[Use : Kb for water = 0.52 K kg mol–1]

Boiling point of water = 100ºC]

Answer: (1)

27. The number of species below that has two lone pairs of electrons in their central atom is ______. (Round off to the Nearest Integer.)

SF4, BF4, CIF3, AsF3, PCl5, BrF5, XeF4, SF6

Answer: (2)

28. 10.0 mL of Na2CO3 solution is titrated against 0.2 M HCl solution. The following litre values were obtained in 5 readings 4.8 mL, 4.9 mL, 5.0 mL, 5.0 mL and 5.0 mL. Based on these readings and the convention of titrimetric estimation the concentration of Na2CO3 solution is ____mM

Answer: (50)

29. In Tollen’s test for aldehyde, the overall number of electron(s) transferred to the Tollen’s reagent formula [Ag(NH3)2]+ per aldehyde group to form silver mirror is ________. (Round off to the Nearest Integer)

Answer: (2)

30. A xenon compound ‘A’ upon partial hydrolysis gives XeO2F2. The number of lone pairs of electrons presents in compound A is ______. (Round off to the Nearest Integer).

Answer: (19)

Mathematics

Section-A

1. Let the system of linear equations

4x + λy + 2z = 0

2x – y + z = 0

μx + 2y + 3z = 0, λ, μ ∈ R

Has a non-trivial solution. Then which of the following is true?

(a)   μ = 6, λ ∈ R

(b)   λ = 2, μ ∈ R

(c)   λ = 3, μ ∈ R

(d)   μ = −6, λ ∈ R

Answer: (a)

2. A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be π/3. If the radius of the circumcircle of △ABC is 2, then the height of the pole is equal to

(a)   1/√3

(b)   √3

(c)   2√3

(d)   2√3/3

Answer: (c)

3. Let in a series of 2n observations, half of them are equal to a and the remaining half are equal to − Also by adding a constant b in each of these observations, the mean and standard deviation of the new set become 5 and 20, respectively. Then the value of a2 + b2 is equal to:

(a)   250

(b)   925

(c)   650

(d)   425

Answer: (4)

4. Let  where f is continuous function in [0, 3] such that  for all t ∈ [0, 1] and  for all t ∈ {1, 3]. The largest possible interval in which g(3) lies is:

(a)   [1, 3]

(b)   [−1, −1/2]

(c)   [−3/2, −1]

(d)   [1/3, 2]

Answer: (d)

5. If 15 sin4 θ + 10 cos4 θ = 6, for some θ ∈ R, then the value of 27 sec6 θ + 8 cosec6 θ is equal to:

(a)   250

(b)   500

(c)   400

(d)   350

Answer: (a)

6. Let f : R − {3} → R − {1] be defined by  Let g : R − R be given as g (x) = 2x − Then, the sum of all the values of x for which f1 (x) + g1 (x) = 13/2 is equal to

(a)   7

(b)   5

(c)   2

(d)   3

Answer: (b)

7. Let S1 be the sum of the first 2n terms of an arithmetic progression. Let S2 be the sum of the first 4n terms of the same arithmetic progression. If (S2 − S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :

(a)   3000  

(b)   7000

(c)   5000

(d)   1000

Answer: (a)

8. Let S1 = x2 + y2 = 9 and S2 = (x − 2)2 + y2 = 1. Then the locus of the centre of a variable circle S which touches S1 internally and S2 externally always passes through the points:

(a)   (1/2, ± √5/2)

(b)   (2, ± 3/2)

(c)   (1, ± 2)

(d)   (0, ± √3)

Answer: (b)

9. Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line x + y = 3. If R and r be the radius of circumcircle and incircle respectively of ΔABC, then (R + r) is equal to

(a)   2√2

(b)   3√2

(c)   7√2

(d)   9/√2

Answer: (d)

10. In a triangle ABC, if vector BC = 8, CA = 7, AB = 10, then the projection of the vector AB on AC is equal to:

(a)   25/4

(b)   85/14

(c)   127/20

(d)   115/16

Answer: (b)

11. Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to:

(a)   80/243

(b)   32/625

(c)   128/625

(d)   40/243

Answer: (b)

12. Let  be two non-zero vectors perpendicular to each other and  then the angle between the vectors  is equal to:

(a)   sin1(1/√3)

(b)   cos1(1/√3)

(c)   sin1(1/√6)

(d)   cos1(1/√2)

Answer: (b)

13. Let a complex number be w = 1 − √3i. Let another complex number z be such that |zw| = 1 and arg (z) − arg (w) = π/2. Then the area of the triangle with vertices origin, z and w is equal to:

(a)   1/2

(b)   4

(c)   2

(d)   1/4

Answer: (a)

14. The area bounded by the curve 4y2 = x2 (4 − x) (x − 2) is equal to:

(a)   3π/2  

(b)   π/16

(c)   π/8

(d)   3π/8

Answer: (a)

15. Define a relation R over a class of n × n real matrices A and B as “ARB if there exists a non-singular matrix P such that PAP1 = B”. Then which of the following is true?

(a)   R is reflexive, symmetric but not transitive

(b)   R is symmetric, transitive but not reflexive

(c)   R is an equivalence relation

(d)   R is reflexive, transitive but not symmetric

Answer: (c)

16. If P and Q are two statements, then which of the following compound statement is a tautology?

(a)   ((P ⇒ Q) ^ ~Q) ⇒ P

(b)   ((P ⇒ Q) ^ ~ Q) ⇒ ~ P

(c)   ((P ⇒ Q) ^ ~ Q)

(d)   ((P ⇒ Q) ^ ~ Q) ⇒ Q

Answer: (b)

17. Consider a hyperbola H : x2 − 2y2 = 4. Let the tangent at a point P (4, √6) meet the x-axis at Q and latus rectum at R (x1, y1), x1 > 0. If F is a focus of H which is nearer to the point P, then the area of ΔQFR is equal to:

(a)   √6 −1

(b)   4√6 −1

(c)   4√6

(d)    

Answer: (d)

18. Let f : R → R be a function defined as

If f is continuous at x = 0, then the value of a + b is equal to

(a)   −2

(b)   −2/5

(c)   −3/2

(d)   −3

Answer: (c)

19. Let y = y (x) be the solution of the differential equation  0 < x < 2.1, with y(2) = 0. Then the value of  at x = 1 is equal to:

(a)     

(b)    

(c)    

(d)    

Answer: (d)

20. Let a tangent be drawn to the ellipse  at (3√3 cos θ, sin θ) where  Then the value of θ such that the sum of intercepts on axes made by a tangent is minimum is equal to:

(a)   π/8

(b)   π/6

(c)   π/3

(d)   π/4

Answer: (b)

Section-B

21. Let P be a plane containing the line and parallel to the line  If the point (1, −1, α) lies on the plane P, then the value of |5α| is equal to __________.

Answer: (38)

22. 

Then the value of α is equal to _________.

Answer: (160)

23. The term independent of x in the expansion of  is equal to ________.

Answer: (210)

24. Let nCr denote the binomial coefficient of xr in the expansion of (1 + x)n. If  α, β ∈ R, then α + β is equal to ________.

Answer: (*)

25. Let P (x) be a real polynomial of degree 3 which vanishes at x = − Let P(x) have local minima at x = 1, local maxima at x = −1 and  then the sum of all the coefficients of the polynomial P (x) is equal to ____________.

Answer: (8)

26. Let the mirror image of the point (1, 3, a) with respect the plane  be (−3, 5, 2). Then, the value of |a + b| is equal to________.

Answer: (1)

27. If f (x) and g (x) are two polynomials such that the polynomial P (x) = f (x3) + x g (x3) is divisible by x2 + x + 1, then P (1) is equal to _______.

Answer: (0)

28. Let I be an identity matrix of order 2 × 2 and Then the value of n ∈ N for which Pn = 5I – 8P is equal to________.

Answer: (6)

29. Let f : R → R satisfy the equation f (x + y) = f (x) . f (y) for all x, y ∈ R and f (x) ≠ 0 for any x ∈ If the function f is differentiable at x = 0 and f’ (0) = 3, then  is equal to ________.

Answer: (3)

30. Let y = y (x) be the solution of the differential equation  with y(1) = 0. If the area bounded by the line x = 1, x = eπ, y = 0 and y = y(x) is αe2π + b, then the value of 10(α + β) is equal to_________.

Answer: (4)

JEE Main Session 2 March 18th Shift 1 Question Paper with Answer Key

Physics

Section-A

1. In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :

(a)  The resonance frequency will increase

(b)  The quality factor will increase

(c)  The quality factor and the resonance frequency will remain constant

(d) The bandwidth of the resonance circuit will increase

Answer: (d)

2. A radioactive sample disintegrates via two independent decay processes having half-livesT1/21 and T1/22 The effective half-life, T1/2 of the nuclei is:

(a)  None of the above

(b)   

(c)   

(d)  

Answer: (d)

3. In the experiment of Ohm’s law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in the resistivity of the conductor is:

(a)  7.5

(b)  3.9

(c)  8.4

(d) 3.0

Answer: (b)

4. An AC source rated 220V, 50 Hz is connected to a resistor. The time taken by the current to change from its maximum to the rms value is:

(a)  0.25 ms

(b)  25 ms

(c)  2.5 ms

(d) 2.5 s

Answer: (c)

5. Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the centre of A is 3 T, the field at the centre of C would be: (Assume that the magnetic field is confined within the volume of the respective solenoid.)

(a)  6T

(b)  12T

(c)  1T

(d) 9T

Answer: (c)

6. A plane electromagnetic wave of frequency 100 MHz is travelling in a vacuum along the x-direction. At a particular point in space and time,   (where,  is unit vector along z-direction). What is  at this point ? (speed of light c = 3 × 108 m/s)

(a)   

(b)   

(c)   

(d)  

Answer: (c)

7. A particle is travelling, 4 times as fast as an electron. Assuming the ratio of the de-Broglie wavelength of a particle to that of the electron is 2:1, the mass of the particle is :

(a)  1/16 times of mass of e

(b)  1/6 times the mass of e

(c)  1/8 times the mass of e

(d) 8 times the mass of e

Answer: (c)

8. What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T? (kB is Boltzmann constant)

(a)  kBT

(b)  (2/3)kB T

(c)  (3/2) kB T

(d) (1/2) kB T

Answer: (d)

9. Your friend is having an eyesight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as:

(a)  Myopia and hypermetropia

(b)  Astigmatism

(c)  Myopia with astigmatism

(d) Presbyopia with astigmatism

Answer: (c)

10. The time period of a simple pendulum is given by  The measured value of the length of the pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 seconds using a clock of 1 s resolution. The percentage accuracy in the determination of ‘g’ using this pendulum is ‘x’. The value of ‘x’ to the nearest integer is.

(a)  5%

(b)  4%

(c)  3%

(d) 2%

Answer: (c)

11. An oil drop of radius 2 mm with a density of 3 g cm–3 is held stationary under a constant electric field 3.55 × 105 V m–1 in Millikan’s oil drop experiment. What is the number of excess electrons that the oil drop will possess? Consider g = 9.81 m/s2.

(a)  1.73 × 1010

(b)  48.8 × 1011

(c)  1.73 × 1012

(d) 17.3 × 1010

Answer: (a)

12. The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is :

(a)  3 T

(b)  9 T

(c)  27 T

(d) 12 T

Answer: (c)

13. A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire

(a)  Loop assumes a circular shape with its plane parallel to field

(b)  Shape of the loop remains unchanged

(c)  Wire gets stretched to become straight

(d) Loop assumes circular shape with its plane normal to the field

Answer: (d)

14. In Young’s double-slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by monochromatic light of 5890 Å is:

(a)  1178 × 106 m

(b)  1178 × 109 m

(c)  5890 × 107 m

(d) 1178 × 1012 m

Answer: (a)

15. Match List – I with List – II

List – I                 

(a) 10 km height over earth’s surface

(b) 70 km height over earth’s surface

(c) 180 km height over earth’s surface

(d) 270 km height over earth’s surface

List-II

(i) Thermosphere

(ii) Mesosphere

(iii) stratosphere

(iv) Troposphere

(a)  (a) – (ii), (b) – (i), (c) – (iv), (d) – (iii)

(b)  (a) – (iv), (b) – (iii), (c) – (ii), (d) – (i)

(c)  (a) – (iii), (b) – (ii), (c) – (i), (d) – (iv)

(d) (a) – (i), (b) – (iv), (c) – (iii), (d) – (ii)

Answer: (b)

16. A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time ‘t’ is proportional to:

(a)  t

(b)  t3/2

(c)  t1/2

(d) t2/3

Answer: (b)

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17. A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ω. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become:

(a)    

(b)   

(c)  

(d)  

Answer: (a)

18. Imagine that the electron in a hydrogen atom is replaced by a muon (μ). The mass of a muon particle is 207 times that of an electron and the charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be:

(a)  27.2 eV

(b)  331.2 eV

(c)  13.6 eV

(d) 2815.2 eV

Answer: (d)

19. The P-V diagram of a diatomic ideal gas system going under cyclic process as shown in the figure. The work done during an adiabatic process CD is (use γ = 1.4):

(a)  200 J

(b)  −500 J

(c)  −400 J

(d) 400 J

Answer: ()

20. The position, velocity and acceleration of a particle moving with constant acceleration can be represented by:

Answer: (a)

Section-B

21. As shown in the figure, a particle of mass 10 kg is placed at point A. When the particle is slightly displaced to its right, it starts moving and reaches point B. The speed of the particle at B is x m/s. (Take g = 10 m/s2).The value of ‘x’ to the nearest integer is _______.

Answer: (10)

22. A parallel plate capacitor has a plate area of 100 m2 and plate separation of 10 m. The space between the plates is filled up to a thickness of 5 m with a material of dielectric constant 10. The resultant capacitance of the system is ‘x’ pF. The value of ε0 = 8.85 × 1012m1. The value of ‘x’ to the nearest integer is _______.

Answer: (161)

23. An NPN transistor operates as a common emitter amplifier with a power gain of 106. The input circuit resistance is 100 Ω and the output load resistance is 10 kΩ. The common-emitter current gain ‘β’ will be ______. (Round off to the nearest integer)

Answer: (100)

24. The voltage across the 10 Ω resistor in the given circuit is x volt.

The value of ‘x’ to the nearest integer is_________.

Answer: (70)

25. Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of the same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b, Then a/b can be expressed as 1/x where x is.

Answer: (32)

26. A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of the bullet before hitting the wood is 10 m/s and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is ‘x’ N. The value of ‘x’ to the nearest integer is

Answer: (10)

27. A ball of mass 10 kg moving with a velocity 10√ 3 m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, the first ball comes to rest while the second ball disintegrates into two equal pieces. One-piece starts moving along the y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30° with respect to the x-axis. The velocity of the ball moving at 30° with x-axis is x m/s. The configuration of pieces after collision is shown in the figure below The value of x to the nearest integer is ______.

Answer: (20)

28. The circuit shown in the figure consists of a charged capacitor of capacity 3 µF and a charge of 30 µC. At time t = 0, when the key is closed, the value of current flowing through the 5M Ω resistor is ‘x’ µA. The value of ‘x’ to the nearest integer is _______.

Answer: (2)

29. A person is swimming with a speed of 10 m/s at an angle of 120° with the flow and reaches to a point directly opposite on the other side of the river. Then the speed of the flow is ‘x’ m/s. The value of ‘x’ to the nearest integer is _____.

Answer: (5)

30. A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is  The value of ‘a’ to the nearest integer is _____.

Answer: (6)

Chemistry

Section-A

1. The ionic radius of Na+ ion is 1.02 Å. The ionic radii (in Å) of Mg2+ and Al3+, respectively are:

(a)  0.72 and 0.54

(b)  0.68 and 0.72

(c)  1.05 and 0.99

(d) 0.85 and 0.99

Answer: (a)

2. Match List-I with List-II:

List-I

(Chemicals)

List-II

(Use/Preparation/Constituent)

(a) Alcoholic potassium hydroxide (i) electrodes in batteries
(b) Pd/BaSO4 (ii) obtained by addition reaction
(c) BHC (Benzene hexachloride (iii) used for β-elimination reaction
(d) Polyacetylene (iv) Lindlar’s Catalyst

 

Choose the most appropriate match:

(a)  (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

(b)  (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

(c)  (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

(d) (a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)

Answer: (d)

3. The statements that are TRUE:

(A) methane leads to both global warming and photochemical smog

(B) methane is generated from paddy fields

(C) methane is a stronger global warming gas than CO2

(D) methane is a part of reducing smog.

Choose the most appropriate answer from the option given below:

(a)  (B), (C), (D) only

(b)  (A), (B), (C) only

(c)  (A), (B), (D) only

(d) (A) and (B) only

Answer: (b)

4. Compound with molecular formula C3H6O can show:

(a)  Both positional isomerism and metamerism

(b)  Metamerism

(c)  Positional isomerism

(d) Functional group isomerism

Answer: (d)

5. Match List-I with List-II:

List-I List-II
(a) Ca(OCl)2 (i) Antacid
(b)   (ii) Cement
(c) CaO (iii) Bleach
(d) CaCO3 (iv) Plasters of Paris

 

Choose the most appropriate answer from the option given below:

(a)  (a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)

(b)  (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)

(c)  (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)

(d) (a)-(i), (b)-(iv), (c)-(iii), (d)-(ii)

Answer: (a)

6. In a binary compound, atoms of element A form a hcp structure and those of element M occupy 2/3 of the tetrahedral voids of the hcp structure. The formula of the binary compound is:

(a)  M2A3

(b)  MA3

(c)  M4A

(d) M4A3

Answer: (d)

7. Match List-I with List-II:

List-I

(Class of Drug)

List-II

(Example)

(a) Antacid (i) Novestrol
(b) Artificial Sweetener (ii) Cimetidine
(c) Antifertility (iii) Valium
(d) Tranquilizers (iv) Alitame

 

Choose the most appropriate answer from the option given below:

(a)  (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)

(b)  (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

(c)  (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)

(d) (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)

Answer: (b)

8. Reagent, 1-naphthylamine and sulfanilic acid in acetic acid is used for the detection of:

(a)  NO

(b)  N2O

(c)  NO3

(d) NO2

Answer: (d)

9. The correct structures of trans-[NiBr2(PPh3)2] and meridional-[Co(NH3)3(NO2)3] respectively are:

Answer: (b)

10. Match List-I with List-II:

List-I                                 List-II

(a) Chlorophyll                  (i) Ruthenium

(b) Vitamin-B12                 (ii) Platinum

(c) Anticancer drug           (iii) Cobalt

(d) Grubbs catalyt             (iv) Magnesium

Choose the most appropriate answer from the option given below:

(a)  (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)

(b)  (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)

(c)  (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

(d) (a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)

Answer: (c)

11. The number of ionisable hydrogens present in the product obtained from a reaction of phosphorus trichloride and phosphonic acid is:

(a)  3

(b)  1

(c)  0

(d) 2

Answer: (d)

12. A certain orbital has no angular nodes and two radial nodes. The orbital is:

(a)  2p

(b)  3p

(c)  2s

(d) 3s

Answer: (d)

13. Consider the above chemical reaction and identity product “A”:

Answer: (c)

14. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R:

Assertion A: During the boiling of water having a temporary hardness, Mg(HCO3)2 is converted to MgCO3.

Reason R: The solubility product of Mg(OH)2 is greater than that of MgCO3.

In the light of the above statements, choose the most appropriate answer from the options given below.

(a)  A is false but R is true

(b)  Both A and R are true and R is the correct explanation of A

(c)  Both A and R are true but R is NOT the correct explanation of A

(d) A is true but R is false

Answer: (a)

15. The chemical is added to reduce the melting point of the reaction mixture during the extraction of aluminium is:

(a)  Cryolite

(b)  Calamine

(c)  Kaolite

(d) Bauxite

Answer: (a)

16. Considering the below chemical reaction, identity the product “X”:

Answer: (c)

17. Considering the below reaction, X and Y respectively are:

Answer: (d)

18. Reaction of Grignard reagent, C2H5MgBr with C8H8O followed by hydrolysis gives compound “A” which reacts instantly with Lucas reagent to give compound B, C10H13 The Compound B is:

Answer: (d)

19. A non-reducing sugar ”A” hydrolyses to give two reducing monosaccharides. Sugar A is:

(a)  Glucose

(b)  Fructose

(c)  Sucrose

(d) Galactose

Answer: (c)

20. Match List-I with List-II:

List-I

(Process)

List-II

(Catalyst)

(a) Deacon’s process (i) ZSM-5
(b) Contact process (ii) CuCl2
(c) Cracking of hydrocarbons (iii) iParticles ’Ni’
(d) Hydrogenation of vegetable oils (iv) V2O5

 

Choose the most appropriate answer from the option given below:

(a)  (a)-(i), (b)-(iii), (c)-(ii), (d)-(iv)

(b)  (a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)

(c)  (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

(d) (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

Answer: (c)

Section-B

21. 2 molal solution of a weak acid HA has a freezing point of 3.885° The degree of dissociation of this acid is _________ × 10–3. (Round off to the Nearest Integer). [Given: Molal depression constant of water = 1.85 K kg mol–1Freezing point of pure water = 0°C]

Answer: (50)

22. The total number of unpaired electrons present in the complex K3[Cr(oxalate)3] is _______.

Answer: (3)

23. AX is a covalent diatomic molecule where A and X are second-row elements of the periodic table. Based on Molecular orbital theory, the bond order of AX is 2.5. The total number of electrons in AX is __________. (Round off to the Nearest Integer).

Answer: (15)

24. ___________ grams of 3-Hydroxy propanal (MW = 74) must be dehydrated to produce 7.8 g of acrolein (MW = 56) (C3H4O) if the percentage yield is 64. (Round off to the Nearest Integer).

[Given: Atomic masses: C : 12.0 u, H : 1.0 u, O : 16.0 u]

Answer: (16)

25. A reaction of 0.1 mole of Benzyl amine with bromomethane gave 23 g of Benzyl trimethyl ammonium bromide. The number of moles of bromomethane consumed in this reaction are n × 10–1, when n = ___________ . (Round off to the Nearest Integer). [Given: Atomic masses: C: 12.0 u, H : 1.0 u, N : 14.0 u, Br : 80.0 u]

Answer: (3)

26. 2NO (g) + Cl2 (g) → 2 NOCl (s): This reaction was studied at – 10°C and the following data was obtained.

Run           [NO]0              [Cl2]0               r0

1                0.10                 0.10                 0.18

2                0.10                 0.20                 0.35

3                0.20                 0.20                 1.40

[NO]0 and [Cl2]0 are the initial concentrations and r0 is the initial reaction rate. The overall order of the reaction is _________. (Round off to the Nearest Integer).

Answer: (3)

27. For the reaction: 2Fe3+ (aq) + 2I (aq) → 2Fe2+ (aq) + I2(s)

The magnitude of the standard molar free energy change, ΔrGm° = – _______ kJ (Round off the Nearest Integer).

Answer: (45 kJ)

28. For the reaction: C2H6→ C2H4 + H2: The reaction enthalpy ΔrH = __________ kJ mol–1. (Round off to the Nearest Integer).

[Given: Bond enthalpies in kJ mol–1; C – C: 347, C = C : 611; C – H : 414; H – H ; 436]

Answer: (131 kJ/mol)

29. In order to prepare a buffer solution of pH 5.74, sodium acetate is added to acetic acid. If the concentration of acetic acid in the buffer is 1.0 M, the concentration of sodium acetate in the buffer is _________ M. (Round off to the Nearest Integer).

[Given: pKa (acetic acid) = 4.74]

Answer: (10)

30. Complete combustion of 3 g of ethane gives x × 1022 molecules of water. The value of x is ________. [Round off to the Nearest Integer].

[Use: NA = 6.023 × 1023; Atomic masses in u : C : 12.0; O : 16.0 : H : 1.0 ]

Given: 18

Answer: (18)

Mathematics

Section-A

1. If the functions are defined as f(x) = √x and  then what is the common domain of the following functions: f + g, f – g, f / g, g / f, g – f where (f ± g) (x) = f (x) ± g (x), (f / g) (x) =

(a)   0 < x ≤ 1

(b)   0 ≤ x < 1

(c)   0 ≤ x ≤ 1

(d)   0 < x < 1

Answer: (d)

2. Let α, β, γ be the roots of the equations, x3 + ax2 + bx + c = 0, (a, b, c ∈ R and a, b and a, b ≠ 0). The system of the equations (in u, v, w) given by αu + βv + γw = 0; βu + γv + αw = 0; γu + αv + βw = 0 has non-trivial solutions, then the value of a2/b is

(a)   5

(b)   1

(c)   0

(d)   3

Answer: (d)

3. If the equation a  represents a circle where a, d are real constants, then which of the following condition is correct?

(a)   |α|2 − ad ≠ 0

(b)   |α|2 − ad > 0 and a ∈ R − {0}

(c)   α = 0, a, d ∈ R+

(d)   |α|2 − ad ≥ 0 and a ∈ R

Answer: (b)

4. is equal to:

(a)   101/404

(b)   101/408

(c)   99/400

(d)   25/101

Answer: (d)

5. The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:

(a)   3

(b)   2

(c)   1

(d)   0

Answer: (b)

6. The solutions of the equation  (0 < x < π), are:

(a)   π/6, 5π/6

(b)   7π/12, 11π/12

(c)   5π/12, 7π/12

(d)   π/12, π/6

Answer: (b)

7. If  is differentiable at every point of the domain, then the values of a and b are respectively:

(a)   5/2, −3 / 2

(b)   −1/2, 3/2

(c)   1/2, 1/2

(d)   1/2, −3/2

Answer: (b)

8. A vector a has components 3p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counterclockwise sense. If with respect to the new system, a has components p + 1 and √10, then a value of p is equal to:

(a)   1

(b)   −1

(c)   4/5

(d)   −5/4

Answer: (b)

9. The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is:

(a)   26664

(b)   122664

(c)   122234

(d)   22264

Answer: (a)

10. Choose the correct statement about two circles whose equations are given below:

x2 + y2 – 10x – 10y + 41 = 0

x2 + y2 – 22x – 10y + 137 = 0

(a)   circles have no meeting point

(b)   circles have two meeting points

(c)   circles have only one meeting point

(d)   circles have the same centre

Answer: (c)

11. If α, β are natural numbers such that 100α – 199β = (100) (100) + (99) (101) + (98) (102) + …. + (1) (199), then the slope of the line passing through (α, β) and origin is:

(a)   510

(b)   550

(c)   540

(d)   530

Answer: (b)

12. The value of  is equal to:

(a)   3 + 2√3

(b)   4 + √3

(c)   2 + √3

(d)   1.5 + √3

Answer: (d)

13. The integral  is equal to:

(where c is a constant of integration)

(a)    

(b)    

(c)    

(d)    

Answer: (b)

14. The differential equations satisfied by the system of parabolas y2 = 4a (x + a) is:

(a)    

(b)    

(c)    

(d)     

Answer: (b)

15. The real-valued function  where [x] denotes the greatest integer less than equal to x, is defined for all x belonging to:

(a)   all non- integers except the interval [–1, 1]

(b)   all integers except 0, –1, 1

(c)   all reals except integers

(d)   all reals except the interval [–1, 1]

Answer: (a)

16. If  is equal to L, then the value of (6L + 1) is :

(a)   1/2

(b)   2

(c)   1/6

(d)   6

Answer: (b)

17. For all four circles M, N, O and P, the following four equations are given:

Circle M : x2 + y2 = 1

Circle N : x2 + y2 – 2x = 0

Circle O : x2 + y2 – 2x – 2y + 1 = 0

Circle P : x2 + y2 –2y = 0

If the centre of circle M is joined with the centre of the circle N, further centre of circle N is joined with the centre of the circle O, centre of circle O is joined with the centre of circle P and lastly, the centre of circle P is joined with the centre of circle M, then these lines form the sides of a:

(a)   Rectangle

(b)   Square

(c)   Parallelogram

(d)   Rhombus

Answer: (b)

18. Let (1 + x + 2x2)20 = a0 + a1x + a2x2 + …… + a40x40. Then, a1 + a3 +a5 + ….+ a37 is equal to

(a)   220(220 + 21)

(b)   219(220 + 21)

(c)   220(220 – 21)

(d)   219(220 – 21)

Answer: (d)

19. Let  and  If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) – Tr(B) has value equal to:

(a)   0

(b)   1

(c)   3

(d)   2

Answer: (d)

20. The equations of one of the straight lines which pass through the point (1, 3) and make an angle tan1 √2 with the straight line, y + 1 = 3√2x is:

(a)   5√2x + 4y − 15 + 4√2 = 0

(b)   4√2x – 5y − 5 + 4√2 = 0

(c)   4√2x + 5y − 4√2 = 0

(d)   4√2x + 5y − (15 + 4√2) = 0

Answer: (d)

Section-B

21. The number of times digit 3 will be written when listing the integers from 1 to 1000 is ______.

Answer: (300)

22. The equation of the planes parallel to the plane x – 2y + 2z – 3 = 0 which are at unit distance from the point (1, 2, 3) is ax + by + cz + d = 0. If (b – d) = K (c – a), then the positive value of K is ______.

Answer: (4)

23. Let f (x) and g (x) be two functions satisfying f (x2) + g (4 – x) = 4x3 and g (4 –x) + g(x) = 0, then the value of is__________.

Answer: (512)

24. The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is ______.

Answer: (35)

25. A square ABCD has all its vertices on the curve x2y2 = 1. The midpoints of its sides also lie on the same curve. Then, the square of the area of ABCD is ______.

Answer: (80)

26. The missing value in the following figure is ______.

Answer: (4)

27. The numbers of solutions of the equation  in the interval [0, 2π] is _______.

Answer: (1)

28. Let z1, z2 be the roots of the equations z2 + az + 12 = 0 and z1, z2 form an equilateral triangle with origin. Then, the value of |a| is ______.

Answer: (6)

29. Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, –3, 1) and (2, 3, –5) at the right angles. If a, b, c, d are integers, then the minimum value of (a2 + b2 + c2 +d2) is ______.

Answer: (28)

30. If  f (0) = 0 and  then the value of K is ________.

Answer: (4)

JEE Main Session 2 March 17th Shift 2 Question Paper with Answer Key

Physics

Section-A

1. Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K. A third block C of mass m moving with a speed v along the line joining A and B collides elastically with A. The maximum compression in the spring is

(a) 

(b) 

(c) 

(d) 

Answer: (d)

2. A solid sphere of mass 2 kg radius 0.5m is rolling with an initial speed of 1 ms1 goes up an inclined plane which makes an angle of 300 with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A?

(a)  0.80 s

(b)  0.60 s

(c)  0.52 s

(d) 0.57 s

Answer: (d)

3. If one mole of a polyatomic gas has two vibrational modes and β is the ratio of molar specific heats for polyatomic gas β=Cp/ Cv then the value of β is :

(a)  1.35

(b)  1.02

(c)  1.25

(d) 1.2

Answer: (d)

4. Two cells of emf 2E and E with internal resistance r1 and r2 respectively are connected in series to an external resistor R (see figure). The value of R, at which the potential difference across the terminals of the first cell becomes zero is

(a)  r­1 – r2

(b)  r1 + r2

(c) 

(d) 

Answer: (d)

5. A sound wave of frequency 245 Hz travels with a speed of 300 ms1 along the positive x-axis. Each point of the medium moves to and fro through a total distance of 6 cm. What will be the mathematical expression of the travelling wave?

(a)  Y (x, t) = 0.03 [ sin 5.1x − (0.2 x 103)t]

(b)  Y (x, t) = 0.06 [ sin 5.1x − (1.5 x 103)t]

(c)  Y (x, t) = 0.06 [ sin 0.8x − (0.5 x 103)t]

(d) Y (x, t) = 0.03 [ sin 5.1x − (1.5 x 103)t]

Answer: (d)

6. A carrier signal C(t) = 25 sin (2.512 × 1010t) is amplitude modulated by a message signal m(t)= 5 sin (1.57 × 108t) and transmitted through an antenna. What will be the bandwidth of the modulated signal?

(a)  1987.5 MHz

(b)  2.01 GHz

(c)  50 MHz

(d) 8 GHz

Answer: (c)

7. Two particles A and B of equal masses are suspended from two massless springs of spring constants K1 and K2 If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is :

(a) 

(b) 

(c) 

(d) 

Answer: (c)

8. Match List I with List II

List I List II
(a) Phase difference between current and voltage in a purely resistive AC circuit (i) 𝜋/2, current leads voltage
(b) Phase difference between current and voltage in a pure inductive AC circuit (ii) zero
(c) Phase difference between current and voltage in a pure capacitive AC circuit (iii) 𝜋/2, current lags voltage
(d) Phase difference between current and voltage in an LCR series circuit (iv) 

Choose the most appropriate answer from the options given below :

(a)  (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)

(b)  (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)

(c)  (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)

(d) (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)

Answer: (d)

9. A geostationary satellite is orbiting around an arbitrary planet ‘P’ at a height of 11R above the surface of ‘P’, R being the radius of ‘P’. The time period of another satellite in hours at a height of 2R from the surface of ‘P’ is _____. ‘P’ has a time period of rotation of 24 hours.

(a)  6/√2

(b)  3

(c)  6√2

(d) 5

Answer: (d)

10. The velocity of a particle is v=v0 + gt + Ft2. Its position is x = 0 at t = 0; then its displacement after time (t = 1) is :

(a) 

(b)  v0 + 2g + 3f

(c)  v0 + g + F

(d) 

Answer: (d)

11. A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12 cm. After 2 minutes the amplitude decreases to 6 cm. Determine the value of the damping constant for this motion. (take ln 2 = 0.693).

(a)  3.3 × 102 kg s1

(b)  5.7 × 103 kg s−1

(c)  1.16 × 102 kg s−1

(d) 0.69 × 102 kg s−1

Answer: (c)

12. An object is located 2 km beneath the surface of the water. If the fractional compression ∆V/V is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ……..

[Given: density of water is 1000 kgm–3 and g= 9.8 ms–2]

(a)  2.26 ×109 Nm2

(b)  1.96 ×109 Nm2

(c)  1.44 ×107 Nm2

(d) 1.44 ×109 Nm2

Answer: (d)

13. Two identical photocathodes receive the light of frequencies f1 and f2 If the velocities of the photo-electrons coming out are v1 and v2 respectively, then

(a) 

(b) 

(c) 

(d) 

Answer: (d)

14. The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra lie in the visible region?

(a)  Balmer series

(b)  Lyman series

(c)  Brackett series

(d) Paschen series

Answer: (a)

15. Which one of the following will be the output of the given circuit?

(a)  NAND Gate

(b)  AND Gate

(c)  XOR Gate

(d) NOR Gate

Answer: (c)

16. The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15 resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 V is maintained across AC.

(a)  4.87 mA

(b)  4.87 μA

(c)  2.44 μA

(d) 2.44 mA

Answer: (a)

17. Which one is the correct option depicting the two different thermodynamic processes?

(a)  (c) and (d)

(b)  (b) and (c)

(c)  (a) only

(d) (c) and (a)

Answer: (a)

18. A hairpin-like shape as shown in the figure is made by bending a long current-carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?

(a) 

(b) 

(c) 

(d) 

Answer: (b)

19. A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to (81/100) of the height through which it falls. Find the average speed of the ball. (Take g=10 ms2)

(a)  2.50 ms1

(b)  3.50 ms1

(c)  3.0 ms1

(d) 2.0 ms1

Answer: (a)

20. What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

(a)  Both, including reactance and current, will be doubled

(b)  Both, inductive reactance and current will be halved

(c)  Inductive reactance will be halved and current will be doubled

(d) Inductive reactance will be doubled and current will be halved

Answer: (c)

Section-B

21. The electric field intensity produced by the radiation coming from a 100 W bulb at a distance of 3 m is E. The electric field intensity produced by the radiation coming from 60 W at the same distance is  Where the value of x = ________

Answer: (3)

22. The image of an object placed in the air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at 2nd/3 of the distance of the object from the surface. The wavelength of light inside the surface is 2/3 times the wavelength in air, The radius of the curved surface is x/13 m. The value of ‘x’ is _____

Answer: (30)

23. A 2μF capacitor C1 is first charged to a potential difference of 10V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C2 of 8 μF. The charge in C2 on equilibrium condition is ________ μC. (Round off to the Nearest Integer)

Answer: (16)

24. A particle of mass m moves in a circular orbit in a central potential field U(r) =U0r4. If Bohr’s quantization conditions are applied, radii of possible orbital rn vary with n1/α, where α is _____

Answer: (3)

25. The electric field in a region is given by  with  The flux of this field through a rectangular surface are 0.4 m2 parallel to Y-Z plane is _______Nm2C1.

Answer: (640)

26. A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction 1/√3. It is desired to make the body move by applying the minimum possible force F N. The value of F will be __________. (Round off to the Nearest Integer)

[Take g = 10 ms2]

Answer: (5)

27. Seawater at a frequency f = 9 × 102 Hz, has permittivity ∈ = 80∈0 and resistivity ρ = 0.25 Ωm. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source V(t) = V0 sin(2πft). Then the conduction current density becomes 10x times the displacement current density after time t= 1800. The value of x is __________.

(Given : )

Answer: (6)

28. The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position  x is _____(Round off to the Nearest Integer) [a is an area as shown in the figure)

Answer: (4)

29. Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm3 of oleic acid per cm3 of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm2 by considering 100 spherical drops of radius  Then the thickness of the oleic acid layer will be x × 1014 m where x is _________.

Answer: (25)

30. A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is ________N. (Round off to the Nearest Integer)

[Take g = 10 ms2]

Answer: (30)

Chemistry

Section-A

1. Match List-I with List-II.

List-I                                                         List-II

Chemical Compound                                Used as

(a) Sucralose                                              (i) Synthetic detergent

(b) Glyceryl ester of stearic acid               (ii) Artificial sweetener

(c) Sodium benzoate                                 (iii) Antiseptic

(d) Bithionol                                             (iv) Food preservative

Choose the correct match:

(a)  (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)

(b)  (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

(c)  (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

(d) (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)

Answer: (b)

2. In the below reactions, enzyme A and enzyme B respectively are:

(a)  Invertase and Amylase

(b)  Amylase and Invertase

(c)  Invertase and Zymase

(d) Zymase and Invertase

Answer: (c)

3. The correct pair(s) of the ambident nucleophiles is (are):

(A) AgCN/KCN

(B) RCOOAg/RCOOK

(C) AgNO2/KNO2

(D) AgI/KI

(a)  (A) and (C) only

(b)  (B) only

(c)  (B) and (C) only

(d) (A) only

Answer: (a)

4. During which of the following processes, does entropy decrease?

(A) Freezing of water to ice at 0°C

(B) Freezing of water to ice at -10°C

(C) N2(g) + 3H2(g) →2NH3(g)

(D) Adsorption of CO(g) on lead surface.

(E) Dissolution of NaCI in water

(a)  (A), (B), (C) and (D) only

(b)  (A), (C) and (E) only

(c)  (A) and (E) only

(d) (B) and (C) only

Answer: (a)

5. Match List-I with List-II:

List – I                                          List – II

(a) [Co(NH3)6] [Cr(CN)6]              (i) Linkage isomerism

(b) [Co(NH3)3 (NO2)3]                  (ii) Solvate isomerism

(c) [Cr(H2O)6]Cl3              (iii) Coordination isomerism

(d) cis-[CrCl2(ox)2]3        (iv) Optical isomerism

Choose the correct answer from the options given below:

(a)  (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)

(b)  (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)

(c)  (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)

(d) (a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)

Answer: (a)

6. The common positive oxidation states for an element with atomic number 24, are

(a)  +1 and +3

(b)  +1 to +6

(c)  +1 and +3 to +6

(d) +2 to +6

Answer: (d)

7. The set of elements that differ in a mutual relationship from those of the other sets is:

(a)  Be – Al

(b)  Li – Na

(c)  B – Si

(d) Li – Mg

Answer: (b)

8. Given below are two statements:

Statement I: 2-methyl butane on oxidation with KMnO4 gives 2-methyl butane-2-ol.

Statement II: n-alkanes can be easily oxidized to corresponding alcohols with KMnO4.

Choose the correct option:

(a)  Both statement I and statement II are incorrect

(b)  Statement I is correct but statement II is incorrect

(c)  Both statement I and statement II are correct

(d) Statement I is incorrect but statement II is correct

Answer: (b)

9. Amongst the following, the linear species is:

(a)  N3

(b)  Cl2O

(c)  O3

(d) NO2

Answer: (a)

10. For the coagulation of a negative sol, the species below, that has the highest flocculating power is:

(a)  SO42

(b)  Na+

(c)  Ba2+

(d) PO43

Answer: (c)

11. The functional groups that are responsible for the ion-exchange property of cation and anion exchange resins, respectively, are:

(a)  –SO3H and –COOH

(b)  –SO3H and –NH2

(c)  –NH2 and –SO3H

(d) –NH2 and –COOH

Answer: (b)

12. Choose the correct statement regarding the formation of carbocations A and B given.

(a)  Carbocation A is more stable and formed relatively at a faster rate

(b)  Carbocation B is more stable and formed relatively at a faster rate

(c)  Carbocation A is more stable and formed relatively at a slow rate

(d) Carbocation B is more stable and formed relatively at a slow rate

Answer: (b)

13. In the below reaction, the structural formula of (A), “X” and “Y” respectively are:

Answer: (b)

14. Fructose is an example of:

(a)  Heptose

(b)  Aldohexose

(c)  Pyranose

(d) Ketohexose

Answer: (d)

15. Which of the following statement(s) is (are) the incorrect reason for eutrophication?

(A) excess usage of fertilisers

(B) excess usage of detergents

(C) dense plant population in water bodies

(D) lack of nutrients in water bodies that prevent plant growth

Choose the most appropriate answer from the option given below:

(a)  (D) only

(b)  (C) only

(c)  (B) and (D) only

(d) (A) only

Answer: (a)

16. Primary, secondary and tertiary amines can be separated using:

(a)  Para-Toluene sulphonyl chloride

(b)  Chloroform and KOH

(c)  Acetyl amide

(d) Benzene sulphonic acid

Answer: (a)

17. Match List-I with List-II

List-I                                 List-II

(a) Haematite                    (i) Al2O3. xH2O

(b) Bauxite                        (ii) Fe2O3

(c) Magnetite                     (iii) CuCO3. Cu(OH)2

(d) Malachite                     (iv) Fe3O4

Choose the correct answer from the options given below:

(a)  (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)

(b)  (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)

(c)  (a)-(i), (b)-(iii), (c)-(ii), (d)-(iv)

(d) (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

Answer: (d)

18. The set that represents the pair of neutral oxides of nitrogen is:

(a)  NO and N2O

(b)  NO and NO2

(c)  N2O and NO2

(d) N2O and N2O3

Answer: (a)

19. Nitrogen can be estimated by Kjeldahl’s method for which of the following compound?

Answer: (d)

20. One of the by-products formed during the recovery of NH3 from Solvay process is:

(a)  NaHCO3

(b)  Ca(OH)2

(c)  CaCl2

(d) NH4Cl

Answer: (c)

SECTION – B

21. The reaction 2A + B2→ 2AB is an elementary reaction. For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of 3, the rate of the reaction increases by a factor of ……………. (Round off to the Nearest Integer).

Answer: (27)

22. In the ground state of atomic Fe (Z = 26), the spin-only magnetic moment is ……………..x 101 (Round off to the Nearest Integer).

[Given: √3 = 1.73, √2 = 1.41]

Answer: (49)

23. Consider the below-given reaction. The percentage yield of an amide product is ………………. (Round off to the Nearest Integer). [Given: Atomic mass: C: 12.0 u, H : 1.0 u, N : 14.0, O : 16.0 u, Cl : 35.5 u]

Answer: (77)

24. On complete reaction of FeCl3 with oxalic acid in an aqueous solution containing KOH, resulted in the formation of product A. The secondary valency of Fe in the product A is …………..(Round off to the Nearest Integer)

Answer: (6)

25. Consider the reaction N2O4 (g) ⇌ 2NO2 (g). The temperature at which KC = 20.4 and KP = 600.1, is …………………. K. (Round off to the Nearest Integer). [Assume all gases are ideal and R = 0.0831 L bar K1 mol1]

Answer: (354)

26. A KCl solution of conductivity 0.14 S m-1 shows a resistance of 4.19 Ω in a conductivity cell. If the same cell is filled with an HCl solution, the resistance drops 1.03 Ω. The conductivity of the HCl solution is ……………….. × 102 S m1. (Round off to the Nearest Integer).

Answer: (56)

27. A 1 molal K4Fe(CN)6 solution has a degree of dissociation of 0.4. Its boiling point is equal to that of another solution which contains 18.1 weight per cent of a nonelectrolyte solute A. The molar mass of A is …………… g/mol. (Round off to the Nearest Integer).

Answer: (85)

28. The number of chlorine atoms in 20 mL of chlorine gas at STP is ………1021. (Round off to the Nearest Integer).

[Assume chlorine is an ideal gas at STP

R=0.083 L bar mol1 K1, NA = 6.023 × 1023]

Answer: (1)

29. KBr is doped with 105 mole per cent of SrBr2. The number of cationic vacancies in 1 g of KBr crystal is ……… 1014. (Round off to the Nearest Integer).

[Atomic Mass: K = 39.1 u, Br = 79.9 u, NA = 6.023 × 1023]

Answer: (5)

30 The total number of C–C sigma bond/s in mesityl oxide (C6H10O) is …… (Round off to the Nearest Integer).

Answer: (5)

Mathematics

Section-A

1. If the Boolean expression (p ∧ q) ⍟ (p ⊗ q) is a tautology, then ⍟ and ⊗ are respectively given by :

(a)  ∧, →

(b)  →, →

(c)  ∨, →

(d) ∧, ∨

Answer: (b)

2. Let the tangent to the circle x2 + y2 = 25 at the point R (3, 4) meet the x-axis and y-axis at points P and Q, respectively. If r is the radius of the circle passing through the origin O and having a centre at the incentre of the triangle OPQ, then r2 is equal to:

(a)  625/72

(b)  585/66

(c)  125/72

(d) 529/64

Answer: (a)

3. Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with a probability of occurrence of 0 at even places be 1/2 and probability of occurrence of 0 at the odd place be 1/3. Then the probability that ‘10’ is followed by ‘01’ is equal to :

(a)  1/6

(b)  1/18

(c)  1/9

(d) 1/3

Answer: (c)

4. The number of solutions of the equation x + 2 tan x = π/2 in the interval [0, 2π] is :

(a)  5

(b)  2

(c)  4

(d) 3

Answer: (d)

5. If the equation of the plane passing through the mirror image of a point (2, 3, 1) with respect to line  and containing the line  is ɑx + βy + γz = 24, then, then ɑ + β + γ is equal to:

(a)  21

(b)  19

(c)  18

(d) 20

Answer: (b)

6. Consider the function f : R → R defined by  Then f is

(a)  monotonic on (0, ∞) only

(b)  Not monotonic on (–∞, 0) and (0, ∞)

(c)  monotonic on (–∞, 0) only

(d) monotonic on (–∞, 0) ⋃ (0, ∞)

Answer: (b)

7. Let O be the origin. Let  x, y ∈ R, x > 0, be such that |PQ| = √20 and the vector   is perpendicular to If  z ∈ R, is coplanar with  then the value of x2 + y2 + z2 is equal to:

(a)  2

(b)  9

(c)  1

(d) 7

Answer: (b)

8. Let L be a tangent line to the parabola y2 = 4x – 20 at (6, 2). If L is also a tangent to the ellipse  then the value of b is equal to:

(a)  20

(b)  14

(c)  16

(d) 11

Answer: (b)

9. Let f : R → R be defined as f (x) = e–x sin x. If F : [0,1] R→ is a differentiable function such that  then the value of  lies in the interval

(a)  [330/360, 331/360]

(b)  [327/360, 329/360]

(c)  [331/360, 334/360]

(d) [335/360, 336/360]

Answer: (a)

10. If x, y, z are in arithmetic progression with common difference d, x ≠ 3d, and the determinant of the matrix  is zero, then the value of k2 is :

(a)  6

(b)  36

(c)  72

(d) 12

Answer: (c)

11. If the integral  where ɑ, β, γ are integers and [x] denotes the greatest integer less than or equal to x, then the value of ɑ + β + γ is equal to:

(a)  20

(b)  0

(c)  25

(d) 10

Answer: (b)

12. Let y = y (x) be the solution of the differential equation cos x (3 sin x + cos x + 3) dy = (1 + y sin x (3 sin x + cos x + 3)) dx, 0 ≤ x ≤ π/2, y(0) = 0. Then, y (π/3) is equal to :

(a)   

(b)   

(c)   

(d)  

Answer: (a)

13. The value of the limit  is equal to:

(a)  −1/2

(b)  −1/4

(c)  0

(d) 1/4

Answer: (a)

14. If the curve y = y(x) is the solution of the differential equation 2 (x2 + x5/4) dy − y (x + x1/4) dx = 2x9/4 dx, x > 0 which passes through the point  then the value of y(16) is equal to:

(a)   

(b)    

(c)   

(d)  

Answer: (d)

15. Let S1, S2 and S3 be three sets defined as S1 = {z ∈ C : |z – 1| ≤ √2}, S2 = {z ∈ C : Re ((1 – i) z) ≥ 1}, S3 = {z ∈ C : Im (z) ≤ 1}. Then the set S1 ⋂ S2 ⋂ S3

(a)  has infinitely many elements

(b)  has exactly two elements

(c)  has exactly three elements

(d) is a singleton

Answer: (a)

16. If the sides AB, BC, and CA of a triangle ABC have, 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices is equal to:

(a)  360

(b)  240

(c)  333

(d) 364

Answer: (c)

17. The value of   where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to:

(a)  0

(b)  r

(c)  r/2

(d) 2r

Answer: (c)

18. The value of The value of  is equal to:

(a)  1124

(b)  924

(c)  1324

(d) 1024

Answer: (b)

19. Two tangents are drawn from a point P to the circle x2 + y2 – 2x – 4y + 4 = 0, such that the angle between these tangents is If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of △PAB and △CAB is :

(a)  11 : 4

(b)  9 : 4

(c)  2 : 1

(d) 3 : 1

Answer: (b)

20. The number of solutions of the equation  and [x] denotes the greatest integer less than or equal to x, is:

(a)  0

(b)  2

(c)  4

(d) Infinite

Answer: (a)

Section-B

21. Let the coefficients of third, fourth and fifth terms in the expansion of  be in the ratio 12:8:3. Then the term independent of x in the expansion is equal to ………

Answer: (4)

22. Let  such that AB = B and a + d = 2021, then the value of ad-bc is equal to …………….

Answer: (2020)

23. Let f : [–1,1] → R be defined as f (x) = ax2 + bx + c for all x ∈ [–1, 1], where a, b, c ∈ R such that f (–1) = 2, f’ (–1) = 1 and for x ∈ [–1, 1] the maximum value of f’’ (x) is 1/2. If f (x) ≤ ɑ, x ∈ [–1, 1], then the least value of ɑ is equal to …………… .

Answer: (5)

24. Let where n ∈ If (20)I10 = αI9 + βIB, for natural numbers α and β, then α – β equal to ………………… .

Answer: (1)

25. Let f : [−3, 1] → R be given as

If the area bounded by y = f(x) and x-axis is A, then the value of 6A is equal to …………… .

Answer: (41)

26. Let  be a vector in the plane containing vectors  If the vector is perpendicular to   and its projection on  then the value of  is equal to ……………… .

Answer: (486)

27. Consider a set of 3n numbers having variance 4. In this set, the mean of the first 2n numbers is 6 and the mean of the remaining n numbers is 3. A new set is constructed by adding 1 into each of the first 2n numbers and subtracting 1 from each of the remaining n numbers. If the variance of the new set is k, then 9k is equal to ………………..

Answer: (68)

28. If 1, log10(4x – 2) and  are in arithmetic progression for a real number x, then the value of the determinant  is equal to:

Answer: (2)

29. Let P be an arbitrary point having the sum of the squares of the distances from the planes x + y + z = 0, lx – nz = 0 and x – 2y + z = 0, equal to 9. If the locus of the point P is x2 + y2 +z2 = 9, then the value of l – n is equal to ………………

Answer: (0)

30. Let tan α, tan β and tan γ;  be the slopes of three-line segment OA, OB and OC, respectively, where O is the origin. If the circumcentre of ∆ABC coincides with the origin and its orthocentre lies on the y-axis, then the value of  is equal to

Answer: (144)

JEE Main Session 2 March 17th Shift 1 Question Paper with Answer Key

Physics

Section-A

1. The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it was noted that ‘o’ on the vernier scale lies between 8.5 cm and 8.6 cm, vernier coincidence is 6, then the correct value of the measurement is ……………………. cm. (least count = 0.01 cm)

(a)  8.36 cm

(b)  8.56 cm

(c)  8.58 cm

(d) 8.54 cm

Answer: (d)

2. For what value of displacement do the kinetic energy and potential energy of a simple harmonic oscillation become equal?

(a)  x = A/2

(b)  x = 0

(c)  x = ±A

(d) x = ± A/√2

Answer: (d)

3. An electron of mass m and a photon have the same energy E. The ratio of the wavelength of an electron to that of the photon is : (c being the velocity of light)

(a)  (E/2m)1/2

(b)   

(c)  c(2mE)1/2

(d)  

Answer: (b)

4. A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate to come to rest. If the total time elapsed is t seconds, the total distance travelled is :

(a)    

(b)   

(c)   

(d)  

Answer: (a)

5. A Carnot’s engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

(a)  1800 J

(b)  3200 J

(c)  2400 J

(d) 1600 J

Answer: (c)

6. A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with the steady speed in a circular path of constant radius. Assume that the system is in a steady circular motion with constant angular velocity ω. The angular momentum of M about point A is LA which lies in the positive z-direction and the angular momentum of M about point B is LB. The correct statement for this system is:

(a)  LA and LB are both constant in magnitude and direction

(b)  LB is constant, both in magnitude and direction

(c)  LA is constant, both in magnitude and direction

(d) LB is constant in direction with varying magnitude

Answer: (c)

7. Two ideal polyatomic gases at temperatures T1 and T2 are mixed so that there is no loss of energy. If F1 and F2, m1 and m2, n1 and n2 be the degrees of freedom, masses, the number of molecules of the first and second gas respectively, the temperature of the mixture of these two gases is :

(a)   

(b)   

(c)   

(d)  

Answer: (a)

8. The output of the given combination gates represents :

(a)  XOR Gate

(b)  NOR Gate

(c)  NAND Gate

(d) AND Gate

Answer: (c)

9. A triangular plate is as shown. A force is  applied at point P. The torque at point P with respect to point ‘O’ and ‘Q’ are :

(a)  15 – 20√3, 15 + 20√3

(b)  15 + 20√3, 15 – 20√3

(c)  –15 + 20√3, 15 + 20√3

(d) –15–20√3, 15 – 20√3

Answer: (d)

10. A modern grand-prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is μs, then the magnitude of negative lift F1acting downwards on the car is : (Assume forces on the four tyres are identical and g = acceleration due to gravity)

(a)   

(b) 

(c)   

(d)  

Answer: (a)

11. The thickness at the centre of a plano-convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 × 108 mm1. The focal length of the lens kept in the air is ______.

(a)  0.30 cm

(b)  1.5 cm

(c)  15 cm

(d) 30 cm

Answer: (d)

12. If an electron is moving in the nth orbit of the hydrogen atom, then its velocity (vn) for the nth orbit is given as :

(a)  vn ∝ n

(b)    

(c)  vn ∝ n2

(d)   

Answer: (d)

13. An AC current is given by I = I1 sin ωt + I2 cos ωt. A hot wire ammeter will give a reading :

(a)    

(b)   

(c)    

(d)  

Answer: (b)

14. Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combination is :

(a)   

(b)   

(c)    

(d)  

Answer: (a)

15. A boy releases a 0.5 kg ball on the frictionless floor with the speed of 20 ms1. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now ?

(a)  14.41 ms1

(b)  1.00 ms1

(c)  19.0 ms1

(d) 4.47 ms1

Answer: (d)

16. A polyatomic ideal gas has 24 vibrational modes. What is the value of γ?

(a)  1.03

(b)  1.30

(c)  10.3

(d) 1.37

Answer: (a)

17. A current of 10 A exists in a wire of cross-sectional area of 5 mm2 with a drift velocity of 2 × 103 ms1. The number of free electrons in each cubic meter of the wire is ________

(a)  1 × 1023

(b)  2 × 106

(c)  2 × 1025

(d) 625 × 1025

Answer: (d)

18. A solenoid of 1000 turns per metre has a core with a relative permeability of 500. Insulated windings of the solenoid carry an electric current of 5 A. The magnetic flux density produced by the solenoid is: (Permeability of free space = 4 × 107 H/m)

(a)  2 × 103 πT

(b)  π/5

(c)  104πT

(d) πT

Answer: (d)

19. When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is –

(a)   

(b)   

(c)    

(d)  

Answer: (b)

20. Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

(a)  8

(b)  1

(c)  6

(d) 4

Answer: (c)

Section-B

21. A parallel plate capacitor whose capacitance C is 14pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates, with a constant mechanical energy of ____ pJ. (Assume no friction)

Answer: (864)

22. If 2.5 × 106 N average force is exerted by a light wave on a non-reflecting surface of 30 cm2 area during 40 minutes of time span, the energy flux of light just before it falls on the surface is _______ W/cm2. (Round off to the nearest integer) (Assume complete absorption and normal incidence conditions are there)

Answer: (25)

23. The following bodies

(a) a ring

(b) a disc

(c) a solid cylinder

(d) a solid sphere

of same mass ‘m’ and radius ‘R’ are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is________.

[Mark the body as per their respective numbering given in the question]

Answer: (4)

24. For VHF signal broadcasting, _______ km2 of the maximum service area will be covered by an antenna tower of height 30 m, if the receiving antenna is placed on the ground. Let the radius of the earth be 6400 km. (Round off to the nearest integer) (Take π as 3.14)

Answer: (1206)

25. Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig.1 shows one of them and Fig. 2 shows their series combination. The ratio of the time period of oscillation of the two SHM is Tb/Ta = √x, where the value of x is ______. (Round off to the nearest integer)

Answer: (2)

26. Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is 3/7. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is _______ N. (Round off to the nearest integer) [Take g as 9.8 ms2]

Answer: (21)

27. The radius in kilometre to which the present radius of the earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 times is ______.

Answer: (64)

28. The equivalent resistance of a series combination of two resistors is ‘s’. When they are connected in parallel, the equivalent resistance is ‘p’. If s = np, then the maximum value for n is ______. (Round off to the nearest integer)

Answer: (4)

29. The angular speed of the truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck wheel during this time is ______.

(Assuming the acceleration to be uniform).

Answer: (728)

30. Four identical rectangular plates with length, l =2 cm and breadth, b = 3/2 cm are arranged as shown in figure. The equivalent capacitance between A and C is x∈0/d. The value of x is ______. (Round off to the nearest integer)

Answer: (2)

Chemistry

Section-A

1. The INCORRECT statement(s) about heavy water is (are)

(A) Used as a moderator in a nuclear reactor

(B) Obtained as a by-product in the fertilizer industry

(C) Used for the study of the reaction mechanism

(D) Has a higher dielectric constant than water

Choose the correct answer from the option given below:

(a)  (B) only

(b)  (B) and (D) only

(c)  (C) only

(d) (D) only

Answer: (d)

2. Given below are two statements:

Statement I: Potassium permanganate on heating at 573 K forms potassium manganate.

Statement II: Both potassium permanganate and potassium manganate are tetrahedral and paramagnetic in nature.

In the light of the above statements, choose the most appropriate Ans from the options given below:

(a)  Both statement I and statement II are true

(b)  Both statement I and statement II are false

(c)  Statement I is true but and statement II is false

(d) Statement I is false but statement II is true

Answer: (c)

3. Which of the following is the correct structure of tyrosine?

Answer: (c)

4. Given below are two statements:

Statement I: Retardation factor (Rf) can be measured in meter/centimetre

Statement II: Rf value of a compound remains constant in all solvents.

Choose the most appropriate answer from the options given below:

(a)  Statement I is false but statement II is true

(b)  Both statement I and statement II are false

(c)  Both statement I and statement II are true

(d) Statement I is true but statement II is false

Answer: (b)

5. Mesityl oxide is a common name of:

(a)  3-Methyl cyclohexane carbaldehyde

(b)  4-Methyl pent-3-en-2-one

(c)  2,4-Dimethyl pentan-3-one

(d) 2-Methyl cyclohexanone

Answer: (b)

6. What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic number 25, in its aqueous solution?

(a)  5.92

(b)  5.26

(c)  Zero

(d) 5.0

Answer: (a)

7. A central atom in a molecule has two lone pairs of electrons and forms three single bonds. The shape of this molecule is:

(a)  Trigonal pyramidal

(b)  T-shaped

(c)  See-saw

(d) Planar triangular

Answer: (b)

8. Product “A” in the below chemical reaction is:

Answer: (d)

9. The point of intersection and sudden increase in the slope, in the diagram given below respectively, indicates:

(a)  ΔG = 0 and melting or boiling point of the metal oxide.

(b)  ΔG < 0 and decomposition of the metal oxide.

(c)  ΔG = 0 and reduction of the metal oxide.

(d) ΔG > 0 and decomposition of the metal oxide.

Answer: (a)

10. The reaction given below requires which of the following reaction conditions:

(a)  623 K, 300 atm

(b)  573 K, 300 atm

(c)  573 K, Cu, 300 atm

(d) 623 K, Cu 300 atm

Answer: (a)

11. The correct order of conductivity of ions in water is:

(a)  Cs+ > Rb+ > K+ > Na+

(b)  K+ > Na+ > Cs+ > Rb+

(c)  Rb+ > Na+ > K+ > Li+

(d) Na+ > K+ > Rb+ > Cs+

Answer: (a)

12. A colloidal system consisting of a gas dispersed in a solid is called a/an:

(a)  Aerosol

(b)  Solid Sol

(c)  Foam

(d) Gel

Answer: (b)

13. The absolute value of the electron gain enthalpy of halogen satisfies:

(a)  I > Br >Cl> F

(b)  F >Cl> Br > I

(c)  Cl> F > Br > I

(d) Cl> Br > F > I

Answer: (c)

14. Which of the following reaction is an example of ammonolysis?

(a)  C6H5CH2CN → C6H5CH2CH2NH2

(b)  C6H5COCl + C6H5NH2 → C6H5CONHC6H5

(c)  C6H5CH2Cl +NH3 → C6H5CH2NH2

(d) C6H5NH2 → C6H5NH3+Cl

Answer: (c)

15. Reducing smog is a mixture of:

(a)  Smoke, fog and N2O3

(b)  Smoke, fog and O3

(c)  Smoke, fog and SO2

(d) Smoke, fog and CH2=CH–CHO

Answer: (c)

16. Which of the following is an aromatic compound?

Answer: (a)

17. With respect to drug-enzyme interaction, identify the wrong statement.

(a)  Allosteric inhibitor competes with the enzyme’s active site

(b)  Competitive inhibitor binds to the enzyme’s active site

(c)  Non-competitive inhibitor binds to the allosteric site

(d) Allosteric inhibitor changes the enzyme’s active site

Answer: (a)

18. Hoffmann bromamide degradation of benzamide gives product A, which upon heating with CHCl3 and NaOH gives product B. The structures of A and B are:

Answer: (a)

19. The product “A” in the above reaction is:

Answer: (b)

20. Which of the following compound CANNOT act as a Lewis base?

(a)  ClF3

(b)  PCl5

(c)  NF3

(d) SF4

Answer: (b)

Section-B

21. A certain orbital has n = 4 and ml = –3. The number of radial nodes in this orbital is ____.(Round off to the Nearest Integer).

Answer: (0)

22. 15 mL of an aqueous solution of Fe2+ in the acidic medium completely reacted with 20 mL of 0.03 M aqueous Cr 2O72. The molarity of the Fe2+ solution is _____× 10–2(Round off to the Nearest Integer).

 

Answer: (24)

23. The reaction of white phosphorus on boiling with alkali in an inert atmosphere resulted in the formation of product ‘A’. The reaction of 1 mol of ‘A’ with an excess of AgNO3 in an aqueous medium gives _______ mol(s) of Ag. (Round off to the Nearest Integer).

Answer: (8)

24. The oxygen dissolved in water exerts a partial pressure of 20 kPa in the vapour above water. The molar solubility of oxygen in water is _____ × 10–5 mol dm–3.

(Round off to the Nearest Integer).

[Given : Henry’s law constant = KH = 8.0 × 104 kPa for O2. Density of water with dissolved oxygen = 1.0 kg dm–3 ]

Answer: (25)

25. The standard enthalpies of formation of Al2O3 and CaO are –1675 kJ mol–1 and –635 kJ mol–1 For the reaction 3CaO + 2Al → 3Ca + Al2O3 the standard reaction enthalpy ΔrH0=______ kJ. (Round off to the Nearest Integer)

Answer: (230)

26. For a certain first-order reaction 32% of the reactant is left after 570s. The rate constant of this reaction is _______ × 10–3 s–1. (Round off to the Nearest Integer).

[Given: log102 = 0.301, ln10 = 2.303]

Answer: (2)

27. The pressure exerted by a non-reactive gaseous mixture of 6.4 g of methane and 8.8 g of carbon dioxide in a 10 L vessel at 27°C is _____ kPa. (Round off to the Nearest Integer). [Assume gases are ideal, R = 8.314 J mol–1 K–1 Atomic masses: C : 12.0u, H : 1.0u, O : 16.0 u]

Answer: (150)

28. The mole fraction of a solute in a 100 molal aqueous solution is _____ × 10–2. (Round off to the Nearest Integer). [Given : Atomic masses : H : 1.0 u, O : 16.0 u]

Answer: (64)

29. In the above reaction, 3.9 g of benzene on nitration gives 4.92 g of nitrobenzene. The percentage yield of nitrobenzene in the above reaction is _____%. (Round off to the Nearest Integer). (Given atomic mass : C : 12.0 u, H : 1.0 u, O : 16.0 u, N : 14.0 u)

Answer: (80)

30. 0.01 moles of a weak acid HA (Ka = 2.0 × 10–6 ) is dissolved in 1.0 L of 0.1 M HCl solution. The degree of dissociation of HA is_______ × 10–5 (Round off to the Nearest Integer). Assume degree of dissociation << 1

Answer: (2)

Mathematics

Section-A

1. Which of the following is true for y(x) that satisfies the differential equation 

(a)  y(1) = 1

(b)  y(1) = e1/2 – 1

(c)  y(1) = e1/2 – e1/2

(d) y(1) = e1/2 – 1

Answer: (d)

2. The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k2 has no solution if k is equal to

(a)  −2

(b)  −1

(c)  1

(d) 0

Answer: (a)

3. The value of  is:

(a)   

(b)    

(c)    

(d)  

Answer: (c)

4. If the Boolean expression (p ⇒ q) ⇔ (q * (~ P)) is a tautology, then the Boolean expression p * (~q) is equivalent to:

(a)  p ⇒ ~ q

(b)  p ⇒ q

(c)  q ⇒ p

(d) ~q ⇒ p

Answer: (c)

5. Choose the incorrect statement about the two circles whose equations are given below:

x2 + y2 − 10x − 10y + 41 = 0 and x2 + y2 − 16x − 10y + 80 = 0

(a)  Distance between two centres is the average radii of both the circles

(b)  Circles have two intersection points

(c)  Both circles’ centres lie inside the region of one another

(d) Both circles pass through the centre of each other

Answer: (c)

6. The sum of possible values of x for  is:

(a)  −33/4

(b)  −32/4

(c)  −31/4

(d) −30/4

Answer: (b)

7. Let  If  then  is equal to:

(a)  10

(b)  13

(c)  12

(d) 8

Answer: (c)

8. The equation of the plane which contains the y-axis and passes through the point (1, 2, 3) is:

(a)  3x + z = 6

(b)  3x − z = 0

(c)  x + 3z = 10

(d) x + 3z = 0

Answer: (b)

9. If  and  then a possible value of α is:

(a)  π/6

(b)  π/2

(c)  π/3

(d) π/4

Answer: (d)

10. The line 2x − y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x − 2y = 4. Then, the radius of the circle is:

(a)  4√5

(b)  3√5

(c)  5√3

(d) 5√4

Answer: (b)

11. Team ‘A’ consists of 7 boys and n girls and Team ‘B’ has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to

(a)  5

(b)  6

(c)  2

(d) 4

Answer: (d)

12. In a triangle PQR, the coordinates of the points P and Q are (−2, 4) and (4, −2) respectively. If the equation of the perpendicular bisector of PR is 2x – y + 2 = 0, then the centre of the circumcircle of the △PQR is:

(a)  (−2, −2)

(b)  (0, 2)

(c)  (−1, 0)

(d) (1, 4)

Answer: (a)

13. If cot−1 (ɑ) = cot−1 2 + cot−1 8 + cot−1 18 + cot−1 32 + …….. upto 100 terms, then ɑ is:

(a)  1.03

(b)  1.00

(c)  1.01

(d) 1.02

Answer: (c)

14. Which of the following statements is incorrect for the function g (ɑ) for ɑ ∈ R such that 

(a)  g(α) is a strictly decreasing function

(b)  g (ɑ) has an inflexion point at ɑ = −1/2

(c)  g(ɑ) is an even function

(d) g(ɑ) is a strictly increasing function

Answer: (*)

15. If the fourth term in the expansion of  is 4480, then the value of x when x ∈ N is equal to:

(a)  4

(b)  3

(c)  2

(d) 1

Answer: (c)

16. Two dice are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is:

(a)  17/36

(b)  4/9

(c)  5/12

(d) 1/2

Answer: (a)

17. The inverse of y = 5logx is:

(a)  x = 5logy

(b)  x = ylog5

(c)  x = y1/log5

(d) x = 51/logy

Answer: (c)

18. In a school, there are three types of games to be played. Some of the students play two types of games, but none play all three games. Which Venn diagrams can justify the above statements.

(a)  P and R

(b)  P and Q

(c)  None of these

(d) Q and R

Answer: (c)

19. The area of the triangle with vertices A (z), B (iz) and C (z + iz) is:

(a)   

(b)  1

(c)  1/2

(d)  

Answer: (d)

20. The value of  where [x] denotes the greatest integer ≤ x is :

(a)  0

(b)  π/4

(c)  π/2

(d) π

Answer: (c)

Section-B

Integer Type:

21. Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is ɑ, only E2 occurs is β and only E3 occurs is 𝛾. Let ‘p’ denote the probability of none of the events that occur that satisfies the equations (ɑ − 2β) p = ɑβ and (β − 3𝛾) p = 2β𝛾. All the given probabilities are assumed to lie in the interval (0, 1) Then,  is equal to _______

Answer: (6)

22. If the equation of the plane passing through the line of intersection of the planes 2x − 7y + 4z − 3 = 0, 3x − 5y + 4z + 11 = 0 and the point (−2, 1, 3) is ax + by + cz − 7 = 0, then the value of 2a + b + c − 7 is __________

Answer: (4)

23. If  then the value of det (A4) + det (A10 − Adj (2A))10) is equal to _______

Answer: (16)

24. The minimum distance between any two points P1 and P2 while considering point P1 on one circle and point P2 one the other circle for the given circles’ equations x2 + y2 − 10x − 10y + 41 = 0 and x2 + y2 − 24x − 10y + 160 = 0 ________

Answer: (1)

25. If (2021)3762 is divided by 17, then the remainder is______

Answer: (4)

26. If [ . ] represents the greatest integer function, then the value of  is_______

Answer: (1)

27. If  and its first derivative with respect to x is  when x = 1, where a and b are integers, then the minimum value of |a2 – b2| is_______

Answer: (481)

28. If the function  is continuous at each point in its domain and f(0) = 1/k, then k is_______

Answer: (6)

29. The maximum value of z in the following equation z = 6xy + y2, where 3x + 4y ≤ 100 and 4x + 3y ≤ 75 for x ≥ 0 and y ≥ 0 is _________

Answer: (625)

30. If  and  such that  then  is equal to_________

Answer: (2)

JEE Main Session 2 March 16th Shift 2 Question Paper with Answer Key

Physics

Section-A

1. A mosquito is moving with a velocity  and accelerating in uniform conditions. What will be the direction of the mosquito after 2s?

(a) 

(b) 

(c) 

(d) 

Answer: (*)

2. Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh1 and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve.

(g = 9.8 m/s2)

Statement-II: If the road is banked at an angle of 45°, cyclists can cross the curve of 2m radius with the speed of 18.5 kmh1 without slipping.

In the light of the above statements, choose the correct answer from the options given below:

(a)  Both statement I and statement II are false

(b)  Both statement I and statement II are true

(c)  Statement I is correct and statement II is incorrect

(d) Statement I is incorrect and statement II is correct

Answer: (b)

3. Calculate the time interval between 33% decay and 67%decay if half-life of a substance is 20 minutes:

(a)  40 minutes

(b)  20 minutes

(c)  60 minutes

(d) 13 minutes

Answer: (b)

4. A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before the collision is: (take g = 9.8 ms2)

(a)  831.4 m/s

(b)  841.4 m/s

(c)  811.4 m/s

(d) 821.4 m/s

Answer: (a)

5. What will be the nature of the flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water is 0.5 cm and 103 Pa s, respectively. (Density of water: 103 kg/m3)

(a)  Remains steady flow

(b)  Unsteady to steady flow

(c)  Steady flow to unsteady flow

(d) Remains turbulent flow

Answer: (c)

6. The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of the same refractive index? Assume the radii of curvature of the faces of the lens are R1 and R2

(a)  Zero

(b) 

(c)  Infinite

(d) 1

Answer: (c)

7. For the given circuit, comment on the type of transformer used.

(a)  Step down transformer

(b)  Auxiliary transformer

(c)  Step-up transformer

(d) Autotransformer

Answer: (c)

8. Red light differs from blue light as they have:

(a)  Same frequencies and same wavelengths

(b)  Different frequencies and different wavelengths

(c)  Different frequencies and same wavelengths

(d) Same frequencies and different wavelengths

Answer: (b)

9. The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through the same potential of 100 V. What should nearly be the ratio of their wavelengths? (mp = 1.00727u; me = 0.00055u)

(a)  (1860)2 : 1

(b)  43 : 1

(c)  1860 : 1

(d) 41.1 : 1

Answer: (b)

10. A charge Q is moving  distance in the magnetic field Find the value of work done by

(a)  Infinite

(b)  1

(c)  −1

(d) Zero

Answer: (d)

11. Amplitude of a mass spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay constant = 20 g/s then how much time is required for the amplitude of the system to drop to half of its initial value?

(ln 2 = 0.693)

(a)  15.01 s

(b)  17.32 s

(c)  0.034 s

(d) 34.65 s

Answer: (d)

12. A resistor develops 500 J of thermal energy in 20s when a current of 1.5A is passed through it. If the current is increased from 1.5A to 3A, what will be the energy developed in the 20s.

(a)  500 J

(b)  1000 J

(c)  2000 J

(d) 1500 J

Answer: (c)

13. Calculate the value of mean free path (λ) for oxygen molecules at temperature 27°C and pressure 1.01 × 105 Assume the molecular diameter 0.3nm and the gas is ideal. (k = 1.38 × 1023 jK1)

(a)  102 nm

(b)  32 nm

(c)  58 nm

(d) 86 nm

Answer: (a)

14. A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will:

(a)  Not bend but shrink

(b)  Neither bend nor shrink

(c)  Bend towards the right

(d) Bend towards the left

Answer: (d)

15. The following logic gate is equivalent to:

(a)  NOR Gate

(b)  AND Gate

(c)  OR Gate

(d) NAND Gate

Answer: (a)

16. Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nearly be the minimum height of the receiving antenna to receive the signals in line of sight? (Assume radius of earth is 6400 km)

(a)  19.77 m

(b)  79.1 m

(c)  158.2 m

(d) 39.55 m

Answer: (d)

17. The magnetic field in a region is given by  A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity  The emf induced in the loop is:

(a) 

(b) 

(c) 

(d) 

Answer: (b)

18. The half-life of Au198 is 2.7 days. The activity of 1.50 mg of Au198 if its atomic weight is 198 g mol1 is (NA = 6 × 1023/mol).

(a)  252 Ci

(b)  357 Ci

(c)  240 Ci

(d) 535 Ci

Answer: (b)

19. In order to determine the Young’s Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least count = 1 g) was hanged to get the elongation of 0.5 cm (measured using a scale of least count 0.001 cm). What will be the fractional error in the value of Young’s Modulus determined by this experiment.

(a)  9%

(b)  1.4%

(c)  0.9%

(d) 0.14%

Answer: (b)

20. Find out the surface charge density at the intersection of point x = 3 m plane and x-axis in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.

(a)  47.88 C/m

(b)  0.07 nC m2

(c)  0.424 nC m2

(d) 4.0 nC m2

Answer: (c)

Section-B

21. A closed organ pipe of length L and an open organ pipe contains gases of densities ρ1 and ρ2 The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with the same frequency. The length of the open pipe  is where x is ______(Round off to the Nearest Integer)

Answer: (4)

22. A deviation of 2° is produced in the yellow ray when the prism of crown and flint glass are chromatically combined. Taking dispersive powers of crown and flint glass as 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be _______ ° (in degree). (Round off to the Nearest Integer)

Answer: (12)

23. If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be  where x is __________. (Round off to the Nearest Integer). (M is the mass of earth, R is the radius of earth, G is the gravitational constant)

Answer: (3)

24. In a parallel plate capacitor set up, the plate area of the capacitor is 2 m2 and the plates are separated by 1 m. If the space between the plates is filled with a dielectric material of thickness 0.5 m and area 2 m2 (see fig) the capacitance of the set-up will be ________∈0. (Dielectric constant of the material = 3.2) (Round off to the Nearest Integer)

Answer: (3.04)

25. For an ideal heat engine, the temperature of the source is 127ºC. In order to have 60% efficiency the temperature of the sink should be _________ºC. (Round off to the Nearest Integer)

Answer: (113)

26. A force  is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is _______. (Round off to the Nearest Integer)

Answer: (20)

27. The energy dissipated by a resistor is 10 ml in 1 s when an electric current of 2mA flows through it. The resistance is ________. (Round off to the Nearest Integer)

Answer: (2500)

28. A swimmer can swim with a velocity of 12 km/h in still water. Water flowing in a river has a velocity of 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ______°. (Round off to the Nearest Integer) (Find the angles in degrees)

Answer: (120)

29. A solid disc of radius ‘a’ and mass ‘m’ rolls down without slipping on an inclined plane making an angle θ with the horizontal. The acceleration of the disc will be  where b is _______ . (Round off to the Nearest Integer). (g = acceleration due to gravity; θ = angles as shown in figure)

Answer: (3)

30. A body of mass 2 kg moves under a force of  It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is _______. (Round off to the Nearest Integer)

Answer: (12)

Chemistry

Section-A

1. Identify the reagent(s) ‘A’ and condition(s) for the reaction:

(a)  A = HCl; Anhydrous AlCl3

(b)  A = HCl, ZnCl2

(c)  A = Cl2, dark, Anhydrous AlCl3

(d) A = Cl2; UV Light

Answer: (d)

2. The INCORRECT statement regarding the structure of C60 is:

(a)  It contains 12 six-membered rings and 24 five-membered rings.

(b)  Each carbon atom forms three sigma bonds.

(c)  The five-membered rings are fused only to six-membered rings.

(d) The six-membered rings are fused to both six and five-membered rings.

Answer: (a)

3. Match List-I with List-II:

List-I

Test/Reagents/Observation(s)

List-II

Species detected

(a) Lassaigne’s Test (i) Carbon
(b) Cu(II) oxide (ii) Sulphur
(c) Silver nitrate (iii) N, S, P and halogen
(d) The sodium fusion extract gives black precipitate with acetic acid & lead acetate (iv) Halogen Specifically

(a)  (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

(b)  (a)-(i), (b)-(iv), (c)-(iii), (d)-(ii)

(c)  (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)

(d) (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)

Answer: (a)

4. The structure of X is:

Answer: (a)

5. Ammonolysis of alkyl halides followed by the treatment with NaOH solution can be used to prepare primary, secondary and tertiary amines. The purpose of NaOH in the reaction is:

(a)  to remove basic impurities

(b)  to activate NH3 used in the reaction

(c)  to increase the reactivity of alkyl halide

(d) to remove acidic impurities

Answer: (d)

6. Arrange the following metal complex/compounds in the increasing order of spin only magnetic moment. Presume all three, high spin systems.

(Atomic numbers Ce = 58, Gd = 64 and Eu = 63)

(1) (NH4)2[Ce(NO3)6]

(2) Gd(NO3)3

(3) Eu(NO3)3

(a)  (1) < (3) < (2)

(b)  (1) < (2) < (3)

(c)  (3) < (1) < (2)

(d) (2) < (1) < (3)

Answer: (a)

7. Identify the elements X and Y using the ionisation energy values given below:

1st                   2nd

X               195                  4563

Y               731                  1450

(a)  X = F; Y = Mg

(b)  X = Mg; Y = F

(c)  X = Na; Y = Mg

(d) X = Mg; Y = Na

Answer: (c)

8. The INCORRECT statement below regarding colloidal solutions is:

(a)  A colloidal solution shows colligative properties

(b)  An ordinary filter paper can stop the flow of colloidal particles

(c)  A colloidal solution shows the Brownian motion of colloidal particles

(d) The flocculating power of Al3+ is more than that of Na+

Answer: (b)

9. The characteristics of elements X, Y and Z with atomic numbers, respectively, 33, 53 and 83 are:

(a)  X and Z are non-metals and Y is a metalloid.

(b)  X and Y are metalloids and Z is a metal.

(c)  X, Y and Z are metals.

(d) X is a metalloid, Y is a non-metal and Z is a metal.

Answer: (d)

10. The exact volumes of 1 M NaOH solution required to neutralise 50 mL of 1 M H3PO3 solution and 100 mL of 2 M H3PO2 solution, respectively, are:

(a)  100 mL and 50 mL

(b)  50 mL and 50 mL

(c)  100 mL and 100 mL

(d) 100 mL and 200 mL

Answer: (d)

11. Which of the following reduction reaction CANNOT be carried out with coke?

(a)  Fe2O3 → Fe

(b)  ZnO → Zn

(c)  Al2O3 → Al

(d) Cu2O → Cu

Answer: (c)

12. An unsaturated hydrocarbon X on ozonolysis gives A. Compound A when warmed with ammoniacal silver nitrate forms a bright silver mirror along the sides of the test tube. The unsaturated hydrocarbon X is:

Answer: (c)

13. Two statements are given below:

Statement-I: Sodium hydride can be used as an oxidising agent.

Statement-II: The lone pair of electrons on nitrogen in pyridine makes it basic.

(a)  Statement I is true but statement II is false

(b)  Both statement I and statement II are false

(c)  Both statement I and statement II are true

(d) Statement I is false but statement II is true

Answer: (d)

14. Which of the following polymer is used in the manufacture of wood laminates?

(a)  Melamine formaldehyde resin

(b)  Cis-poly isoprene

(c)  Phenol and formaldehyde resin

(d) Urea-formaldehyde resin

Answer: (a)

15. The correct statements about H2O2 are:

(1) used in the treatment of effluents.

(2) used as both oxidizing and reducing agents.

(3) the two hydroxyl groups lie in the same plane.

(4) miscible with water.

Choose the correct answer from the options given below:

(a)  (1), (3) and (4) only

(b)  (1), (2) and (4) only

(c)  (1), (2), (3) and (4)

(d) (2), (3) and (4) only

Answer: (b)

16. The greenhouse gas/es is (are)

(1) Carbon dioxide

(2) Oxygen

(3) Water vapour

(4) Methane

Choose the most appropriate answer from the options given below:

(a)  (1) and (2) only

(b)  (1), (3) and (4) only

(c)  (1) and (3) only

(d) (1) only

Answer: (b)

17. In the below reaction, the reagent “A” is:

(a)  NaBH4, H3O+

(b)  HCl, Zn-Hg

(c)  Alkaline KMnO4, H+

(d) LiAlH4

Answer: (c)

18. Which of the following is least basic?

(a) 

(b) 

(c) 

(d) 

Answer: (a)

19. Fex2 and Fey3 are known when x and y are:

(a)  x=Cl, Br, I and y=F, Cl, Br, I

(b)  x=F, Cl, Br, I and y=F, Cl, Br

(c)  x=F, Cl, Br, I and y=F, Cl, Br, I

(d) x=F, Cl, Br and y =F, Cl, Br, I

Answer: (b)

20. The secondary structure of protein is stabilized by:

(a)  van der Waals forces

(b)  Peptide bond

(c)  Hydrogen bonding

(d) Glycosidic bond

Answer: (c)

Section-B

21. At 25°C, 50 g of iron reacts with HCl to form FeCl2. The evolved hydrogen gas expands against a constant pressure of 1 bar. The work done by the gas during this expansion is ________________ J. (Round off to the nearest integer).

[Given: R = 8.14 J mol–1 K–1. Assume, hydrogen is an ideal gas]

[Atomic mass of Fe is 55.85 u]

Answer: (2218)

22. A 5.0 m moldm–3 aqueous solution of KCl has a conductance of 0.55 mS when measured in a cell of cell constant 1.3 cm–1. The molar conductivity of this solution is ___________ mSm2mol1. (Round off to the nearest integer).

Answer: (14)

23. The number of orbitals with n = 5, m1 = +2 is ___________. (Round off to the nearest integer).

Answer: (3)

24. A and B decompose via first-order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimolar non-reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is __________ min. (Round off to the nearest integer).

Answer: (108)

25. [Ti(H2O)6]3+ absorbs light of wavelength 498 nm during a d–d transition. The octahedral splitting energy for the above complex is ___________ × 10–19 (Round off to the nearest integer). h = 6.626 × 10–34 Js; c = 3 × 108 ms–1.

Answer: (4)

26. Sulphurous acid (H2SO3) has Ka1 = 1.7 × 10–2 and Ka2 = 6.4 × 10–8. The pH of 0.588 M H2SO3 is _________. (Round off to the nearest integer)

Answer: (5)

27. In Duma’s method of estimation of nitrogen, 0.1840 g of an organic compound gave 30 mL of nitrogen collected at 287 K and 758 mm of Hg pressure. The percentage composition of nitrogen in the compound is __________. (Round off to the nearest integer). [Given: Aqueous tension at 287 K = 14 mm of Hg]

Answer: (19)

28. Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is ________ × 1021. (Round off to the nearest integer). [Given: NA = 6.023 × 1023]

Answer: (15)

29. When 35 mL of 0.15 M lead nitrate solution is mixed with 20 mL of 0.12 M chromic sulphate solution, _________ × 10–5 moles of lead sulphate precipitate out. (Round off to the nearest integer).

Answer: (525)

30. At 363 K, the vapour pressure of A is 21 kPa and that of B is 18 kPa. One mole of A and 2 moles of B are mixed. Assuming that this solution is ideal, the vapour pressure of the mixture is _______ kPa. (Round off to the nearest integer).

Answer: (19)

Mathematics

Section-A

1. The least value of |z| where z is a complex number which satisfies the inequality  is equal to:

(a)  2

(b)  3

(c)  8

(d) √5

Answer: (b)

2. Let f : S → S where S = (0, ∞) be a twice differentiable function such that f (x + 1) = x f (x). If g : S → R be defined as g (x) = loge f(x), then the value of |g”(5) – g”(1)| is equal to:

(a)  197/144

(b)  187/144

(c)  205/144

(d) 1

Answer: (c)

3. If y = y (x) is the solution of the differential equation  with y(0) = 0, then  equal to:

(a)  loge 2

(b) 

(c) 

(d) 

Answer: (c)

4. If the foot of the perpendicular from point (4, 3, 8) on the line   ℓ ≠ 0 is (3, 5, 7) then the shortest distance between the line L1 and line  is equal to:

(a) 

(b)  1/√3

(c)  1/2

(d) 1/√6

Answer: (d)

5. If (x, y, z) be an arbitrary point lying on a plane P which passes through the points (42, 0, 0), (0, 42, 0) and (0, 0, 42), then the value of the expression   is equal to:

(a)  3

(b)  0

(c)  39

(d) −45

Answer: (a)

6. Consider the integral  where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to:

(a)  45(e – 1)

(b)  45(e + 1)

(c)  9(e – 1)

(d) 9(e + 1)

Answer: (a)

7. Let A (–1, 1), B (3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q respectively. Let A1 and A2 be the areas of ΔABC and ΔPQC respectively, such that A1 = 3A2, then the value of m is equal to:

(a)  4/15

(b)  1

(c)  2

(d) 3

Answer: ()

8. Let f be a real-valued function, defined on R – {–1, 1} and given by  Then in which of the following intervals, function f (x) is increasing?

(a)  (–∞,–1) ⋃ ([1/2, ∞) – {1})

(b)  (–1, 1/2]

(c)  (–∞, ∞) – {–1, 1}

(d) (–∞, 1/2] – {–1}

Answer: (a)

9. Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2 √2 and 2 √5, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to:

(a)  √10

(b)  √6

(c)  √11

(d) √7

Answer: (b)

10. Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then the probability of event A is equal to:

(a)  4/9

(b)  9/56

(c)  3/7

(d) 11/27

Answer: (a)

11. Let α ∈ R be such that the function  is continuous at x = 0, where {x} = x – [x], [x] is the greatest integer less than or equal to x. Then:

(a)  α = π/4

(b)  No such α exists

(c)  α = 0

(d) α = π/√2

Answer: (b)

12. The maximum value of  , x ∈ R is:

(a)  √7

(b)  √5

(c)  5

(d) 3/4

Answer: (b)

13. Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let α be the number of triangles having these points from different sides as vertices and β be the number of quadrilaterals having these points from different sides as vertices. Then (β – α) is equal to:

(a)  1890

(b)  795

(c)  717

(d) 1173

Answer: (c)

14. Let C be the locus of the mirror image of a point on the parabola y2 = 4x with respect to the line y = x. Then the equation of tangent to C at P(2, 1) is:

(a)  2x + y = 5

(b)  x + 2y = 4

(c)  x + 3y = 5

(d) x – y = 1

Answer: (d)

15. Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy  is:

(a)  1

(b)  2

(c)  3

(d) 0

Answer: (c)

16. Let C1 be the curve obtained by the solution of the differential equation  Let the curve C2 be the solution of  If both the curves pass through (1, 1), then the area enclosed by the curves C1 and C2 is equal to :

(a) 

(b) 

(c)  π − 1

(d) π + 1

Answer: (a)

17. Let  If  and  then the value of  is equal to:

(a)  11

(b)  15

(c)  9

(d) 13

Answer: (b)

18. Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that  and P(x) leaves remainder 5 when it is divided by (x – 2). Then the value of 9(b + c) is equal to :

(a)  7

(b)  11

(c)  15

(d) 9

Answer: (a)

19. If the points of intersections of the ellipse  and the circle x2 + y2 = 4b, b > 4 lie on the curve y2 = 3x2, then b is equal to :

(a)  5

(b)  6

(c)  12

(d) 10

Answer: (c)

20. Let A = {2, 3, 4, 5, ……, 30} and ‘≅’ be an equivalence relation on A×A, defined by (a, b) ⩭ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4, 3) is equal to :

(a)  7

(b)  5

(c)  6

(d) 8

Answer: (a)

Section-B

21. Let  be a vector perpendicular to the vectors   and  If  then the value of  is equal to_____

Answer: (28)

22. In ΔABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of ΔABC is 30 cm2 and R and r are respectively the radii of circumcircle and incircle of ΔABC, then the value of 2R + r (in cm) is equal to ______

Answer: (15)

23. Consider the statistics of two sets of observations as follows:

Size Mean
Observation I 10 2
Observation II N 3

If the variance of the combined set of these two observations is 17/9, then the value of n is equal to ______

Answer: (5)

24. Let   up to n-terms, where a >1. If S24(x) = 1093 and S12(2x) = 265, then value of a is equal to______

Answer: (16)

25. Let n be a positive integer. Let  If  then n is equal to ________

Answer: (6)

26. Let f : R → R and g : R → R be defined as  where a, b are non-negative real numbers. If (gof) (x) is continuous for all x ∈ R, then a + b is equal to ______

Answer: (1)

27. If the distance of the point (1, – 2, 3) from the plane x + 2y – 3z + 10 = 0 measured parallel to the line,  then the value of |m| is equal to________

Answer: (2)

28. Let 1/16, a and b be in G.P. and 1/a, 1/b, 6 be in A.P., where a, b, > 0. Then 72 (a + b) is equal to ______

Answer: (14)

29. Let  be two 2 × 1 matrices with real entries such that A = XB, where   and k ∈ If  and  then the value of k is ________

Answer: (1)

30. For real numbers α, β, γ and δ, if

where C is an arbitrary constant, then the value of 10 (α + βγ + δ) is equal to______.

Answer: (6)

JEE Main Session 2 March 16th Shift 1 Question Paper with Answer Key

Physics

Section-A

1. A 25 m long antenna is mounted on an antenna tower. The height of the antenna tower is 75 m. The wavelength (in meter) of the signal transmitted by this antenna would be:

(a)  200

(b)  400

(c)  100

(d) 300

Answer: (c)

2. A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle θ as shown in the figure. The coefficient of kinetic friction is μK. Then, the block’s acceleration ‘a’ is given by (g is the acceleration due to gravity)

(a) 

(b) 

(c) 

(d)

Answer: (a)

3. Four equal masses, m each is placed at the corners of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be:

(a)  ml2

(b)  3ml2

(c)  √3ml2

(d) 2ml2

Answer: (b)

4. The stopping potential in the context of the photoelectric effect depends on the following property of incident electromagnetic radiation:

(a)  Amplitude

(b)  Phase

(c)  Frequency

(d) Intensity

Answer: (c)

5. One main scale division of a vernier callipers is ‘a’ cm and nth division of the vernier scale coincides with (n–1)th division of the main scale. The least count of the callipers in mm is:

(a) 

(b) 

(c) 

(d)

Answer: (b)

6. A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time,  The value of electric field at this point is: (speed of light = 3×108 ms–1) Assume x, y, z are unit vectors along  are unit vectors along x, y and z directions.

(a) 

(b) 

(c) 

(d)

Answer: (d)

7. The maximum and minimum distances of a comet from the Sun are 1.6 × 1012 m and 8.0 × 1010 m respectively. If the speed of the comet at the nearest point is 6 × 104 ms–1, the speed at the farthest point is :

(a)  1.5 × 103 m/s

(b)  4.5 × 103 m/s

(c)  3.0 × 103 m/s

(d) 6.0 × 103 m/s

Answer: (c)

8. A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical sidewalls of a radius of 20 cm. If the block takes 40 s to complete one round, the normal force by the sidewalls of the groove is:

(a)  6.28 × 103 N

(b)  0.0314 N

(c)  9.859 × 102 N

(d) 9.859 × 104 N

Answer: (d)

9. An RC circuit as shown in the figure is driven by an AC source generating a square wave. The output wave pattern monitored by CRO would look close to:

Answer: (b)

10. In thermodynamics, heat and work are:

(a)  Intensive thermodynamics state variables

(b)  Extensive thermodynamics state variables

(c)  Path functions

(d) Point functions

Answer: (c)

11. A conducting wire of length ‘l’, area of cross-section A and electric resistivity ρ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be:

(a) 

(b) 

(c) 

(d) 

Answer: (d)

12. The pressure acting on a submarine is 3 × 105 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be :(Assume that atmospheric pressure is 1 × 105 Pa, the density of water is 103 kg m–3, acceleration due to gravity g = 10 ms–2)

(a) 

(b) 

(c) 

(d) 

Answer: (a)

13. A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of 18 cm from the centre of the magnet. If BH = 0.4 G, the magnetic moment of the magnet is (1 G = 10–4 T)

(a)  28.80 J T1

(b)  2.880 J T1

(c)  2.880 × 103 J T1

(d) 2.880 × 102 J T1

Answer: (b)

14. The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as a universal gas constant. The pressure of the mixture of gases is:

(a)  4RT/V

(b)  88RT/V

(c) 

(d) 3RT/V

Answer: (c)

15. A conducting bar of length L is free to slide on two parallel conducting rails as shown in the figure

Two resistors R1 and R2 are connected across the ends of the rails. There is a uniform magnetic field  pointing into the page. An external agent pulls the bar to the left at a constant speed v. The correct statement about the directions of induced currents I1 and I2 flowing through R1 and R2 respectively is :

(a)  I1 is in the clockwise direction and I2 is in the anticlockwise direction

(b)  Both I1 and I2 are in a clockwise direction

(c)  I1 is in the anticlockwise direction and I2 is in a clockwise direction

(d) Both I1 and I2 are in the anticlockwise direction

Answer: (a)

16. The velocity-displacement graph describing the motion of a bicycle is shown in the figure.

The acceleration-displacement graph of the bicycle’s motion is best described by:

Answer: (a)

17. For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is  where ‘d’ is the separation between the plates of parallel plate capacitors. The new capacitance (C’) in terms of original capacitance (C0) is given by the following relation:

(a) 

(b) 

(c) 

(d)

Answer: (a)

18. For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (Ue) and magnetic (Um) fields is :

(a)  Ue ≠ Um

(b)  Ue = Um

(c)  Ue > Um

(d) Ue < Um

Answer: (b)

19. Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of the pendulum will be:

(a) 

(b) 

(c) 

(d)

Answer: (c)

20. The angle of deviation through a prism is minimum when

(A) Incident ray and emergent ray are symmetric to the prism

(B) The refracted ray inside the prism becomes parallel to its base

(C) Angle of incidence is equal to that of the angle of emergence

(D) When the angle of emergence is double the angle of incidence

Choose the correct answer from the options given below:

(a)  Only statement (D) is true

(b)  Statements (A), (B) and (C)

(c)  Statements (B) and (C) are true

(d) Only statement (A) and (B) are true

Answer: (b)

Section-B

21. A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is ‘x’ nm. The value of ‘x’ to the nearest integer is ________.

Answer: (600)

22. The value of power dissipated across the Zener diode (Vz = 15 V) connected in the circuit as shown in the figure is x × 10–1

The value of x, to the nearest integer, is _________.

Answer: (5)

23. The resistance R=V/I, where V = (50 ± 2) V and I = (20 ± 0.2) A. The percentage error in R is ‘x’ %. The value of ‘x’ to the nearest integer is _________.

Answer: (5)

24. A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8Ω, L=24 mH and C=60 μF. The value of power dissipated at resonant conditions is ‘x’ kW. The value of x to the nearest integer is _________.

Answer: (4)

25. A ball of mass 10 kg moving with a velocity 10√3 ms–1 along the X-axis, hits another ball of mass 20 kg which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along the Y-axis at a speed of 10 m/s. The second piece starts moving at a speed of 20 m/s at an angle θ (degree) with respect to the X-axis. The configuration of pieces after the collision is shown in the figure. The value of θ to the nearest integer is ________.

Answer: (30)

26. In the figure given, the electric current flowing through the 5 kΩ resistor is ‘x’ mA.

The value of x to the nearest integer is ________.

Answer: (3)

27. Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its centre and is at rest initially. The disk is acted upon by a constant force F=20 N through a massless string wrapped around its periphery as shown in the figure.

Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s–1. The value of n, to the nearest integer is ________. [Given: In one complete revolution, the disk rotates by 6.28 rad]

Answer: (20)

28. The first three spectral lines of H-atom in the Balmer series are given λ1, λ2, λ3 considering the Bohr atomic model, the wavelengths of first and third spectral lines (λ13) are related by a factor of approximately ‘x’ × 10–1. The value of x, to the nearest integer, is ________.

Answer: (15)

29. Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force  of magnitude 100 N is applied at point A of the frame.

Suppose the force is  resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is x N. The value of x, to the nearest integer, is ________. [Given: sin (35°) = 0.573, cos (35°) = 0.819, sin (110°) = 0.939, cos (110°) = −0.342]

Answer: (82)

30. In the logic circuit shown in the figure, if input A and B are 0 to 1 respectively, the output at Y would be ‘x’. The value of x is ________.

Answer: (0)

Chemistry

Section-A

1. Among the following, the aromatic compounds are:

Choose the correct answer from the following options:

(a)  (A) and (B) only

(b)  (A), (B) and (C) only

(c)  (B), (C) and (D) only

(d) (B) and (C) only

Answer: (d)

2. Given below are two statements:

Statement I: H2O2 can act as both oxidizing and reducing agent in the basic medium.

Statement II: In the hydrogen economy, energy is transmitted in the form of dihydrogen.

In the light of the above statements, choose the correct Ans: from the options given below:

(a)  Statement I is false but statement II is true

(b)  Both Statement I and Statement II are true

(c)  Statement I is true but statement II is false

(d) Both Statement I and Statement II are false

Answer: (b)

3. Which of the following is Lindlar catalyst?

(a)  Zinc chloride and HCl

(b)  Partially deactivated palladised charcoal

(c)  Sodium and Liquid NH3

(d) Cold dilute solution of KMnO4

Answer: (b)

4. In chromatography technique, the purification of a compound is independent of:

(a)  Length of the column or TLC plate

(b)  Mobility or flow of solvent system

(c)  Physical state of the pure compound

(d) Solubility of the compound

Answer: (c)

5. Which among the following pairs of Vitamins is stored in our body relatively for longer duration?

(a)  Ascorbic acid and Vitamin D

(b)  Thiamine and Ascorbic acid

(c)  Vitamin A and Vitamin D

(d) Thiamine and Vitamin A

Answer: (c)

6. In the below chemical reaction, intermediate “X” and reagent/condition “A” are:

Answer: (c)

7. Which of the following reaction/reactions DOES NOT involve Hoffmann bromamide degradation?

Answer: (d)

8. A group 15 element, which is a metal and forms a hydride with strongest reducing power among group 15 hydrides. The element is:

(a)  Bi

(b)  As

(c)  P

(d) S

Answer: (a)

9. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R:

Assertion A: The size of the Bk3+ ion is less than the Np3+ ion.

Reason R: The above is a consequence of the lanthanoid contraction.

In the light of the above statements, choose the correct Ans: from the options given below:

(a)  A is false but R is true

(b)  Both A and R are true but R is not the correct explanation of A

(c)  A is true but R is false

(d) Both A and R are true and R is the correct explanation of A

Answer: (c)

10. The products “A” and “B” formed in the below reactions are:

Answer: (a)

11. The type of pollution that gets increased during the day time and in the presence of O3 is:

(a)  Global warming

(b)  Reducing smog

(c)  Acid rain

(d) Oxidizing smog

Answer: (d)

12. The product “P” in the below reaction is:

Answer: (d)

13. Match List-I with List-II:

List-I

Industrial process

List-II

Application

(a) Haber’s Process (i) HNO3 synthesis
(b) Ostwald’s process (ii) Aluminium extraction
(c) Contact process (iii) NH3 synthesis
(d) Hall-Heroult process (iv) H2SO4 synthesis

Choose the correct answer from the options given below:

(a)  (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)

(b)  (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)

(c)  (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

(d) (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

Answer: (d)

14. Given below are two statements:

Statement I: The Eo value for Ce4+/Ce3+ is +1.74 V.

Statement II: Ce is more stable in Ce4+ state than Ce3+ state.

In the light of the above statements, choose the correct answer from the options given below:

(a)  Both Statement I and Statement II are correct

(b)  Statement I is incorrect but statement II is correct

(c)  Both Statement I and Statement II are incorrect

(d) Statement I is correct but statement II is incorrect

Answer: (d)

15. Given below are two statements:

Statement I: Both CaCl2.6H2O and MgCl2.8H2O undergo dehydration on heating.

Statement II: BeO is amphoteric whereas the oxides of other elements in the same group are acidic.

In the light of the above statements, choose the correct Ans: from the options given below:

(a)  Statement I is true but statement II is false

(b)  Both Statement I and Statement II are false

(c)  Statement I is false but statement II is true

(d) Both Statement I and Statement II are true

Answer: (b)

16. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Enol form acetone [CH3COCH3] exists in <0.1% quantity. However, the enol forms acetylacetone [CH3COCH2OCCH3] that exists in approximately 15% quantity.

Reason R: Enol form of acetylacetone is stabilized by intramolecular hydrogen bonding, which is not possible in enol form of acetone.

In the light of the above statements, choose the correct statement:

(a)  A is true but R is false

(b)  Both A and R are true but R is the correct explanation of A

(c)  A is false but R is true

(d) Both A and R are true but R is not the correct explanation of A

Answer: (b)

17. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R

Assertion A: The H–O–H bond angle in a water molecule is 104.5°

Reason R: The lone pair – lone pair repulsion of electrons is higher than the bond pair-bond pair repulsion.

In the light of the above statements, choose the correct answer from the options given below:

(a)  A is false but R is true

(b)  A is true but R is false

(c)  Both A and R are true, and R is the correct explanation of A

(d) Both A and R are true, but R is not the correct explanation of A

Answer: (c)

18. Match List – I with List – II:

List-I

Name of oxo acid

List-II

Oxidation state of ‘P’

(a) Hypophosphorous acid (i) +5
(b) Orthophosphoric acid (ii) +4
(c) Hypophosphoric acid (iii) +3
(d) Orthophosphorous acid (iv) +2
(v) +1

Choose the correct answer from the options given below:

(a)  (a)-(iv), (b)-(v), (c)-(ii), (d)-(iii)

(b)  (a)-(v), (b)-(iv), (c)-(ii), (d)-(iii)

(c)  (a)-(v), (b)-(i), (c)-(ii), (d)-(iii)

(d) (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)

Answer: (c)

19. The process that involves the removal of sulphur from the ores is:

(a)  Refining

(b)  Roasting

(c)  Smelting

(d) Leaching

Answer: (b)

20. The functions of antihistamine are:

(a)  Antiallergic and Analgesic

(b)  Antacid and antiallergic

(c)  Antiallergic and antidepressant

(d) Analgesic and antacid

Answer: (b)

Section-B

21. If the equation below is balanced with integer coefficients, the value of c is__________. (Round off to the nearest integer)

2MnO4 + bC2O42 + cH+ → xMn2+ yCO2 + zH2O.

Answer: (16)

22. Complete combustion of 750 g of an organic compound provides 420 g of CO2 and 210 g of H2 The percentage composition of carbon and hydrogen in organic compounds is 15.3 and _______ respectively. (Round off to the Nearest Integer).

Answer: (3)

23. AB2 is 10% dissociated in water to A2+ and B. The boiling point of a 10.0 molal aqueous solution of AB2 is ____________ ° (Round off to the Nearest Integer).

Answer: (106)

24. A certain element crystallizes in a bcc lattice of unit cell edge length 27Å. If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cell in Å will be _________. (Round off to the Nearest Integer).

[Assume each lattice point has a single atom]

[Assume √3 = 1.73, √2 = 1.41]

Answer: (33)

25. The equivalents of ethylene diamine required to replace the neutral ligands from the coordination sphere of the trans-complex of CoCl3.4NH3 is __________. (Round off to the nearest Integer).

Answer: (2)

26. For the reaction A(g) ⇌ B(g) at 495 K, ΔrG° = –9.478 kJ mol–(1)

If we start the reaction in a closed container at 495 K with 22 millimoles of A, the amount of B in the equilibrium mixture is ________millimoles. (Round off to the nearest Integer).

[R = 8.314] mol–1 K–1; ln 10 = 2.303]

Answer: (20)

27. When light of wavelength 248 nm falls on a metal of threshold energy 3.0 eV, the de-Broglie wavelength of emitted electrons is ____________Å. (Round off to the Nearest Integer).

[Use : √3 = 1.73, h = 6.63×10–34 Js

me = 9.1×10–31 kg; c = 3.0 × 108ms–1; 1eV = 1.6×10–19J]

Answer: (9)

28. A 6.50 molal solution of KOH (aq.) has a density of 1.89 g cm–3The molarity of the solution is __________ moldm–3 (Round off to the Nearest Integer).

[Atomic masses : K : 39.0 u; O: 16.0 u; H: 1.0 u]

Answer: (9)

29. Two salts A2X and MX have the same value of solubility product of 4.0 × 10–12. The ratio of their molar solubilities i.e. ________. (Round off to the Nearest Integer).

Answer: (50)

30. The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at 300 K is 1.0 × 10–3 s–1 and the activation energy Ea = 11.488 kJ mol–1, the rate constant at 200 K is __________ × 10–5 s–1. (Round off to the Nearest Integer).

Answer: (10)

Mathematics

1. Consider three observations a, b and c such that b = a+c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

(a)  b2 = a2 + c2 + 3d2

(b)  b2 = 3 (a2 + c2) − 9d2

(c)  b2 = 3 (a2 + c2) + 9d2

(d) b2 = 3 (a2 + c2 + d2)

Answer: (b)

2. Let vector  be obtained by rotating the vector  by an angle 45° about the origin in counterclockwise direction in the first quadrant. Then the area of triangle having vertices (ɑ, β), (0, β) and (0, 0) is equal to:

(a)  1

(b)  1/2

(c)  1/√2

(d) 2√2

Answer: (b)

3. If for a > 0, the feet of perpendiculars from the points A (a, –2a, 3) and B (0, 4, 5) on the plane lx + my + nz = 0 are points C (0, –a, –1) and D respectively, then the length of line segment CD is equal to :

(a)  √41

(b)  √31

(c)  √55

(d) √66

Answer: (d)

4. The range of a ∈ R for which the function  x ≠ 2nπ, n ∈ N has critical points, is:

(a)  [–4/3, 2]

(b)  [1, ∞)

(c)  (–∞,–1]

(d) (–3, 1)

Answer: (a)

5. Let the functions f: R→R and g: R →R be defined as:

and 

Then, the number of points in R where (fog)(x) is NOT differentiable is equal to:

(a)  1

(b)  2

(c)  3

(d) 0

Answer: (a)

6. Let a complex number z, |z| ≠ 1, satisfy  Then, the largest value of |z| is equal to ____

(a)  5

(b)  8

(c)  6

(d) 7

Answer: (d)

7. A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade is:

(a)  3/4

(b)  52/867

(c)  39/50

(d) 22/425

Answer: (c)

8. If n is the number of irrational terms in the expansion of [31/4 + 51/8]60, then (n − 1) is divisible by

(a)  8

(b)  26

(c)  7

(d) 30

Answer: (b)

9. Let the position vectors of two points P and Q be,  respectively. Let R and S be two points such that the direction ratios of lines PR and QS are (4, –1, 2) and (–2,1,–2) respectively. Let lines PR and QS intersect at T. If the vector TA is perpendicular to both  the length of vector   is √5 units, then the modulus of a position vector of A is:

(a)  √5

(b)  √227

(c)  √171

(d) √482

Answer: (b)

10. If the three normals drawn to the parabola, y2 = 2x pass through the point (a, 0) a ≠ 0, then ‘a’ must be greater than

(a)  1

(b)  −1/2

(c)  1/2

(d) −1

Answer: (a)

11. Let  Then  is equal to :

(a)  tan1 (3/2)

(b)  π/2

(c)  cot1(3/2)

(d) tan1(3)

Answer: (b)

12. The number of roots of the equation,  in the interval [0, π] is equal to :

(a)  3

(b)  4

(c)  2

(d) 8

Answer: (3)

13. If y = y(x) is the solution of the differential equation,  then the maximum value of the function y(x) over R is equal to :

(a)  8

(b)  −15/4

(c)  1/2

(d) 1/8

Answer: (d)

14. Which of the following Boolean expression is a tautology?

(a)  (p ∧ q) ∧ (p → q)

(b)  (p ∧ q) ∨ (p ∨ q)

(c)  (p ∧ q) ∨ (p → q)

(d) (p ∧ q) → (p → q)

Answer: (d)

15. Let  Then, the system of linear equations  has:

(a)  No solution

(b)  A unique solution

(c)  Exactly two solutions

(d) Infinitely many solutions

Answer: (a)

16. If for log10sin x + log­10 cos x =−1 and  then the value of n is equal to :

(a)  16

(b)  12

(c)  20

(d) 9

Answer: (c)

17. The locus of the midpoints of the chord of the circle, x2 + y2 = 25 which is tangent to the hyperbola,  is:

(a)  (x2 + y2)2 − 16x2 + 9y2 = 0

(b)  (x2 + y2)2 − 9x2 + 144y2 = 0

(c)  (x2 + y2)2 − 9x2 − 16y2 = 0

(d) (x2 + y2)2 − 9x2 + 16y2 = 0

Answer: (d)

18. Let [x] denote the greatest integer less than or equal to x. If for n ∈ N,  then  is equal to:

(a)  1

(b)  2n1

(c)  n

(d) 2

Answer: (a)

19. Let P be a plane lx + my + nz = 0 containing the line,  If plane P divides the line segment AB joining points A (–3, –6, 1) and B (2, 4, –3) in ratio k : 1 then the value of k is equal to :

(a)  1.5

(b)  2

(c)  4

(d) 3

Answer: (b)

20. The number of elements in the set {x ∈ R : (|x| − 3) |x + 4| = 6} is equal to

(a)  2

(b)  3

(c)  1

(d) 4

Answer: (a)

Section-B

21. Let f: (0, 2) → R be defined as  Then,   is equal to_______

Answer: (1)

22. The total number of 3 × 3 matrices A having entries from the set {0, 1, 2, 3} such that the sum of all the diagonal entries of AAT is 9, is equal to ____

Answer: (766)

23. Let f:R→R be a continuous function such that f (x) + f (x + 1) = 2, for all x ∈ If  then the value of I1 + 2I2 is equal to______

Answer: (16)

24. Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four-digit numbers, then the number of common terms in these two series is equal to ____

Answer: (3)

25. If the normal to the curve  at a point (a, b) is parallel to the line x + 3y = – 5, a > 1, then the value of |a + 6b| is equal to ______

Answer: (406)

26. If  then a +  b + c is equal to_______

Answer: (d)

27. Let ABCD be a square of the side of unit length. Let a circle C1 centred at A with a unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB is tangent to it, is also drawn. Let a tangent line from point C to the circle C2 meet the side AB at E. If the length of EB is ɑ + √3β, where ɑ, β are integers, then ɑ + β is equal to ______

Answer: (a)

28. Let z and w be two complex numbers such that  and Re (w) has a minimum value. Then, the minimum value of n ∈ N, for which wn is real, is equal to ____

Answer: (4)

29. Let  and  and I3 be the identity matrix of order 3. If the determinant of the matrix (P1AP − I3)2 is ɑω2, then the value of ɑ is equal to _____

Answer: (36)

30. Let the curve y = y(x) be the solution of the differential equation,  If the numerical value of area bounded by the curve y = y(x) and the x-axis is   then the value of y(1) is equal to_______

Answer: (2)

JEE Main Session 1 February 26th Shift 2 Question Paper with Answer Key

Physics

1. A tuning fork A of unknown frequency produces 5 beats/sec with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

(a)  342 Hz

(b)  335 Hz

(c)  338 Hz

(d) 345 Hz

Answer: (b)

2. The trajectory of a projectile in a vertical plane is y = αx − βx2, where α and β are constants and x and y, are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection θ and the maximum height attained H are respectively given by

(a)   

(b)   

(c)   

(d)  

Answer: (a)

3. A cord is wound around the circumference of a wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance ‘h’, the square of the angular velocity of the wheel will be: (there is no slipping between the wheel and the cord)

(a)   

(b)  2gh

(c)   

(d)   

Answer: (d)

4. Find the peak current and resonant frequency of the following circuit (as shown in the figure)

(a)  0.2 A and 100 Hz

(b)  2 A and 50 Hz

(c)  2 A and 100 Hz

(d) 0.2 A and 50 Hz

Answer: (d)

5. The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors respectively. Then choose the correct relation for these vectors.

(a)   

(b)   

(c)   

(d)  

Answer: (d)

6. A radioactive sample is undergoing α decay. At any time t1, its activity is A and at another time t2, the activity is A/5. What is the average lifetime for the sample?

(a)   

(b)    

(c)   

(d)  

Answer: (a)

7. A particle executes S.H.M., the graph of velocity as a function of displacement is:

(a)  a circle

(b)  a parabola

(c)  an ellipse

(d) a helix

Answer: (c)

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8. A scooter accelerates from rest for time t1 at constant rate α1 and then retards at constant rate α2 for time t2 and comes to rest. The correct value of t1/t2 will be:

(a)   

(b)   

(c)    

(d)  

Answer: (b)

9. Draw the output Y in the given combination of gates.

Answer: (a)

10. An inclined plane making an angle of 300 with the horizontal is placed in a uniform horizontal electric field  as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest from a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.

[g = 9.8 m/s2,  ]

(a)  2.3 s

(b)  0.46 s

(c)  1.3 s

(d) 0.92 s

Answer: (c)

11. If ‘C’ and ‘V’ represent capacitance and voltage respectively then what are the dimensions of λ where C/V = λ?

(a)  [M2L4I3T7]

(b)  [M2L3I2T6]

(c)  [M1L3I2T7]

(d) [M3L4I3T7]

Answer: (a)

12. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: For a simple microscope, the angular size of the object equals the angular size of the image.

Reason R: Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends at a large angle.

In light of the above statements, choose the most appropriate answer from the options given below:

(a)  Both A and R are true but R is NOT the correct explanation of A

(b)  Both A and R are true and R is the correct explanation of A

(c)  A is true but R is false

(d) A is false but R is true

Answer: (a)

13. The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be:

(a)  4.17 m/s

(b)  4.34 m/s

(c)  219 m/s

(d) 3.25 m/s

Answer: (a)

14. Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on mass B as shown in the figure. If mass A starts moving away from mass B with acceleration ‘a’, then the acceleration of mass B will be:

(a)   

(b)   

(c)   

(d)  

Answer: (b)

15. A wire of 1Ω has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is:

(a)  25%

(b)  12.5%

(c)  76%

(d) 56%

Answer: (d)

16. Given below are two statements:

Statement (1):- A second’s pendulum has a time period of 1 second.

Statement (2):- It takes precisely one second to move between the two extreme positions.

In light of the above statements, choose the correct answer from the options given below.

(a)  Both Statement I and Statement II are false

(b)  Statement I is true but Statement II is false

(c)  Statement I is false but Statement II is true

(d) Both Statement I and Statement II is true

Answer: (c)

17. An aeroplane with its wings, spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of the magnetic field at that part is 2.5 × 10–4 Wb/m2 and the angle of dip is 60°. The emf induced between the tips of the plane wings will be:

(a)  88.37 mV

(b)  62.50 mV

(c)  54.125 mV

(d) 108.25 mV

Answer: (d)

18. The length of the metallic wire is l1 when the tension in it is T1. It is l2 when the tension is T2. The original length of the wire will be:

(a)   

(b)   

(c)   

(d)  

Answer: (d)

19. The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U = 3PV + 4. The gas is:

(a)  polyatomic only

(b)  monoatomic only

(c)  either monoatomic or diatomic

(d) diatomic only.

Answer: (a)

20. Given below are two statements:

Statement – I: An electric dipole is placed at the centre of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.

Statement – II: If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero.

In the light of the above statements Choose the correct answer from the option given below:

(a)  Statement I is true but Statement II is false

(b)  Statement I is false but Statement II is true

(c)  Both Statement I and Statement II are true

(d) Both Statement I and Statement II are false

Answer: (a)

Section-B

21. If the highest frequency modulating a carrier is 5 kHz, then the number of AM broadcast stations accommodated in a 90 kHz bandwidth are ___________.

Answer: (9)

22. 1 mole of a rigid diatomic gas performs a work of Q/5. when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is xR/8. The value of x is _________.

Answer: (25)

23. A particle executes S.H.M with amplitude ‘a’ and time period T. The displacement of the particle from the mean position when its speed is half of the maximum speed is √xa/2. The value of x is ________

Answer: (3)

24. Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of the ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x : 3. The value of x is ________.

Answer: (1)

25. A point source of light S, placed at a distance 60 cm in front of the centre of the plane mirror of width 50 cm, hangs vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 1.2 m from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is ________cm

Answer: (150)

26. The Zener diode has a VZ = 30 V. The current passing through the diode for the following circuit is ______ mA.

Answer: (9)

27. In the reported figure of the earth, the value of acceleration due to gravity is the same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : 5. The value of x is ____________.

Answer: (4)

28. 27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is _____ times that of a smaller drop.

Answer: (243)

29. The volume V of a given mass of monatomic gas changes with temperature T according to the relation V = KT2/3. The work done when temperature changes by 90 K will be xR. The value of x is ____. [R = universal gas constant]

Answer: (60)

30. Time period of a simple pendulum is T. The time taken to complete 5/8 oscillations starting from mean position is   The value of α is ___________.

Answer: (7)

Chemistry

Section-A

1. 2,4-DNP test can be used to identify

(a)  aldehyde

(b)  halogens

(c)  ether

(d) amine

Answer: (a)

2. Identify A in the following chemical reaction.

Answer: (c)

3. The nature of charge on resulting colloidal particles when FeCl3 is added to excess of hot water is:

(a)  positive

(b)  neutral

(c)  sometimes positive and sometimes negative

(d) negative

Answer: (a)

4. Match List-I with List-II

Choose the correct answer from the option given below:

(a)  (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

(b)  (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

(c)  (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

(d) (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

Answer: (c)

5. In  molecule, the hybridization of carbon 1, 2, 3 and 4 respectively are:

(a)  sp2, sp, sp2, sp3

(b)  sp2, sp2, sp2, sp3

(c)  sp2, sp3, sp2, sp3

(d) sp3, sp, sp3, sp3

Answer: (a)

6. Match List-I with List-II.

List-I                                             List-II

(a) Sucrose                                    (i) b-D-Galactose and b-D-Glucose

(b) Lactose                                    (ii) a-D-Glucose and b-D-Fructose

(c) Maltose                                    (iii) a-d-Glucose and a-D-Glucose

Choose the correct answer from the options given below:

(a)  (a)-(iii), (b)-(ii), (c)-(i)

(b)  (a)-(iii), (b)-(i), (c)-(ii)

(c)  (a)-(i), (b)-(iii), (c)-(ii)

(d) (a)-(ii), (b)-(i), (c)-(iii)

Answer: (d)

7. Which pair of oxides is acidic in nature?

(a)  N2O, BaO

(b)  CaO, SiO2

(c)  B2O3, CaO

(d) B2O3, SiO2

Answer: (d)

8. Calgon is used for water treatment. Which of the following statements is NOT true about Calgon?

(a)  Calgon contains the 2nd most abundant element by weight in the earth’s crust

(b)  It is also known as Graham’s salt.

(c)  It is a polymeric compound and is water-soluble.

(d) It does not remove Ca2+ ion by precipitation.

Answer: (a)

9. Ceric ammonium nitrate and CHCl3/alc. KOH are used for the identification of functional groups present in _________and________ respectively.

(a)  alcohol, amine

(b)  amine, alcohol

(c)  alcohol, phenol

(d) amine, phenol

Answer: (a)

10. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: In TlI3, isomorphous to CsI3, the metal is present in +1 oxidation

state.

Reason R: Tl metals has fourteen f electrons in its electronic configuration.

In the light of the above statements, choose the most appropriate Answer from the options given below:

(a)  Both A and R are correct and R is the correct explanation of A

(b)  A is not correct but R is correct

(c)  Both A and R are correct R is NOT the correct explanation of A

(d) A is correct but R is not correct

Answer: (c)

11. Thallium shows Tl+ state due to inert pair effect. The correct order of electron gain enthalpy is

(a)  S > Se > Te > O

(b)  O > S > Se > Te

(c)  S > O > Se > Te

(d) Te > Se > S > O

Answer: (a)

12. Identify A in the given chemical reaction.

Answer: (a)

13. Match List-I with List-II

List-I                                 List-II

(a) Siderite                         (i) Cu

(b) Calamine                      (ii) Ca

(c) Malachite                     (iii) Fe

(d) Cryolite                       (iv) Al

                                         (v) Zn

Choose the correct answer from the options given below:

(a)  (a)-(i), (b)-(ii), (c)-(v), (d)-(iii)

(b)  (a)-(iii), (b)-(v), (c)-(i), (d)-(iv)

(c)  (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)

(d) (a)-(iii), (b)-(i), (c)-(v), (d)

Answer: (b)

14. Identify A in the given reaction.

Answer: (b)

15. Match List-I with List-II

List-I                                 List-II

(a) Sodium Carbonate       (i) Deacon

(b) Titanium                      (ii) Caster-Kellner

(c) Chlorine                       (iii) Van-Arkel

(d) Sodium hydroxide      (iv) Solvay

Choose the correct answer from the option given below

(a)  (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)

(b)  (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)

(c)  (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)

(d) (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)

Answer: (b)

16. Match List-I with List-II.

List-I                                 List-II

Molecule                           (Bond order)

(a) Ne2                               (i) 1

(b) N2                                           (ii) 2

(c) F2                                 (iii) 0

(d) O2                                           (iv) 3

Choose the correct answer from the options given below:

(a)  (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

(b)  (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)

(c)  (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

(d) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

Answer: (a)

17. Which of the following forms of hydrogen emits low energy b- particles?

(a)  Proton H+

(b)   

(c)   

(d)  

Answer: (d)

18. Choose the correct order of the basic nature of the below given amines.

(A) Phenyl methanamine

(B) N, N-Dimethylaniline

(C) N-Methyl aniline

(D) Benzenamine

(a)  D > C > B > A

(b)  D > B > C > A

(c)  A > C > B > D

(d) A > B > C > D

Answer: (d)

19. Considering the given reaction, the major product among the following is:

Answer: (c)

20. Seliwanoff test and Xanthoproteic test are used for the identification of __________ and ___________ respectively

(a)  ketoses, proteins

(b)  proteins, ketoses

(c)  aldoses, ketoses

(d) ketoses, aldoses

Answer: (a)

Section-B

21. The NaNO3 weighed out to make 50 mL of an aqueous solution containing 70.0 mg Na+ per mL is ________g. (Rounded off to the nearest integer)

[Given: Atomic weight in g mol–1. Na: 23; N: 14; O: 16.

Answer: (13)

22. The number of stereoisomers possible for [Co(ox)2(Br)(NH3)]2 is ____________. [ox = oxalate]

Answer: (3)

23. The average S–F bond energy in kJ mol–1 of SF6 is __________. (Rounded off to the nearest integer)

[Given : The values of standard enthalpy of formation of SF6(g), S(g) and F(g) are – 1100, 275 and 80 kJ mol–1 respectively.]

Answer: (309)

24. e.m.f of the following cell at 298 K in V is x ×102.

Zn|Zn2+ (0.1 M)||Ag+(0.01 M)| Ag

The value of x is _________. (Rounded off to the nearest integer)

Answer: (147)

25. A ball weighing 10g is moving with a velocity of 90ms1. If the uncertainty in its velocity is 5%, then the uncertainty in its position is ________×1033 (Rounded off to the nearest integer)

[Given: h = 6.63×1034 J s]

Answer: (1)

26. In a mildly alkaline medium, thiosulphate ion is oxidized by to “A”. The oxidation state of sulphur in “A” is ________.

Answer: (+6)

27. When 12.2 g of benzoic acid is dissolved in 100g of water, the freezing point of solution was found to be –0.93°C (Kf (H2O) = 1.86 K kg mol1). Then the number (n) of benzoic acid molecules associated (assuming 100% association) is_____________.

Answer: (2)

28. If the activation energy of a reaction is 80.9 kJ mol–1, the fraction of molecules at 700K, having enough energy to react to form products is e–x. The value of x is ______. (Rounded off to the nearest integer)

[Use R = 8.31 JK1 mol1]

Answer: (14)

29. The pH of ammonium phosphate solution, if pka of phosphoric acid and pkb of ammonium hydroxide are 5.23 and 4.75 respectively, is_____________.

Answer: (7)

30. The number of octahedral voids per lattice site in a lattice is __________.

(Rounded off to the nearest integer)

Answer: (1)

Mathematics

Section-A

1. Let L be a line obtained from the intersection of two planes x + 2y + z = 6 and y + 2z = 4. If point P (ɑ, β, γ) is the foot of the perpendicular from (3, 2, 1) on L, then the value of 21 (ɑ + β + γ) equals:

(a)  142

(b)  68

(c)  136

(d) 102

Answer: (d)

2. The sum of the series is equal to:

(a)   

(b)   

(c)   

(d)   

Answer: (c)

3. Let f(x) be a differentiable function at x = a with f’ (a) = 2 and f (a) = 4. Then  equals:

(a)  2a + 4

(b)  2a – 4

(c)  4 – 2a

(d) a + 4

Answer: (c)

4. Let A (1, 4) and B (1, −5) be two points. Let P be a point on the circle (x − 1)2 + (y − 1)2 = 1 such that (PA)2 + (PB)2 have maximum value, then the points P, A and B lie on:

(a)  a parabola

(b)  a straight line

(c)  a hyperbola

(d) an ellipse

Answer: (b)

5. If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circle of the radius r, then r is equal to :

(a)  14

(b)  12

(c)  1

(d) 13

Answer: (b)

6. Let the slope of the tangent line to a curve at any point P (x, y) be given by  If the curve intersects the line x + 2y = 4 at x = −2, then the value of y, for which the point (3, y) lies on the curve, is:

(a)  −18/11

(b)  −18/19

(c)  −4/3

(d) 18/35

Answer: (b)

7. Let A1 be the area of the region bounded by the curves y = sinx, y = cos x and y-axis in the first quadrant. Also, let A2 be the area of the region bounded by the curves y = sinx, y = cosx, the x-axis and x = π/2 in the first quadrant. Then,

(a)  A1 = A2 and A1 + A2 = √2

(b)  A1 : A2 = 1 : 2 and A1 + A2 = 1

(c)  2A1 = A2 and A1 + A2 = 1 + √2

(d) A1 : A2 = 1 : √2 and A1 + A2 = 1

Answer: (d)

8. If 0 < a, b < 1, and tan1 a + tan1 b = π/4, then the value of  is :

(a)  loge 2

(b)  loge (e/2)

(c)  e

(d) e2 – 1

Answer: (1)

9. Let F1 (A, B, C) = (A ∧ ~B) ∨ [~C ∧ (A ∨ B)] ∨ ~A and F2 (A, B) = (A ∨ B) ∨ (B → ~A) be two logical expressions. Then:

(a)  F1 is not a tautology but F2 is a tautology

(b)  F1 is a tautology but F2 is not a tautology

(c)  F1 and F2 both area tautologies

(d) Both F1 and F2 are not tautologies

Answer: (a)

10. Consider the following system of equations:

x + 2y − 3z = a

2x + 6y − 11 z = b

x − 2y + 7z = c,

Where a, b and c are real constants. Then the system of equations:

(a)  has a unique solution when 5a = 2b + c

(b)  has an infinite number of solutions when 5a = 2b + c

(c)  has no solution for all a, b and c

(d) has a unique solution for all a, b and c

Answer: (b)

11. A seven-digit number is formed using the digit 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is:

(a)  6/7

(b)  4/7

(c)  3/7

(d) 1/7

Answer: (c)

12. If vectors are collinear, then a possible unit vector parallel to the vector  is:

(a)   

(b)   

(c)   

(d)  

Answer: (c)

13. For x > 0, if  is equal to:

(a)  1/2

(b)  −1

(c)  1

(d) 0

Answer: (a)

14. Let f : R → R be defined as  If f(x) is continuous on R, then a + b equals:

(a)  3

(b)  −1

(c)  −3

(d) 1

Answer: (b)

15. Let A = {1, 2, 3 ……. , 10} and f : A → A be defined as Then the number of possible functions g : A → A such that gof = f is:

(a)  105

(b)  10C5

(c)  55

(d) 5!

Answer: (a)

16. A natural number has prime factorization given by n = 2x3y5z, where y and z are such that y + z = 5 and y1 + z1 = 5/6, y > z. Then the number of odd divisors of n, including 1, is:

(a)  11

(b)  6x

(c)  12

(d) 6

Answer: (3)

17. Let f(x) = sin1 x and  If  then the domain of the function fog is:

(a)  (−∞, −2] ⋃ [−4/3, ∞]

(b)  (−∞,−1] ⋃ [2, ∞)

(c)  (−∞, −2] ⋃ [−1, ∞]

(d) (−∞, 2] ⋃ [−3/2, ∞)

Answer: (a)

18. If the mirror image of the point (1, 3, 5) with respect to the plane 4x – 5y + 2z = 8 is (ɑ, β, γ), then 5 (ɑ + β + γ) equals:

(a)  47

(b)  39

(c)  43

(d) 41

Answer: (a)

19. Let  be a differentiable function for all x ∈ then f(x) equals.

(a)   

(b)   

(c)    

(d)  

Answer: (a)

20. The triangle of the maximum area that can be inscribed in a given circle of radius ‘r’ is:

(a)  A right-angle triangle having two of its sides of length 2r and r.

(b)  An equilateral triangle of height 2r/3.

(c)  isosceles triangle with base equal to 2r.

(d) An equilateral triangle having each of its side of length √3r.

Answer: (d)

Section-B

21. The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is _______

Answer: (1000)

22. Let ɑ and β be two real numbers such that ɑ + β = 1 and ɑ β = − Let Pn = (ɑ)n + (β)n, Pn – 1 = 11 and Pn+1 = 29 for some integer n ≥ 1. Then, the value of Pn2 is__________.

Answer: (324)

23. Let X1, X2, …. X18 be eighteen observation such that  where ɑ and β are distinct real numbers. If the standard deviation of these observations is 1, then the value of |ɑ − β| is ___________.

Answer: (3)

24. In  for m, n ≥ 1 and  then α equals ______

Answer: (1)

25. Let L be a common tangent line to the curves 4x2 + 9y2 = 36 and (2x)2 + (2y)2 = 31. Then the square of the slope of the line L is __________.

Answer: (3)

26. If the matrix  satisfies the equation  for some real numbers α and β, then β – α is equal to_______.

Answer: (4)

27. If the arithmetic mean and the geometric mean of the pth and qth terms of the sequence −16, 8, −4, 2, … satisfy the equation 4x2 − 9x + 5 = 0, then p + q is equal to ______________.

Answer: (10)

28. Let the normals at all the points on a given curve pass through a fixed point (a, b). If the curve passes through (3, −3) and (4, −2 √2), and given that a − 2√2b = 3, then (a2 + b2 + ab) is equal t