Physics
Section-A
1. Match List I with List II.
List I
(a) Rectifier
(b) Stabilizer
(c) Transformer
(d) Filter
List II
(i) Used either for stepping up or stepping down the A.C. voltage
(ii) Used to convert A.C. voltage into D.C. voltage
(iii) Used to remove any ripple in the rectified output voltage
(iv) Used for constant output voltage even when the input voltage or load current change
Choose the correct answer form the options given below:
(a) (a)-(ii), (b)- (i), (c)-(iv), (d)-(iii)
(b) (a)-(ii), (b)- (iv), (c)-(i), (d)-(iii)
(c) (a)-(ii), (b)- (i), (c)-(iii), (d)-(iv)
(d) (a)-(iii), (b)- (iv), (c)-(i), (d)-(ii)
2. Y = A sin(ωt + ϕ0) is the time – displacement equation of an SHM, At t = 0, the displacement of the particle is Y = A/2 and it is moving along negative x-direction. Then, the initial phase angle ϕ0 will be.
(a) π/6
(b) π/3
(c) 2π/3
(d) 5π/6
3. Two identical springs of spring constant ‘2K’ are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. Then, time period of oscillations of this system is:
(a) 
(b) 
(c) 
(d) 
4. The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is:
(a) 194.8 nm
(b) 490.7 nm
(c) 913.3 nm
(d) 121.8 nm
5. In a ferromagnetic material below the Curie temperature, a domain is defined as:
(a) a macroscopic region with consecutive magnetic diploes oriented in opposite direction.
(b) a macroscopic region with zero magnetization.
(c) a macroscopic region with saturation magnetization.
(d) a macroscopic region with randomly oriented magnetic dipoles.
6. The point A moves with a uniform speed along the circumference of a circle of radius 0.36m and cover 30° in 0.1s. The perpendicular projection ‘P’ form ‘A’ on the diameter MN represents the simple harmonic motion of ‘P’. The restoring force per unit mass when P touches M will be:
(a) 100 N
(b) 50 N
(c) 9.87 N
(d) 0.49 N
7. The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is:
(a) 400 nm
(b) 382 nm
(c) 309 nm
(d) 329 nm
8. A charge ‘q’ is placed at one corner of a cube as shown in figure. The flux of electrostatic field 
through the shaded area is:
(a) q/48ε0
(b) q/8ε0
(c) q/24ε0
(d) q/4ε0
9. A sphere of radius ‘a’ and mass ‘m’ rolls along horizontal plane with constant speed v0. It encounters an inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping how far up the sphere will travel (along the incline)?
(a) 
(b) 
(c) 
(d) 
10. Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1 μm. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that:
(a) its size decreases, but intensity increases
(b) its size increases, but intensity decreases
(c) its size increases, and intensity increases
(d) its size decreases, and intensity decreases
11. An electron of mass me and a proton of mass mp = 1836 me are moving with the same speed. The ratio of their de Broglie wavelength 
will be:
(a) 918
(b) 1836
(c) 1/1836
(d) 1
12. Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V2 = 2V1 then the ratio of temperature T2/T1 is:
(a) 1/√2
(b) 1/2
(c) 2
(d) √2
13. A stone is dropped from the top of a building. When it crosses a point 5m below the top, another stone starts to fall from a point 25m below the top, both stones reach the bottom of building simultaneously. The height of the building is: [Take g = 10 m/s2]
(a) 45 m
(b) 35 m
(c) 25 m
(d) 50 m
14. If a message signal of frequency ‘fm‘ is amplitude modulated with a carrier signal of frequency ‘fc‘ and radiated through an antenna, the wavelength of the corresponding signal in air is:
[Given, C is the speed of electromagnetic waves in vacuum/air]
(a) 
(b) 
(c) c/fm
(d) c/fc
15. Given below are two statements:
Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell’s distribution.
Statement II: In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.
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 false but statement II is true.
(d) Statement I is true but statement II is false.
16. An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle ‘α’ with the plates. It leaves the plates at angle ‘β’ with kinetic energy K2. Then the ratio of kinetic energies K1 : K2 will be:
(a) 
(b) 
(c) 
(d) 
17. An LCR circuit contains resistance of 110 Ω and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45°. If on the other hand, only inductor is removed the current leads by 45° with the applied voltage. The rms current flowing in the circuit will be:
(a) 2.5 A
(b) 2 A
(c) 1 A
(d) 1.5 A
18. For extrinsic semiconductors: when doping level is increased;
(a) Fermi–level of p and n-type semiconductors will not be affected.
(b) Fermi–level of p-type semiconductors will go downward and Fermi–level of n-type semiconductor will go upward.
(c) Fermi–level of both p–type and n–type semiconductors will go upward for T > TFK and downward for T < TFK, where TF is Fermi temperature.
(d) Fermi–level of p-type semiconductor will go upward and Fermi–level of n–type semiconductors will go downward.
19. The truth table for the following logic circuit is:
(a) 
(b) 
(c) 
(d) 
20. If e is the electronic charged, c is the speed of light in free space and h is planck’s constant, the quantity 
has dimensions of :
(a) [LC−1]
(b) [M0 L0 T0]
(c) [M L T0]
(d) [M L T−1]
Section-B
21. The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4% will be _______%.
22. Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. Then charge on each of the sphere is 
The value of ‘a’ will be________. [Take g = 10 m/s2]
23. The peak electric field produced by the radiation coming from the 8 W bulb at a distance of 10 m is 
The efficiency of the bulb is 10% and it is a point source. The value of x is ___.
24. Two identical conducting spheres with negligible volume have 2.1nC and -0.1nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is _______× 10−9 [Given : 
SI unit]
25. The initial velocity v1 required to project a body vertically upward from the surface of the earth to just reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that 
The value of x will be _______.
26. A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 21Ω each and leaves by the corner R. The currents i1 in ampere is______.
27. The wavelength of an X-ray beam is 10 Å. The mass of a fictitious particle having the same energy as that of the X-ray photons is 
The value of x is _______.
28. A reversible heat engine converts one- fourth of the heat input into work. When the temperature of the sink is reduced by 52 K, its efficiency is doubled. The temperature in Kelvin of the source will be_______.
29. Two particles having masses 4g and 16g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n:2. The value of n will be_____.
30. If 
the angle between 
is θ(0° < θ < 360°). The value of ‘θ’ will be _______.
Chemistry
Section-A
1. Given below are two statements:
Statement I: The identification of Ni2+ is carried out by dimethylglyoxime in the presence of NH4OH
Statement II: The dimethylglyoxime is a bidentate neutral ligand.
In the light of the above statements, choose the correct answer 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 false but statement II is true
(d) Statement I is true but statement II is false
2. Carbylamine test is used to detect the presence of a primary amino group in an organic compound. Which of the following compounds is formed when this test is performed with aniline?
3. The correct order of bond dissociation enthalpy of halogen is:
(a) F2 > Cl2 > Br2 > I2
(b) Cl2 > F2 > Br2 >I2
(c) Cl2 > Br2 > F2 >I2
(d) I2 > Br2 > Cl2 > F2
4. Which one of the following statements is FALSE for hydrophilic sols?
(a) These sols are reversible in nature
(b) The sols cannot be easily coagulated
(c) They do not require electrolytes for stability
(d) Their viscosity is of the order of that of H2O
5. Water does not produce CO on reacting with
(a) C3H8
(b) C
(c) CH4
(d) CO2
6. What is ‘X’ in the given reaction?
7. If which of the following orders the given complex ions are arranged correctly with respect to their decreasing spin only magnetic moment?
(i) [FeF6]3−
(ii) [Co(NH3)6]3+
(iii) [NiCl4] 2−
(iv) [Cu(NH3)4]2+
(a) (ii) > (i) > (iii) > (iv)
(b) (iii) > (iv) > (ii) > (i)
(c) (ii) > (iii) > (i) > (iv)
(d) (i) > (iii) > (iv) > (ii)
8. The major product of the following reaction:
9. The correct sequence of reagents used in the preparation of 4-bromo-2-nitroethyl benzene from benzene is:
(a) CH3COCl/AlCl3, Br2/AlBr3, HNO3/H2SO4, Zn/HCl
(b) CH3COCl/AlCl3, Zn-Hg/HCl, Br2/AlBr3, HNO3/H2SO4
(c) Br2/AlBr3, CH3COCl/AlCl3, HNO3/H2SO4, Zn/HCl
(d) HNO3/H2SO4, Br2/AlCl3, CH3COCl/AlCl3, Zn-Hg/HCl
10. The major components of German Silver are:
(a) Cu, Zn and Mg
(b) Ge, Cu and Ag
(c) Zn, Ni and Ag
(d) Cu, Zn and Ni
11. The method used for the purification of Indium is:
(a) Van Arkel method
(b) Vapour phase refining
(c) Zone refining
(d) Liquation
12. Which of the following is correct structure of α-anomer of maltose
13. The major product of the following reaction is:
(a) CH3CH2CH2CHO
(b) CH3CH2CH=CH―CHO
(c) CH3CH2CH2CH2CHO
(d) 
14. The correct order of acid character of the following compounds is:
(a) II > III > IV > I
(b) III > II > I > IV
(c) IV > III > II > I
(d) I > II > III > IV
15. Which among the following species has unequal bond lengths?
(a) XeF4
(b) SiF4
(c) BF4−
(d) SF4
16. Given below are two statements:
Statement I: α and β forms of sulphur can change reversibly between themselves with slow heating or slow cooling.
Statement II: At room temperature the stable crystalline form of sulphur is monoclinic sulphur.
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) Statement I is true but statement II is false
(c) Both statement I and statement II are true
(d) Statement I is false but statement II is true
17. Correct statement about the given chemical reaction is:
(a) Reaction is possible and compound (A) will be a major product.
(b) The reaction will form a sulphonated product instead of nitration.
(c) NH2 group is ortho and para directive, so product (B) is not possible.
(d) Reaction is possible and compound (B) will be the major product.
18. Which of the following compound is added to the sodium extract before addition of silver nitrate for testing of halogens?
(a) Nitric acid
(b) Sodium hydroxide
(c) Hydrochloric acid
(d) Ammonia
19. Given below are two statements:
Statement I: The pH of rain water is normally ~5.6.
Statement II: If the pH of rain water drops below 5.6, it is called acid rain.
In the light of the above statements, choose the correct answer from the option given below.
(a) Statement I is false but Statement II is true
(b) Both statement I and statement II are true
(c) Both statement I and statement II are false
(d) Statement I is true but statement II is false
20. The solubility of Ca(OH)2 in water is:
[Given: The solubility product of Ca(OH)2 in water = 5.5 × 10−6]
(a) 1.1 × 10−6
(b) 1.77 × 10−6
(c) 1.7 × 10−2
(d) 1.11 × 10−2
Section-B
21. If a compound AB dissociates to the extent of 75% in an aqueous solution, the molality of the solution which shows a 2.5 K rise in the boiling point of the solution is ______molal.
22. The spin only magnetic moment of a divalent ion in aqueous solution (atomic number 29) is ____BM.
23. The number of compound/s given below which contain/s —COOH group is ______
(a) Sulphanilic acid
(b) Picric acid
(c) Aspirin
(d) Ascorbic acid
24. The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in kg/m3 is ______.
25. Consider titration of NaOH solution versus 1.25 M oxalic acid solution. At the end point following burette readings were obtained.
(i) 4.5 mL (ii) 4.5 mL (iii) 4.4 mL (iv) 4.4 mL (v) 4.4 mL
If the volume of oxalic acid taken was 10.0 ml. then the molarity of the NaOH solution is ____M. (Rounded-off to the nearest integer)
26. Electromagnetic radiation of wavelength 663 nm is just sufficient to ionize the atom of metal A. The ionization energy of metal A in kJ mol−1 (Rounded off to the nearest integer)
[h=6.63 × 10−34Js, c = 3.00 × 108 ms−1, NA=6.02 × 1023 mol−1]
27. The rate constant of a reaction increases by five times on increasing temperature from 27°C to 52° The value of activation energy in kJ mol−1 is ______.
(Rounded off to the nearest integer)
[R=8.314 J K−1 mol−1]
28. Copper reduces into NO and NO2 depending upon the concentration of HNO3 in solution. (Assuming fixed [Cu2+] and PNO = PNO2), the HNO3 concentration at which the thermodynamic tendency for reduction of into NO and NO2 by copper is same is 10x
The value of 2x is ______. (Rounded-off to the nearest integer)
[Given 
and at 298 K, 
]
29. Five moles of an ideal gas at 293 K is expanded isothermally from an initial pressure of 2.1 MPa to 1.3 MPa against a constant external 4.3 MPa. The heat transferred in this process is ____kJ mol−1. (Rounded-off of the nearest integer)
[Use R = 8.314 J mol−1 K−1]
30. Among the following, the number of metal/s which can be used as electrodes in the photoelectric cell is _____(Integer answer).
(a) Li
(b) Na
(c) Rb
(d) Cs
Mathematics
Section-A
1. A plane passes through the points A(1,2,3), B(2,3,1) and C(2,4,2). If O is the origin and P is (2,–1,1), then the projection of vector 
on this plane is of length:
(a) 
(b) 
(c) 
(d) 
2. The contrapositive of the statement “If you will work, you will earn money” is:
(a) If you will not earn money, you will not work
(b) You will earn money, if you will not work
(c) If you will earn money, you will work
(d) To earn money, you need to work
3. If α, β∈ R are such that 1 – 2i (here i2 = –1) is a root of z2 + αz + β = 0, then (α – β) is equal to:
(a) 7
(b) −3
(c) 3
(d) −7
4. If 
then
(a) 
(b) 
(c) I2 + I4, I3 + I5, I4 + I6 are in A.P.
(d) I2 + I4, I3 + I5, I4 + I6 are in G.P.
5. If for the matrix, 
AAT = I2, then t he value of α4 + β4 is:
(a) 1
(b) 3
(c) 2
(d) 4
6. Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A × B. Then:
(a) y = 273x
(b) 2y = 91x
(c) y = 91x
(d) 2y = 273x
7. If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is:
(a) 
(b) 
(c) 
(d) 
8. The integral 
is equal to:
(where c is a constant of integration)
(a) loge|x2 + 5x – 7| +c
(b) 
(c) 4loge|x2 + 5x – 7| + c
(d) 
9. A hyperbola passes through the foci of the ellipse 
and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:
(a) 
(b) 
(c) x2 – y2 = 9
(d) 
10. 
is equal to:
(a) 1
(b) 1/3
(c) 1/2
(d) 1/4
11. In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from chest disorder. The probability that the selected person is a smoker and non-vegetarian is:
(a) 7/45
(b) 8/45
(c) 14/45
(d) 28/45
12. The following system of linear equations
2x + 3y + 2z = 9
3x + 2y + 2z = 9
x – y + 4z = 8
(a) does not have any solution
(b) has a unique solution
(c) has a solution (α, β, γ) satisfying α + β2 + γ3 = 12
(d) has infinitely many solutions
13. The minimum value of 
where a, x ∈ R and a > 0, is equal to:
(a) 
(b) a + 1
(c) 2a
(d) 2√a
14. A function f(x) is given by 
then the sum of the series 
is equal to:
(a) 19/2
(b) 49/2
(c) 39/2
(d) 29/2
15. Let α and β be the roots of x2 – 6x – 2 = 0. If an = αn – βn for n ≥ 1, then the value of 
is:
(a) 4
(b) 1
(c) 2
(d) 3
16. Let A be a 3 × 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing the operation R2→ 2R2 + 5R3 on 2A, then det(B) is equal to:
(a) 64
(b) 16
(c) 80
(d) 128
17. The shortest distance between the line x – y = 1 and the curve x2 = 2y is:
(a) 1/2
(b) 0
(c) 1/2√2
(d) 1/√2
18. Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is:
(a) 1/5
(b) 2/9
(c) 97/297
(d) 122/297
19. 
is equal to:
(a) 75/56
(b) 65/56
(c) 56/33
(d) 65/33
20. If 0 < x, y < π and cos x + cos y – cos (x + y) = 3/2, then sin x + cos y is equal to:
(a) 
(b) 
(c) 
(d) 
Section-B
21. If 
exists and is equal to b, then the value of a – 2b is _________.
22. A line is a common tangent to the circle (x – 3)2 + y2 = 9 and the parabola y2 = 4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a+c) is equal to ______.
23. The value of 
is ______.
24. If the remainder when x is divided by 4 is 3, then the remainder when (2020 + x)2022 is divided by 8 is ______.
25. A line L passing through origin is perpendicular to the lines
If the co-ordinates of the point in the first octant on L2 at the distance of √17 from the point of intersection of L and L1 are (a, b, c), then 18(a + b + c) is equal to ______.
26. A function f is defined on [–3, 3] as
where [x] denotes the greatest integer ≤ x. The number of points, where f is not differentiable in (–3, 3) is ______.
27. If the curves x = y4 and xy = k cut at right angles, then (4k)6 is equal to ______.
28. The total number of two digit numbers ‘n’, such that 3n + 7n is a multiple of 10, is ______.
29. Let 
If the area of the parallelogram whose adjacent sides are represented by the vectors 
is 8√3 square units, then is equal to________.
30. If the curve y = y(x) represented by the solution of the differential equation (2xy2 – y)dx + xdy = 0, passes through the intersection of the lines, 2x – 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to ______.
is heated at constant pressure. The ratio dU : dQ : dW
will be:
The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (parallel to y-z plane) to that of the surface of area 0.3 m2 (parallel to x-z plane) is a : 2, where a = ________
Where, a and b are positive constants. The equilibrium distance between two atoms will (2α/β)a/b. Where a =_______
is ______ kJ. (Rounded off to the nearest integer). [Assume ideal gases and R = 8.314 J mol–1 K–1]
is
, 
and 
then:
is:
and (2 + i)z + (I – 2)
is tangent to this circle C, then its radius is:
then ordered pair (a, b) is equal to :
intersect each other at an angle of 90°, then which of the following relations is true ?
is equal to:
then this curve also passes through the point :
where [t] denotes the greatest integer ≤ t, is :
and 
then 13(a2 + b2) is equal to ________.
then 5.f(2) is equal to _________.
and 
be three given vectors. If 
is a vector such that 
then 
is equal to ________
where x, y and z are real numbers such that x + y + z > 0 and xyz = 2.
and radius of earth, R = 6400 km.]
Measured value of ‘L’ is 1.0 m from meter-scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of ‘g’ will be:
The value of x will be __________.
is _________× 10–2 (Rounded off to the nearest integer)
is (20, b, −a, −9), then |a + b| is equal to:
for all x ∈ R, then the value of f(1) lies in the interval:
is :
and the point (1, 0, 2) is:
where [x] denotes the greatest integer less than or equal to x, is:
then for what value of b, 
is:
then the value of the expression 
is________.
and n = [|k|] be the greatest integral part of |k|. Then 
is equal to ________.
where x is the displacement, k is the Boltzmann constant and T is the temperature. α and β are constants. Then the dimensions of β will be:
has a positive value for which of the following elements of 3d transition series?
where [.] denotes the greatest integer function, then f is:
and the plane x + y + z = 17 is:
is equal to:
where c is a constant o integration, then the ordered pair (a, b) is equal to:
If P(0) = 850, then the time at which population becomes zero is:
satisfies the equation t2 – 9t + 8 = 0, then the value of 
is:
where α ∈ ℝ. Suppose Q = [qij] is a matrix satisfying PQ = kI3 for some non-zero k ∈ ℝ. If q23 = −k/8 and |Q| = k2/2, then a2 + k2 is equal to________
is equal to _____
has at least one solution in (0, π/2) is_______
is equal to______
(a > 2) and [x] denotes the greatest integer ≤ x, then 
is equal to_________
be such that 
is coplanar with 
is perpendicular to 
and 
then the value of is_______
The instantaneous electric field E corresponding to B is:
collides with another particle B of mass m2 which is at rest initially. Let 
be the velocities of particles A and B after collision 
respectively. If m1 = 2m2 and after collision the angle between 
The magnetic moment of this moving particle:
where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:
are held on the x-axis at distance ‘a’ from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is ‘m’, their speed when they are infinitely far apart is:
(C) Antacid
has exactly one maxima and exactly one minima, is:
equals:
is the solution of the differential equation, 
then the function p(x) is equal to:
Further suppose that for any real number x ≠ −a and f(x) ≠ −a, (fof) (x) = x. Then f(−1/2) is equal to:
If B = A + A4, then det (B):
is 405, then |k| equals:
be two non-zero vectors such that 
is perpendicular to 
then the value of λ is________
then n is equal to ………..
is converted into 
by proton capture, the energy liberated, (in kWh), is: [Mass of nucleon = 1 GeV/c2]
then at equilibrium, the separation between molecules, and the potential energy are:
are given, respectively by:
The rms electric field, in units of V/m associated with this source is close to the nearest integer is __________. (∈0 = 8.86 × 10–12 C2Nm–2; c = 3 × 108 ms–1)
If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is_______.
is:
and x + y + z + 1 = 0, 2x – y + z + 3 = 0 is:
where N is the set of all natural number, then the value of 
is:
is equal to:
from any of its foci?
(n, a > 1) then the standard deviation of n observations x1, x2, x3…xn is:
is :
and 
such that I2 = αI1 then α equals to:
are unit vectors, then the greatest value of 
is ______.
where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is:
are defined where C – capacitance, R – Resistance, L – length, E – Electric field, B – magnetic field and ε0, μ0 – free space permittivity and permeability respectively. Then:
and 
then:
is 460, then x is equal to:
with respect to 
is:
where C is a constant of integration, then 
can be:
is equal to:
and the circle x2 + y2 = 36, then which one of the following is true?
is equal to:
and 
coplanar, then the line L2 passes through the point:
is:
If y(π/3) = 0, then y(π/4) is equal to:
is equal to:
at the point (1, 0) ?
such that 
If the projection of 
is equal to the projection of 
is perpendicular to 
is______
The percentages of error in the measurement of a, b, c and d are 2% , 1.5%, 4% and 2.5% respectively. The percentage of error in z is :
acts at a point 
Then the magnitude of torque about the point 
will be √x N–m. The value of x is ______.
and 
is 158 cu. units then:
defined by 
are m and M respectively, then the ordered pair (m, M) is equal to:
satisfying y(0) = 1, then the value of y(loge 13) is:
then tan(S) is equal to:
is:
then a + b + c is
is twice differentiable, then the ordered pair (k1, k2) is equal to:
and z – 2Re(z) represent the vertices of a square of side 4 units in the Argand plane, then |z| is equal to:
where c is a constant of integration, then g(0) is equal to:
is equal to :
1540 is………….
for −10 < x < 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to………….
Its magnetic field will be given by:
Mass of proton mp = 1.00783 U, mass of neutron mn = 1.00867 U and mass of tin nucleus mSn = 119.902199 U. (take 1U = 931 MeV)
the equilibrium constant for A ⇌ P is:
then the determinant of A is equal to
then a + b is equal to:
is:
If f(x) = 1, then x is equal to:
(2 sec2x ∙ sin2 3x + 3 tan x ∙ sin 6x) dx is equal to:
is:
is: (where c is a constant of integration)
where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi ’s and exactly 6 of sets Yi’s, then n is equal to :
and 10(n2 – n), (n ∈ N, n > 1) are three consecutive terms of a G.P., then n is equal to______
then the value of 
is equal to ______
a particle moves in the x-y plane with a constant acceleration of 
At time t, its coordinates are (20 m, y0 m). The values of t and y0 are, respectively:
in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity, is:
is equal to
is equal to:
If the normal to it at P intersects the x-axis at (9, 0) and e is its eccentricity, then the ordered pair (a2, e2) is equal to:
be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, 
then a2 + b2 is equal to
Then f(3) – f(1) is equal to:
is equal to
is equal to:
where 
and 
Then the value of 
at x = x0 is :
z = x + iy and k > 0. If the curve represented by Re(u) + Im(u) =1 intersects the y-axis at the points P and Q where PQ =5, then the value of k is:
and 
where i = √−1 then which one of the following is not true?
is:
then f´(3) is equal to…………
Then a7/a13 is equal to………..
Then the gravitational field is maximum at:
about the centre of mass (CM) to the torque provided by the horizontal and vertical forces FH and FV about the CM. The value of θ is then such that:
and parallel to 
The magnetic field 
at the moment t = 0 is:
where N is an integer. The value of N is _____.
and B = adj(adj A). If |A| = λ and |(B−1)T|=μ, then the ordered pair, (|λ|, μ) is equal to:
where θ = π/9, then the angle between the vectors 
and 
is
then k is equal to:
is k, then 18 k is equal to:
(b < 5) and the hyperbola, 
respectively satisfying e1e2 = 1. If α and β are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair (α, β) is equal to:
is equal to:
and 
where 0 ≠ p ε R , then the standard deviation of these observations is :
where C is a constant of integration, then the ordered pair (A(x), B(x)) can be:
nth term is 488 and then nth term is negative, then:
and 
If Q(α, β, γ) is the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then 3(α + β + γ) equals_____
If such a cylinder is to be made for a given mass of a material, the ratio L /R for it to have minimum possible I is:
where c = 3 × 108 ms−1 is the speed of light.
If an external magnetic field of 
exists in the region where the particle is moving then the force on the particle is 
The vector 
is:
= AX3 + BX2 + Cx + D, then B + C is equal to:
is equal to:
the standard deviation cannot be:
which passes through the point (0, 1), is:
is
equal to:
and 
then L is equal to:
then the value of k is …….
is equal to………..
and A4[aij]. If a11 = 109, then a22 is equal to…………….
(m, n ∈ N) then the greatest common divisor of the least values of m and n is……………..
What is the unit vector along direction of propagation of the wave.
It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If sinθ1 = √n sin θ2 then value of n is
then the value of n, for which g(n) = 20, is:
can be:
then the set A:
x ≠ 0. Then the function f:
then k is equal to:
is equal to :
ATA = I, then a value of abc can be:
and 
A point ‘P’ divides the line segment AB internally in the ratio λ : 1 (λ > 0). If O is the origin and 
then λ is equal to_______
then (dy/dx) at x = 0 is:
which extends upto x = d. Equation of path of electron in the region x > d is:
collides perfectly elastically with a mass 3m at rest. It moves with a velocity 
after collision, then v is given by:
at the point (x1, y1). Then 
is equal to :
is (−∞, −a] ∪ [a, ∞). Then a is equal to :
be continuous for some a, b, c ∈ R and f´(0) + f´(2) = e, then the value of a is:
is :
and inside the ellipse 
is:
If y(π) = a, and dy/dx at x = π is b, then the ordered pair (a, b) is equal to :
be three unit vectors such that 
Then 
is equal to:
(n ∈ N) then the value of n is equal to:
is equal to:
and carries a current i. The electron gun shoots an electron along the radius of solenoid with speed If the electron does not hit the surface of the solenoid, maximum possible value of v is (all symbols have their standard meaning):
from origin and moves in the x-y plane with a constant acceleration 
The x-coordinate of the particle at the instant when its y-coordinated is 32 m is D meters. The value of D is:
with the polarization along the direction 
The correct form of the magnetic field of the wave would be (here B0 is an appropriate constant)
the value of n is:
where a and b are constants and 0 ≤ x ≤ The value of x for the center of mass of the rod is at:
The horizontal distance covered by the combined mass before reaching the ground is:
passes through the box shown in figure. The flux of the electric field through surface ABCD and BCGF are marked as ϕ1 and ϕ2, then difference between 
if l1 is the least value of the term independent of x when 
and l2 is the least value of the term independent of x when 
then the ratio l2 : l1 is equal to:
Then the function, f(x) = [x2] sin πx discontinuous, when x is equal to
then:
and 
Then the area (in sq. units) of the region bounded by the curves y = f(x) and y = g(x) between the lines 2x = 1 to 2x = √3 is:
and 
where 0 < θ < π/4, then:
then a value of x satisfying y(x) = e is:
then 
is equal to:
where C is constant if integration, then the ordered pair (λ, f(θ)) is equal to:
be three vectors such that 
and the angle between 
is π/3. If 
is perpendicular to vector 
is equal to______
and 
(λ ∈ R) is equal to 
then k is equal to ________.
force Determine the work done on the particle by 
in moving the particle from point A to point B (all quantities are in SI units)
is at the origin (0, 0, 0). The electric field due to this dipole at 
is parallel to [Note that 
]
, another particle of mass m/2 moving at velocity of 
, collides perfectly inelastically with the first particle. Then, the combined body
They collide completely inelastically. Find the loss in kinetic energy.
, where c is speed of light, G is universal gravitational constant and h is the Planck’s constant. Dimension of f is that of;
and 
At t = 0 A charge q is at origin with velocity 
(c is speed of light in vacuum). The instantaneous force on this charge (all data are in SI units)
and a uniform magnetic field 
follow a trajectory from P to Q as shown in figure. The velocities at P and Q are respectively 
Then which of the following statements (A, B, C, D) are correct? (Trajectory shown is schematic and not to scale)
is greater than:
is:
is equal to:
and the hyperbola, 
respectively and (e1, e2) is a point on the ellipse, 15x2 + 3y2 = k. Then k is equal to:
is continuous at x = 0 then a + 2b is equal to:
B = adj A and C = 3A, then 
is equal to:
Then the value of |z + 3i| is:
and f(0) = 0, then f(1) is equal to:
is equal to:
and 
If μ and λ are the mean and the variance of observations, (x1 – 3), (x2 – 3) …. (x10 – 3), then the ordered pair (μ, λ) is equal to:
is equal to: (where C is a constant of integration)
and 
are coplanar and 
then value of λ is ______.
in the interval [0, 2π], is _________.
where ω is a constant and t is time. Then which of the following statements is true for the velocity 
and acceleration 
of the particle?
both are perpendicular to 
both are parallel to 
is perpendicular to 
is directed away from the origin
is perpendicular to 
is directed towards the origin
Then the ratio V1(on S1)/V2 (on S2) of the electrostatic potential on each sphere is
is
The corresponding electric field is given by 
is (speed of light 𝑐 = 3 × 108 m/s)
is an electric field 
If λ0 is initial de-Broglie wavelength of electron. its de-Broglie wavelength at time t is given by
X will be:
be two vectors. If 
is a vector such that 
is equal to:
then:
is equal to:
If 
then a and b are the roots of the quadratic equation:
Which of the following points lies on this plane?
then:
then 10A−1 is equal to:
then tan(α + 2β) is equal to_______.
is equal to ________.
is applicable. In the formula Ɛ0 is permittivity of free space, A is area of Gaussian and qenc is charge enclosed by the Gaussian surface. This equation can be used in which of the following equation?
= constant on the surface.
The minimum density of a liquid in which it float is just
It collides elastically with another body, B of the mass which has an initial velocity of 
After collision, A moves with a velocity 
The energy of B after collision is written as (x/10) J, the value of x is
|x| < 1. If 
is equal to:
is
and y(√3) = π/6, then y(−√3) is equal to:
where c is a constant of integration, then λf(π/3) is equal to :
be 1 cu. unit. If θ be the angle between the edges 
then cos θ can be:
in the interval [3, 4], where a ∈ R, then f′′(c) is equal to:
has real roots is _______.
is _______.
is given by
If an electric field 
and magnetic field 
act on the particle, its speed will double after a time
At t = 0, a positively charged particle is at the point (x, y, z) = (0, 0, π/k). If its instantaneous velocity at t = 0 is 
the force acting on it due to the wave is
for the box not to topple before moving is ______.
such that 
The angle θ (in degrees) that the resultant of 
will make with 
is_______
the value of N is_______
the correct option is______.
for some a ∈ R then the distance between the foci of the ellipse is:
is:
is a real number, then the argument of sin θ + i cos θ is:
then which one of the following is not true?
be three unit vectors such that 
and 
then the ordered pair 
is equal to:
satisfying y(0) = 1 This curve intersects the x-axis at a point whose abscissa is:
is equal to:
where k is a constant and 
is equal to:
are mixed with 3 moles of another ideal gas with 
The value of 
for the mixture is
then what will be expression for electric filed?
The quantity of flux through the loop ABCDEFA (in Wb) is______
where z = x + iy, then the point (x, y) lies on a
is equal to
lies in the plane of the vectors, 
If 
bisects the angle between 
then
where 
is
then the matrix A31 is equal to
then k is
such that y(0) = 0, then y(1) is equal to
is equal to __________.
is ________