71. A jar is filled with two non-mixing liquids 1 and 2 having densities p1 and p2. respectively. A solid ball, made of a material of density p3 is dropped in the jar. It comes to equilibrium in the position shown in the figure:
Which of the following is true for p1 , p2 and p3 ?
(1) p1 < p3 < p2
(2) p3 < p1 < p2
(3) p1 > p3 > p2
(4) p
1 < p
2 < p
3
Ans. As Liquid 1 is above liquid 2, hence
As the ball gets completely immersed in
Also weight of the ball = Net up thrust
72. A working transistor with its three legs marked P, Q and R is tested using a mulimetor. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q. some resistance is seen on the multimeter. Which of the following is true for the transistor ?
(1) It is an npn transistor with R as collector
(2) It is an npn transistor with R as base
(3) It is a pnp transistor with R as collector
(4) It is a pnp transistor with R as emitter
73. A student measures the focal length of a conver lens by putting an object pin at a distance ‘u’ from the lens and measuring the distance ‘v’ of the image pin. The graph between ‘u’ and ‘v’ plotted by the student should look like
(1)
(2)
(3)
(4)
Ans.
=> v is positive
=> u is negative
Ans. (4)
74. Directions : Questions No. 74 and 75 are based on the following paragraph. Consider a block of conducting material of resistively ‘p’ shown in the figure. Current ‘I’ enters at ‘A’ and leaves from ‘D’. We apply superposition principle to find voltage developed between ‘B’ and ‘C’. The calculation is done in the following steps:
(i) Take current ‘I’ entering from ‘A’ and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E(r) at distance ‘r’ from A by using Ohm’s law E = pj. Where j is the current per unit area at ‘r’.
(iii) From the ‘r’ dependence of E(r). obtain the potential V(r) at r.
(iv) Repeat (i), (ii) and (iii) for current ‘I’ leaving ‘D’ and superpose results for ‘A’ and ‘D’.
measured between B and
C is
Ans.
75. Directions : Questions No. 74 and 75 are based on the following paragraph. Consider a block of conducting material of resistively ‘p’ shown in the figure. Current ‘I’ enters at ‘A’ and leaves from ‘D’. We apply superposition principle to find voltage developed between ‘B’ and ‘C’. The calculation is done in the following steps:
(i) Take current ‘I’ entering from ‘A’ and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E(r) at distance ‘r’ from A by using Ohm’s law E = pj. Where j is the current per unit area at ‘r’.
(iii) From the ‘r’ dependence of E(r). obtain the potential V(r) at r.
(iv) Repeat (i), (ii) and (iii) for current ‘I’ leaving ‘D’ and superpose results for ‘A’ and ‘D’.
For current entering at A, the electric field at a distance ‘r’ from A is
Ans.
76. In the circuit below, A and B represent two inputs and C represents the out put.
The circuit represents
(1) OR gate
(2) NOR gate
(3) AND gate
(4) NAND gate
77. A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a another body passes through x = 0 moving in the positive x-direction with a constant speed. The position of the first body is given by x1 (t) after time ‘t’ and that of the second body by x2 (t) after the same time interval. Which of the following graphs correctly describe (x1 – x2) as a function of time ‘t’
(1)
(2)
(3)
(4)
Ans.
Hence => Ans. (3)
78. This question contains Statement-1 and Statement-2, Of the four choices given after the statements, choose the one that best desctibes the two statements.
Statement-1:
Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
And
Statement-2
For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decreases with increasing Z.
(1) Statement-1 is true, Statement-2 is false
(2) Statement-1 is false, Statement-2 is true
(3) Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1
(4) Statement-1 is true, Statement-2 is true; Statement-2 is not correct explanation for Statement-1
79.
This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1:
For a mass M kept at the centre of a cube of side ‘a’ , the flux of gravitational field passing through its sides is 4 
GM.
and
Statement-2:
If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ from the source is given as 
, its flux through a closed surface
depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.
(1) Statement-1 is true, Statement-2 is false
(2) Statement-1 is false, Statement-2 is true
(3) Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1
(4) Statement-1 is true, Statement-2 is true; Statement-2 is not correct explanation for Statement-1
Ans.
As in electrostatics,
In gravitation, 
hence 
Statement-1 is ‘true’.As gauss law can be prone using coulomb’s law, hence Statement-2 is the correct explanation of statement-1. => Ans. (3)
80.
A 5 V battery with internal resistance 2
and a 2 V battery with internal resistance 1 are connected to a 10 resistor as shown in the figure:
The current in the 10resistor is
(1) 0.27 A P1 to P2
(2) 0.27 A P2 to P1
(3) 0.03 A P1 to P2
(4) 0.03 A P2 to P1
2 = -10y + 1(x-y)
=> y = = 0.03A => Ans. (4)
81. An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by
(1) a screw gauge provided on the microscope
(2) a vernier scale provided on the microscope
(3) a standard laboratory scale
(4) a meter scale provided on the microscope
Ans. A screw gauge provided on the microscope is used to measure is used to measure distances on a travelling microscope. Ans. (1)
82.
A horizontal overhead powerline is at a height of 4 m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is 
(1) 2.5 x 10-7 T northward
(2) 2.5 x 10-7 T southward
(3) 5 x 10-6 T northward
(4) 5 x 10-6 T southward
83.
The speed of sound in oxygen (O2) at a certain temperature is 460 ms-1 . The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)
(1) 330 ms-1
(2) 460 ms-1
(3) 500 ms-1
(4) 650 ms-1
84. Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
Ans.
85.
A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms-1 . The magnitude of its momentum is recorded as
(1) 17.57 kg ms-1
(2) 17.6 kg ms-1
(3) 17.565 kg ms-1
(4) 17.56 kg ms-1
Ans
Momentum = mass X velocity = 3.513X5.00 = 17.565
But significant figures allows only two digits after decimal point
=> momentum = 17.57
86.
The dimension of magnetic field in M, L, T and C (Coulomb) is given as
(1) M T-2 C-1
(2) M L T-1C-1
(3) M T2 C-2
(4) M T-1 C-1
Ans.
=> [B] = m T-1 C-1 => Ans. (4)
87. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plats is ‘d’ . The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k1 = 3 and thinkness 
while the other one has dielectric constant k2 = 6 and thickness
Copacitance of the capacitor is now
(1) 20.25 pF
(2) 1.8 pF
(3) 45 pF
(4) 40.5 pF
Ans.
88.
An athlete in the Olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range
(1) 2,000 J – 5,000 J
(2) 200 J – 500 J
(3) 2 x 105 J – 3 x 105 J
(4) 20,000 J – 50,000 J
Ans. Average speed = 10 m/s
Mass of the athlete will be around 40.100 kg
Hence, K. E. [2000 J, 5000 J]
89. Relative permittivity and permeability of a material are and , respectively. Which of the following values of these quantities are allowed for diamagnetic material?
(1) 
=1.5, 
= 1.5
(2) = 0.5, = 1.5
(3) =1.5, = 0.5
(4) = 0.5, = 0.5
90.
A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 
, where r is the distance from the centre of the shell ?
(1)
(2)
(3)
(4)
Ans,
91. A spherical solid ball of volume V is made of a material of density
It is falling through a liquid of density
Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., F
viscous = -kv
2 (k > 0). The terminal speed of the ball is
Ans. M adownwarg = Vp1g – Vp2g – kv2 => terminal velocity is achieved when a becomes zero.
92. Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown resistor R is
(1) 55 (2) 13.75
(3) 220 (4) 110
Ans.
=> Ans. (3)
93. While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, the measures the column length to be x cm for the second resonance. Then
(1) 36 > x > 18
(2) 18 > x
(3) x > 54
(4) 54 > x > 36
Ans.
For first resonance condition
For second resonance condition 
=> C| > C
=> x > 54 => Ans. (3)
94. A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos
If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then
in appropriate units are
Ans.
95. A block of mass 0.05 kg is moving with a speed of 2.00 ms
-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is
(1) 0.34 J
(2) 0.16 J
(3) 1.00 J
(4) 0.67 J
96.
Suppose an electron is attracted towards the origin by a force
where ‘k’ is a constant and ‘r’ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be ‘rn’ and the kinetic energy of the electron to be ‘Tn’ Then which of the following is true ?
Ans.
97.
Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of -0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is
(1) 3.38 mm
(2) 3.32 mm
(3) 3.73 mm
(4) 3.67 mm
Ans.
Observed Reading = M. S. R. + C. S. R.
True Reading = Observed reading – Zero error
= 3.35 – (0.03)
= 3.38 mm
98.
An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure P1 and temperature T1. The other chamber has volume V2 and contains ideal gas at pressure P2 and temperature T2. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be
Ans. From Conservation of energy- 
99.
Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area A = 10 cm2 and length =20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is 
Ans.
100. A capillary tube (A) is dipped in water. Another identical tune (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes ?
(1)
(2)
(3)
(4)
Ans.
In a soap solution, surface tension decreases hence
is smaller than for
=> hsoap < hwater =. Ans. (4)
101. Electrons accelerated by potential V are diffracted from a crystal. If d = 1 A and i = 30
0, V should be about (h = 6.6 10
-34 Js, m
e = 9.1 10
-31 kg, e = 1.6 10
-19 C)
(1) 1000 V
(2) 2000 V
(3) 50 V
(4) 500 V
Ans. For contrive time interferences
Path difference = 
=> 2 d cos i =
102. If a strong diffraction peak is observed when electrons are incident at an angle ‘i’ from the normal to the crystal planes with distance ‘d’ between them (see figure), de Broglie wavelength
of electrons can be calculated by the relationship (n is an integer)
(1) d cos i = n
(2) d sin i = n
(3) 2d cos i = n
(4) 2d sin i = n
103.
In an experiment electrons are made to pass through a narrow slit of width ‘d’ comparable to their de Broglie wavelength. They are detected on a screen at a distance ‘D’ from the slit (see figure)
Which of the following graphs can be expected to represent the number of electrons ‘N’ detected as a function of the detector position ‘y’ (y = 0 corresponds to the
middle of the slit) ?
(1)
104. A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s-1 , the escape velocity from the surface of the planet would be
(1) 0.11 km s-1
(2) 1.1 km s-1
(3) 11 km s-1
(4) 110 km s-1
Ans.
105.
A thin rod of length ‘L’ is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as
., where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against ‘n’, which of the following graphs best approximates the dependence of xCM on n ?
(1)
As the ball gets completely immersed in 
Also weight of the ball = Net up thrust
=> v is positive => u is negative 
Ans. (4)
measured between B and C is 
Hence => Ans. (3)
GM.
, its flux through a closed surface 
In gravitation, 
hence 
Statement-1 is ‘true’.As gauss law can be prone using coulomb’s law, hence Statement-2 is the correct explanation of statement-1. => Ans. (3)
and a 2 V battery with internal resistance 1 
while the other one has dielectric constant k2 = 6 and thickness
Copacitance of the capacitor is now
=1.5, 
= 1.5
, where r is the distance from the centre of the shell ? 
It is falling through a liquid of density 
Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = -kv2 (k > 0). The terminal speed of the ball is
If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then
in appropriate units are
where ‘k’ is a constant and ‘r’ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be ‘rn’ and the kinetic energy of the electron to be ‘Tn’ Then which of the following is true ?
(2) 
(4) 
is smaller than for
., where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against ‘n’, which of the following graphs best approximates the dependence of xCM on n ?
