Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a
simple pendulum. They use different length of the pendulum and/or record time for different number
of oscillations. The observations area shown in the table.
Least count for length = 0.1 cm
Least count for time = 0.1 s
Student
Length of the pendulum (cm)
No. of oscillations (n)
Total time for(n) oscillations (s)
Time periods (s)
I
64.0
8
128.0
16.0
II
64.0
4
64.0
16.0
III
20.0
4
36.0
9.0
If EI, EII and EIII are the percentage errors in g, i.e., $$\left(\frac{\triangle g}g\times100\right)$$ for students I, II and III, respectively,then
Answer
(B)
EI is minimum
2
Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then
Answer
(C)
P2 > P1 > P3
3
Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?
Answer
(B)
Cut-off wavelength of the continuous X-rays depends on the atomic number of the target.
4
Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60$$^\circ$$). In the position of minimum deviation, the angle of refraction will be :
Answer
(A)
30$$^\circ$$ for both the colours
5
An ideal gas is expanding such that PT$$^2$$ = constant. The coefficient of volume expansion of the gas is
Answer
(C)
$$\frac{3}{\mathrm{T}}$$
6
A spherically symmetric gravitational system of particles has a mass density
Where $$\rho_0$$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance $$r(0 < r < \infty)$$ from the centre of the system is represented by
Answer
(C)
7
Two balls, having linear momenta $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$, undergo a collision in free space. There is no external force acting on the balls. Let $${\overrightarrow {p'} _1}$$ and $${\overrightarrow {p'} _2}$$ be their final momenta. The following option(s) is (are) NOT ALLOWED for any non-zero value of $$p,{a_1},{a_2},{b_1},{b_2},{c_1}$$ and $${c_2}$$ :
Answer
A
D
8
Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.
Answer
B
D
9
A particle of mass m and charge q, moving with velocity v enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region II is $$l$$. Choose the correct choice (s).
Answer
A
C
D
10
In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is $$\lambda$$. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).
Answer
A
B
11
STATEMENT - 1
In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
and
STATEMENT - 2
Resistance of a metal increases with increase in temperature.
Answer
(D)
Statement - 1 is False, Statement - 2 is True
12
STATEMENT - 1
An astronaut in an orbiting space station above the Earth experiences weightlessness.
and
STATEMENT - 2
An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall'.
Answer
(A)
Statement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1
13
STATEMENT - 1 :
Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.
and
STATEMENT - 2 :
By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
Answer
(D)
Statement - 1 is False, Statement - 2 is True
14
STATEMENT - 1 :
The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends to narrow down when held vertically down.
and
STATEMENT - 2 :
In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.
Answer
(A)
Statement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1
15
As the bubble moves upwards, besides the buoyancy force the following forces are acting on it
Answer
(D)
The force due to gravity and the force due to viscosity of the liquid
16
When the gas bubble is at a height y from the bottom, its temperature is :
The quantum number n of the state finally populated in He$$^+$$ ions is :
Answer
(C)
4
19
The wavelength of light emitted in the visible region by He$$^+$$ ions after collisions with H atoms is
Answer
(C)
$$4.8\times10^{-7}$$ m
20
The ratio of the kinetic energy of the $$n=2$$ electron for the H atom to that of He$$^+$$ ion is
Answer
(A)
$$\frac{1}{4}$$
21
The speed of the block at point B immediately after it strikes the second incline is
Answer
(B)
$$\sqrt{45}$$ m/s
22
The speed of the block at point C, immediately before it leaves the second incline is
Answer
(B)
$$\sqrt{105}$$ m/s
23
If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is
