A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is
Answer
(D)
0.2 mm
2
If the radius of the opening of the dropper is $$r$$, the vertical force due to the surface tension on the drop of
radius R (assuming $$r$$ << R) is
Answer
(C)
$${{2\pi {r^2}T} \over R}$$
3
If r = 5 $$ \times $$ 10−4 m, $$\rho $$ = 103 kg m−3 , g = 10 m/s2 , T = 0.11 Nm−1 , the radius of the drop when it detaches from
the dropper is approximately
Answer
(A)
1.4 $$ \times $$ 10−3 m
4
After the drop detaches, its surface energy is
Answer
(B)
2.7 $$ \times $$ 10−6 J
5
A diatomic ideal gas is compressed adiabatically $${1 \over {32}}$$ of its initial volume. If the initial temperature of the gas is Ti (in Kelvin) and the final temperature is a Ti, the value of $$a$$ is
Answer
4
6
A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating
in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the
wire is 50 N and the speed of sound is 320 ms−1, the mass of the string is
Answer
(B)
10 grams
7
A tiny spherical oil drop carrying a net charge $$q$$ is balanced in still air with a vertical uniform electric field of strength $${{81\pi } \over 7} \times {10^5}\,\,V{m^{ - 1}}.$$ When the field is switched off, the drop is observed to fall with terminal velocity $$2 \times {10^{ - 3}}\,\,m{s^{ - 1}}.$$ Given $$g = 9.8\,m\,{s^{ - 2}},$$ viscosity of the air $$ = 1.8 \times {10^{ - 5}}\,\,Ns\,{m^{ - 2}}$$ and the density of coil $$=900$$ $$kg$$ $${m^{ - 3}},$$ the magnitude of $$q$$ is
Answer
(D)
$$8.0 \times {10^{ - 19}}C$$
8
A uniformly charged thin spherical shell of radius $$R$$ carries uniform surface charge density of $$\sigma $$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $$F$$ (see figure). $$F$$ is proportional to
Answer
(A)
$${1 \over {{\varepsilon _0}}}{\sigma ^2}{R^2}$$
9
A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards, it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 s is
Answer
(C)
5.06 J
10
A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is
Answer
(B)
real and at a distance of 16 cm from the mirror.
11
A large glass slab ($$\mu$$ = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?
Answer
6
12
Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $${{25} \over 3}$$ m to $${{50} \over 7}$$ m in 30 s. What is the speed of the object in km per hour?
Answer
3
13
To determine the half-life of a radioactive element, a student plots a graph of $$\ln \left| {{{dN(t)} \over {dt}}} \right|$$ versus t. Here, $${{dN(t)} \over {dt}}$$ is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is __________.
Answer
8
14
At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1)
Answer
2
15
A diatomic molecule has moment of inertia I. By Bohr's quantization condition, its rotational energy in the nth level (n = 0 is not allowed) is
It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to $${4 \over \pi } \times {10^{11}}$$ Hz. Then, the moment of inertia of CO molecule about its centre of mass is close to (Take h = 2$$\pi$$ $$\times$$ 10$$-$$34 J-s)
Answer
(B)
1.87 $$\times$$ 10$$-$$46 kg m2
17
In a CO molecule, the distance between C (mass = 12 amu) and O (mass = 16 amu), where 1 amu $$ = {5 \over 3} \times {10^{ - 27}}$$ kg, is close to :
Answer
(C)
1.3 $$\times$$ 10$$-$$10 m
18
Two transparent media of refractive indices $\mu_1$ and $\mu_3$ have a solid lens shaped transparent material of refractive index $\mu_2$ between them as shown in figures in Column II. A ray traversing these media is also shown in the figures. In Column I different relationships between $\mu_1, \mu_2$ and $\mu_3$ are given. Match them to the ray diagram shown in Column II :
Answer
(A)
(A)→(P), (R); (B)→(Q), (S), (T); (C)→(P), (R), (T); (D)→(Q), (S)
19
You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current I (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage $V_1$ and $V_2$ (indicated in circuits) are related as shown in Column I. Match the two :
