Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_1$ and $M_2$ ?
Answer
(A)
$1: 1$
3
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.
Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.
In the light of the above statements, choose the most appropriate answer from the options given below :
Answer
(C)
(A) is not correct but (R) is correct
4
If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \epsilon_0}\right)$ is :
Answer
(B)
$\mathrm{L}^2 / \mathrm{T}^2$
5
A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$-direction in 0.3 sec . The crest P is at $x=0$ at $\mathrm{t}=0 \mathrm{sec}$ and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?
Answer
(A)
$y=2 \cos (0.83 x-3.35 t) \mathrm{cm}$
6
A solenoid having area A and length ' $l$ ' is filled with a material having relative permeability
2. The magnetic energy stored in the solenoid is :
Answer
(A)
$\frac{\mathrm{B}^2 \mathrm{~A} l}{4 \mu_0}$
7
Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :
Answer
(B)
$1 / 2$
8
A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$. The distance travelled and displacement, respectively, are
Answer
(C)
$3 \pi \mathrm{r}, 2 \mathrm{r}$
9
$$ \text { In the digital circuit shown in the figure, for the given inputs the } P \text { and } Q \text { values are : } $$
Answer
(C)
$\mathrm{P}=0, \mathrm{Q}=0$
10
An electron with mass ' m ' with an initial velocity $(\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{i}\left(\mathrm{v}_0>0\right)$ enters a magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{j}$. If the initial de-Broglie wavelength at $\mathrm{t}=0$ is $\lambda_0$ then its value after time ' t ' would be :
Answer
(B)
$\lambda_0$
11
A bi-convex lens has radius of curvature of both the surfaces same as $1 / 6 \mathrm{~cm}$. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides $\left(R_1 \neq R_2\right)$, without any change in lens power then possible combination of $R_1$ and $R_2$ is :
Answer
(B)
$\frac{1}{5} \mathrm{~cm}$ and $\frac{1}{7} \mathrm{~cm}$
12
Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V . The potential difference between the points A and $B$ (shown in the figure) is :
Answer
(D)
$\frac{2}{5} \mathrm{~V}$
13
Two water drops each of radius ' $r$ ' coalesce to form a bigger drop. If ' $T$ ' is the surface tension, the surface energy released in this process is :
Energy released when two deuterons $\left({ }_1 \mathrm{H}^2\right)$ fuse to form a helium nucleus $\left({ }_2 \mathrm{He}^4\right)$ is :
(Given : Binding energy per nucleon of ${ }_1 \mathrm{H}^2=1.1 \mathrm{MeV}$ and binding energy per nucleon of ${ }_2 \mathrm{He}^4=7.0 \mathrm{MeV}$ )
Consider a circular loop that is uniformly charged and has a radius $\mathrm{a} \sqrt{2}$. Find the position along the positive $z$-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in $x y$ plane at the origin :
Answer
(A)
a
17
A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions $\mathrm{T}_1$ and $\mathrm{T}_2$, respectively, are (in N ) :
(Take acceleration due to gravity $10 \mathrm{~m} / \mathrm{s}^2$ )
Answer
(A)
$5 \sqrt{3}, 5$
18
Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the change in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a constant.
(E) The work done to change the temperature from $\mathrm{T}_1$ to $\mathrm{T}_2$ is proportional to $\left(\mathrm{T}_2-\mathrm{T}_1\right)$.
Choose the correct answer from the options given below :
Answer
(B)
(B), (E) only
19
Given a charge q , current I and permeability of vacuum $\mu_{\mathrm{o}^*}$. Which of the following quantity has the dimension of momentum ?
Answer
(D)
$\mathrm{q} \mu_{\mathrm{o}} \mathrm{I}$
20
Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li}^{++}$ ion in its ground state is given by $\frac{1}{X} a_0$, where $X=$ __________ (Where $\mathrm{a}_0$ is the first Bohr's radius.)
Answer
(D)
3
21
A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to $60^{\circ}$. The refractive index of the prism material is $\sqrt{2}$. The angle of incidence (in degrees) is__________
Answer
45
22
The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.
Answer
1
23
A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of $2 \mathrm{rad} / \mathrm{s}^2$. Moment of intertia of the wheel is___________ $\mathrm{kg} \mathrm{}\,\, \mathrm{m}^2$. (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ )
Answer
1
24
The internal energy of air in $4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}$ sized room at 1 atmospheric pressure will be___________________$\times 10^6 \mathrm{~J}$
(Consider air as diatomic molecule)
Answer
12
25
A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is____________ $\times 10^{10} \mathrm{~J}$.
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