In terms of basic units of mass (M), length (L), time (T) and charge (Q), the dimensions of magnetic permeability of vacuum would be

1. $[ ML Q^{-2}]$

2. $[L T^{-1} Q^{-1}]$

3. $[M{L}^2 T^{-1}{Q}^{-2}]$

4. $[LT Q^{-1}]$

The black body spectrum of an object ${}_{}$\(O_1\) is such that its radiant intensity (i.e. intensity per unit wavelength interval) is maximum at a wavelength of \(200~\text{nm}\). Another object ${}_{}$\(O_2\) has a radiant intensity maximum at a wavelength of \(600~\text{nm}\). The ratio of power emitted per unit area by the source ${}_{}$\(O_1\) to that of the source ${}_{}$\(O_2\) is:
1. \(1:81\)
2. \(1:9\)
3. \(9:1\)
4. \(81:1\)

A beam of light of wavelength 400 nm and power 1.55 mW is directed at the cathode of a photoelectric cell. If only 10% of the incident photons effectively produce photoelectron then find current due to these electrons. 
(given, )

1. $5\mu A$

2. $\mathit{40}\mu A$

3. $50\mu A$

4. $114\mu A$

The molar specific heat of a gas as given from the kinetic theory is . If it is not specified whether it is , one could conclude that the molecules of the gas

1. are definitely monoatomic

2. are definitely rigid diatomic

3. are definitely non-rigid diatomic

4. can be monoatomic or rigid diatomic

The length of a metal wire is  when the tension in it is  and is  when the tension is . The natural length of the wire is

1. $\frac{l_1+l_2}{2}$

2. $\sqrt{l_1{l}_2}$

3. $\frac{l_2{T}_2-l_2{T}_1}{T_2-T_1}$

4. $\frac{l_1{T}_2+l_2{T}_1}{T_1-T_2}$

The velocity velocity vector v and displacement vector x of a particle executing SHM are related as 
 with the initial condition  at x = 0. The velocity v, when displacement is x, is

1. $v= \sqrt{v_0^2+{\omega }^2{x}^2}$

2. $v= \sqrt{v_0^2-{\omega }^2{x}^2}$

3. $v=\sqrt[3]{v_0^2+{\omega }^2{x}^2}$

4. $v=v_0-({\omega }^3{x}^3{e}^{x^3}{)}^{1/3}$

Consider the diagram shown below in which two masses of m and 2m are placed on a fixed triangular wedge. 
 
The coefficient of friction between block A and the wedge is 2/3, while that for block B and the wedge is 1/3. 
If the whole system is released from rest, then acceleration of block A is

1. Zero

2. $\frac{2 m^2}{3}g$

3. $\frac{4 m^2}{3}$g

4. $\frac{m^2}{\sqrt{2}}g$

In the arrangement shown in figure, the current through 5 Ω resistor is 

1. 2 A

2. zero

3. $\frac{12}{7}$A

4. 1 A

A hemispherical bowl of radius r is set rotating about its axis of symmetry in vertical. A small block kept in the bowl rotates with the bowl without slipping on its surface. If the surface of the bowl is smooth and the angle made by the radius through the block with the vertical is θ, then find the angular speed at which the ball is rotating.

1. $\omega =\sqrt{rg \sin \theta }$

2. \(\omega= \sqrt{\frac{g}{rcos\theta }}\)

3. $\omega =\sqrt{\frac{gr}{\cos \theta }}$

4. $\omega =\sqrt{\frac{gr}{\tan \theta }}$

The phase difference between the flux linked with a ball rotating in a uniform magnetic field and induced emf produced in it is

$1. \mathrm{\pi }/2$
$$
$2. \mathrm{\pi }/3$
$$
$3. -\mathrm{\pi }/6$
$$
$4. \mathrm{\pi }$