Consider the circular loop having current I and with central point O. The magnetic field at the central point O is 
                                      

1. $\frac{2 {\mu }_0 i}{3 \mathrm{\pi } \mathrm{R}}$ acting downward

2. $\frac{5 {\mu }_0 i}{12 \mathrm{R}}$ acting downward

3. $\frac{6 {\mu }_0 i}{11 \mathrm{R}}$ acting downward

4. $\frac{3 {\mu }_0 i}{7 \mathrm{R}}$ acting downward

The Boolean expression , where P and Q are the inputs of the logic circuit, represents

1. AND gate

2. NAND gate

3. NOT gate

4. OR gate

Consider the diagram shown below. 
                       
A voltmeter of resistance 150 Ωis connected across A and B. The potential drop across B and C measured by voltmeter is

1. 33 V

2. 26 V

3. 31 V

4. 28 V

Two spherical nuclei have mass numbers 216 and 64 with their radii R₁ and R₂ respectively. The ratio,  \(R_1 \over R_2\) is equal to

1. 3:2 

2. 1:3

3. 1:2

4. 2:3

A massless rod S having length 2l has equal point masses attached of its tow ends as shown in the figure. The rod is rotating about an axis passing through its centre and making angle α with the axis. The magnitude of change of momentum of rod i.e. equals 

1. $2 m I^3 {\omega }^2 \sin \theta ·\cos \theta$

2. $m{I}^2 {\omega }^2 \sin 2\theta$

3. $m{I}^2 \sin 2\theta$

4. $m^{1/2}{I}^{1/2} \omega \sin \theta ·\cos \theta$

A semiconductor having electron and hole mobilities respectively. 
If its intrinsic carrier density is , then what will be the value of hole concentration P for which the conductivity will be minimum at a given temperature?

1. $ni\sqrt{\frac{{\mu }_n}{{\mu }_p}}$

2. $nh\sqrt{\frac{{\mu }_n}{{\mu }_p}}$

3. $ni\sqrt{\frac{{\mu }_p}{{\mu }_n}}$

4. $nh\sqrt{\frac{{\mu }_p}{{\mu }_n}}$

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