If a solid sphere of mass \(5\,kg\) and a disc of mass \(4\,kg\) have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be \(\frac{x}{7}\). The value of \(x\) is \(.........\)

Two \(4\) bits binary numbers, \(A = 1101\) and \(B = 1010\) are given in the inputs of a logic circuit shown in figure below. The output \((Y)\) will be:

A metal wire of uniform mass density having length \(L\) and mass \(M\) is bent to form a semicircular arc and a particle of mass \(m\) is placed at the centre of the arc. The gravitational force on the particle by the wire is _______.

In the given circuit if the power rating of Zener diode is \(10 \mathrm{~mW}\), the value of series resistance \(R_s\) to regulate the input unregulated supply is _______.

An ideal gas exists in a state with pressure \(P_0\) volume \(\mathrm{V}_0\).It is isothermally expanded to 4 times of its initial volume \(\left(\mathrm{V}_0\right)\), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is :

A uniform solid cylindrical roller of mass \('m'\) is being pulled on a horizontal surface with force \(F\) parallel to the surface and applied at its centre. If the acceleration of the cylinder is \('a'\) and it is rolling without slipping then the value of \('F'\) is 

For the four sets of three measured physical quantities as given below. Which of the following options is correct ? \((i)\) \(\mathrm{A}_{1}=24.36, \mathrm{B}_{1}=0.0724, \mathrm{C}_{1}=256.2\) \((ii)\) \(\mathrm{A}_{2}=24.44, \mathrm{B}_{2}=16.082, \mathrm{C}_{2}=240.2\) \((iii)\) \(\mathrm{A}_{3}=25.2, \mathrm{B}_{3}=19.2812, \mathrm{C}_{3}=236.183\) \((iv)\) \(\mathrm{A}_{4}=25, \mathrm{B}_{4}=236.191, \mathrm{C}_{4}=19.5\)

In photo electric effect \(A.\) The photocurrent is proportional to the intensity of the incident radiation. \(B.\) Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light. \(C.\) Max. \(K.E\) with which photoelectrons are emitted depends on the frequency of incident light. \(D.\) The emission of photoelectrons require a minimum threshold intensity of incident radiation. \(E.\) Max. K.E of the photoelectrons is independent of the frequency of the incident light. Choose the correct answer from the options given below:

Time taken by light to travel in two different materials \(A\) and \(B\) of refractive indices \(\mu_{A}\) and \(\mu_{B}\) of same thickness is \(t_{1}\) and \(t_{2}\) respectively. If \(t_{2}-t_{1}=5 \times 10^{-10}\) s and the ratio of \(\mu_{A}\) to \(\mu_{B}\) is \(1: 2\). Then the thickness of material, in meter is: (Given \(v_{A}\) and \(v_{B}\) are velocities of light in \(A\) and \(B\) materials respectively).