The equivalent resistance of the circuit shown below between points \(a\) and \(b\) is \(..........\Omega\)

An electromagnetic wave of intensity \(50\,Wm^{-2}\) enters in a medium of refractive index \(’ n’\) without any loss . The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively. Given by

The equations of two waves are given by \(y_{1}=5 \sin 2 \pi(x-v t) \,c m\,\) \(y_{2}=3 \sin 2 \pi(x-v t+1.5) \,c m\) These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........\(cm\)

Acceleration due to gravity on the surface of earth is ' \(g\) '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is \(\ldots\ldots\) g.

A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \(\omega_0\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

A particle starts moving from time \(t=0\) and its coordinate is given as \(x(t)=4t^{3}-3t.\)
A. The particle returns to its original position (origin) 0.866 units later
B. The particle is 1 unit away from origin at its turning point.
C. Acceleration of the particle is non-negative.
D. The particle is 0.5 units away from origin at its turning point.
E. Particle never turns back as acceleration is non-negative.
Choose the correct answer from the options given below :

In a medium the speed of light wave decreases to \(0.2\) times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is \(x: 1\). The value of \(x\) is \(...........\) (Given speed of light in free space \(=3 \times 10^8 m s ^{-1}\) and for the given medium \(\mu_{ r }=1\) )

Magnetic materials used for making permanent magnets \((P)\) and magnets in a transformer \((T)\) have different properties of the following, which property best matches for the type of magnet required \(?\)

A moving coil galvanometer has a coil with \(175\, turns\) and area \(1\, cm^2\) It uses a torsion band of torsion constant \(10^{-6}\, N\, -m/rad\). The coil is placed in a magnetic field \(B\) parallel to its plane. The coil deflects by \(10\) for a current of \(1\, mA\). The value of \(B\) (in Tesla) is approximately

For \(a\) gas \(C_{p}-C_{V}=R\) in a state \(P\) and \(C_{p}-C_{V}=1.10 R\) in a state \(Q, T_{p}\) and \(T_{Q}\) are the temperatures in two different states \(P\) and \(Q\) respectively. Then