Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz, then the original frequency of tuning fork A is ___________ Hz.

A sinusoidal voltage \(V(t)=210\,\sin 3000 t\) volt is applied to a series \(LCR\) circuit in which \(L =10\) \(mH , C =25 \mu F\) and \(R =100 \Omega\). The phase difference \((\Phi)\) between the applied voltage and resultant current will be

Match List-I with List-II.

List-I	List-II
A. \(\sin^2 \omega t\)	I. Periodic with time period \(T = \dfrac{\pi}{\omega}\) but not simple harmonic motion (SHM)
B. \(\sin^3(2\omega t)\)	II. Periodic with time period \(T = \dfrac{2\pi}{\omega}\) but Not SHM
C. \(\sin(\omega t) + \cos(\pi \omega t)\)	III. Periodic with time period \(T = \dfrac{\pi}{\omega}\) and SHM
D. \(\cos\omega t + \cos 2\omega t\)	IV. Non-periodic

Choose the correct answer from the options given below :

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

Which of the following statement is not true about stopping potential \(\left(\mathrm{V}_0\right)\)?

A body of mass 2 kg is moving along x -direction such that its displacement as function of time is given by \(x ( t )=\alpha t ^2+\beta t +\gamma m\), where \(\alpha=1 m / s ^2\), \(\beta=1 m / s\) and \(\gamma=1 m\). The work done on the body during the time interval \(t =2 s\) to \(t =3 s\), is _________ J.

To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are

In an experiment with Vernier callipers of least count \(0.1\,mm\), when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and \(6^{\text {th }}\) division of Vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between \(3.2\,cm\) and \(3.3\,cm\) marks, and \(4^{\text {th }}\) division of vernier scale coincides with the main scale division. The diameter of bob is measured as \(.......\,cm\)

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2} .\) The temperature of the hot reservoir of the first engine is \(\mathrm{T}_{1}\) and the temperature of the cold reservoir of the second engine is \(\mathrm{T}_{2} . T\) is temperature of the sink of first engine which is also the source for the second engine. How is \(T\) related to \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2}\), if both the engines perform equal amount of work?

If \(\vec{E}\) and \(\vec{K}\) represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by : \((\omega-\) angular frequency) :

A paramagnetic material has \(10^{28}\,atoms/m^3.\) Its magnetic susceptibility at temperature \(350\,K\) is \(2.8 \times 10^{-4}.\) Its susceptibility at \(300\,K\) is