A sinusoidal voltage of peak value \(283\, V\) and angular frequency \(320/s\) is applied to a series \(LCR\) circuit. Given that \(R\, = 5\,\Omega \) , \(L\,= 25\, mH\) and \(C\, = 1000\, \mu F\). The total impedance, and phase difference between the voltage across the source and the current will respectively be

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength \(6630 \; \mathring A\) is \(0.42 \; V\). If the threshold frequency is \(x \times\) \(10^{13}  / s\), where \(x\) is\(\dots\) (nearest integer). (Given, speed light \(=3 \times 10^{8} \; m / s\), Planck's constant \(=6.63 \times 10^{-34} \; Js\) )

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is \({\theta _{iC}}\) and Brewster's angle of incidence is \({\theta _{iB}}\), such that \(\sin \,{\theta _{iC}}/\sin \,{\theta _{iB}} = \eta  = 1.28\). The  relative refractive index of the two media 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 :

Consider a frame that is made up of two thin massless rods \(AB\) and \(AC\) as shown in the figure. \(A\) vertical force \(\overrightarrow{ P }\) of magnitude \(100 \;N\) is applied at point \(A\) of the frame. Suppose the force is \(\overrightarrow{ P }\) resolved parallel to the arms \(AB\) and \(AC\) of the frame. The magnitude of the resolved component along the arm \(AC\) is \(xN\). The value of \(x\), to the nearest integer, is ............ [Given : \(\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819\) \(\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]\)  

The energy released per fission of nucleus of \({ }^{240} X\) is \(200 MeV\). The energy released if all the atoms in \(120 g\) of pure \({ }^{240} X\) undergo fission is \(........\times 10^{25}\,MeV\).\(\left(\right.\) Given \(\left.N_A=6 \times 10^{23}\right)\)

An \(npn\) transistor operates as a common emitter amplifier with a power gain of \(10^{6} .\) The input circuit resistance is \(100\, \Omega\) and the output load resistance is \(10\, K \Omega\). The common emitter current gain ' \(\beta\) ' will be............. (Round off to the Nearest Integer)

A capacitor of reactance \(4 \sqrt{3} \Omega\) and a resistor of resistance \(4 \Omega\) are connected in series with an ac source of peak value \(8 \sqrt{2} \mathrm{~V}\). The power dissipation in the circuit is _______ \(W\).

In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

The volume of an ideal gas increases 8 times and temperature becomes (1/4) of initial temperature during a reversible change. If there is no exchange of heat in this process (\( \Delta Q=0 \)) then identify the gas from the following options:

A block of mass \(m\), lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant \(k\). The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force \(F\), the maximum speed of the block is

Given below are two statements : Statement \(I\) : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation \(\mathrm{P}_1-\mathrm{P}_2=\rho \mathrm{g}\left(\mathrm{h}_2-\mathrm{h}_1\right)\) Statement \(II\) : In ventury tube shown \(2 \mathrm{gh}=v_1^2-v_2^2\) In the light of the above statements, choose the most appropriate answer from the options given below.

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of \(P_1\) and \(P_2\) are orthogonal to each other. The polarizer \(P_3\) covers both the slits with its transmission axis at \(45^{\circ}\) to those of \(P_1\) and \(P_2\). An unpolarized light of wavelength \(\lambda\) and intensity \(I_0\) is incident on \(P_1\) and \(P_2\). The intensity at a point after \(P_3\) where the path difference between the light waves from \(s_1\) and \(s_2\) is \(\frac{\lambda}{3}\), is _______.