A displacement current of \(4.0\) A can be set up in the space between two parallel plates of \(6\) \(\mu\)F capacitor. The rate of change of potential difference across the plates of the capacitor is nearly \(\alpha \times 10^6\) V/s. The value of \(\alpha\) is __________.

The activity of a radioactive sample falls from \(700 \;\mathrm{s}^{-1}\) to \(500\; \mathrm{s}^{-1}\) in \(30\;min\). Its half life is close to.........\(min\)

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 : \(\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819\) \(\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]\)  

A large drum having radius \(R\) is spinning around its axis with angular velocity \(\omega\), as shown in figure. The minimum value of \(\omega\) so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M is \(\mu\), is :

For the \(LCR\) circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor \(C '\) , when joined with the capacitor \(C\) present in the circuit , makes the power factor of the circuit unity. The capacitor \(C'\), must have been connected in

If microwaves, \(X\) rays, infrared, gamma rays, ultraviolet, radio waves and visible parts of the electromagnetic spectrum by are denoted \(M, X, I, G, U, R\) and \(V\) then which of the following is the arrangement in ascending order of wavelength ?

The energy equivalent of \(1 \mathrm{~g}\) of substance is _______.

A circular disc reaches from top to bottom of an inclined plane of length \('L'.\) When it slips down the plane, it takes time \('t_{1}'\). when it rolls down the plane, it takes time \(t_{2}\). The value of \(\frac{t_{2}}{t_{1}}\) is \(\sqrt{\frac{3}{x}}\). The value of \(x\) will be .... .

Two nuclei of mass number \(3\) combine with another nucleus of mass number \(4\) to yield a nucleus of mass number \(10\). If the binding energy per nucleon for the mass numbers \(3\), \(4\) and \(10\) are \(5.6\) MeV, \(7.4\) MeV and \(6.1\) MeV, respectively, then in the process, \(\Delta Mc^2 = \) _____ MeV.

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by \({E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .\) The dielectric constant of the medium is equal to : (Take \(\mu_{{r}}=1\) )