Two charges of \(5 Q\) and \(-2 Q\) are situated at the points \((3 a, 0)\) and \((-5 a, 0)\) respectively. The electric flux through a sphere of radius \(4a\) having center at origin is

Electric charge is transferred to an irregular metallic disk as shown in figure. If \(\sigma_1, \sigma_2, \sigma_3\) and \(\sigma_4\) are charge densities at given points then, choose the correct answer from the options given below:

The series combination of two batteries, both of the same emf \(10 \mathrm{\;V},\) but different internal resistance of \(20\; \Omega\) and \(5\; \Omega,\) is connected to the parallel combination of two resistors \(30\; \Omega\) and \(\mathrm{R}\; \Omega .\) The voltage difference across the battery of internal resistance \(20\; \Omega\) is zero, the value of \(\mathrm{R}(\text { in } \Omega)\) is 

What is the position and nature of image formed by lens combination shown in figure? (\(f_1, f_2\) are focal lengths)

A particular hydrogen - like ion emits the radiation of frequency \(3 \times 10^{15} \mathrm{~Hz}\) when it makes transition from \(n=2\) to \(n=1\). The frequency of radiation emitted in transition from \(n=3\) to \(n=1\) is \(\frac{x}{9} \times 10^{15} \mathrm{~Hz}\), when \(x=\) = _____.

In a hydrogen like atom, when an electron jumps from the \(M -\) shell to the \(L-\) shell the wavelength of emitted radiation is \(\lambda \). If an electron jumps from \(N-\) shell to the \(L-\) shell the wavelength of emitted radiation will be

The angular frequency of alternating current in a \(L-C-R\) circuit is \(100\, rad / s\). The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

A particle is moving with speed \(v= b\sqrt x\) along positive \(x-\) axis. Calculate the speed of the particle at time \(t = \tau\) (assume that the particle is at origin at \(t = 0\) ).

A particle of mass \(2\, kg\) is moving such that at time \(t\), its position, in meter, is given by \(\overrightarrow r \left( t \right) = 5\hat i - 2{t^2}\hat j\) . The angular momentum of the particle at \(t\, = 2\, s\) about the origin in \(kg\, m^{-2}\, s^{-1}\) is

The parallel combination of two air filled parallel plate capacitors of capacitance \(C\) and \(nC\) is connected to a battery of voltage, \(V\). When the capacitor are fully charged, the battery is removed and after that a dielectric material of dielectric constant \(K\) is placed between the two plates of the first capacitor. The new potential difference of the combined system is