Which one of the following will be the output of the given circuit?

The electric fields of two plane electromagnetic plane waves in vacuum are given by \(\overrightarrow{\mathrm{E}}_{1}=\mathrm{E}_{0} \hat{\mathrm{j}} \cos (\omega \mathrm{t}-\mathrm{kx})\) and \(\overrightarrow{\mathrm{E}}_{2}=\mathrm{E}_{0} \hat{\mathrm{k}} \cos (\omega \mathrm{t}-\mathrm{ky})\) At \(t=0,\) a particle of charge \(q\) is at origin with a velocity \(\overrightarrow{\mathrm{v}}=0.8 \mathrm{c} \hat{\mathrm{j}}\) (\(c\) is the speed of light in vacuum). The instantaneous force experienced by the particle is 

A uniform cable of mass \(‘M’\) and length \(‘L’\) is placed on a horizontal surface such that its \({\left( {\frac{1}{n}} \right)^{th}}\)  part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

Hydrogen atom is bombarded with electrons accelerated through a potential different of \(\mathrm{V}\), which causes excitation of hydrogen atoms. If the experiment is being formed at \(\mathrm{T}=0 \mathrm{~K}\). The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be \(\frac{\alpha}{10} \mathrm{~V}\), where \(\alpha=\) _______.

A uniform thin rod \(AB\) of length \(L\) has linear mass density \(\mu \left( x \right) = a + \frac{{bx}}{L}\) , where \(x\) is measured from \(A\). If the \(CM\) of the rod lies at a distance of \(\left( {\frac{7}{12}} \right)L\) from \(A\), then \(a\) and \(b\) are related as

A proton with a kinetic energy of \(2.0\,eV\) moves into a region of uniform magnetic field of magnitude \(\frac{\pi}{2} \times 10^{-3}\,T\). The angle between the direction of magnetic field and velocity of proton is \(60^{\circ}\). The pitch of the helical path taken by the proton is \(..........cm\) (Take, mass of proton \(=1.6 \times 10^{-27}\,kg\) and Charge on proton \(=1.6 \times 10^{-19}\,kg)\)

A liquid of density \(\rho \) is coming out of a hose pipe of radius \(a\) with horizontal speed \(v\) and hits a mesh. \(50\%\) of the liquid passes through the mesh unaffected. \(25\%\) looses all of its momentum and \(25\%\) comes back with the same speed. The resultant pressure on the mesh will be

A potentiometer wire of length \(300\,cm\) is connected in series with a resistance \(780\,\Omega\) and a standard cell of emf \(4\,V\). A constant current flows through potentiometer wire. The length of the null point for cell of emf \(20\,mV\) is found to be \(60\,cm\). The resistance of the potentiometer wire is\(...\Omega\)

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample is _______.

An ac circuit has an inductor and a resistor of resistance \({R}\) in series, such that \({X}_{{L}}=3 {R}\). Now, a capacitor is added in series such that \({X}_{{C}}=2 {R}\). The ratio of new power factor with the old power factor of the circuit is \(\sqrt{5}: {x}\). The value of \({x}\) is ...... .

The energy dissipated by a resistor is \(10 \,mJ\) in \(1\,s\) when an electric current of \(2\, mA\) flows through it. The resistance is \(....... \Omega\) (Round off to the Nearest Integer)