The logic gate equivalent to the given circuit diagram is:

A copper wire of length \(1.0\, m\) and a steel wire of length \(0.5\, m\) having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by \(1\, mm\). If the Young's modulii of copper and steel are respectively \(1.0\times10^{11}\, Nm^{-2}\) and \(2.0\times10^{11}\, Nm^{- 2}\), the total extension of the composite wire is ........ \(mm\)

A simple pendulum of length \(1 \mathrm{~m}\) has a wooden bob of mass \(1 \mathrm{~kg}\). It is struck by a bullet of mass \(10^{-2} \mathrm{~kg}\) moving with a speed of \(2 \times 10^2 \mathrm{~ms}^{-1}\). The bullet gets embedded into the bob. The height to which the bob rises before swinging back is _______. (use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

A particle of mass \(\mathrm{m}\) and charge \(\mathrm{q}\) has an initial velocity \(\overline{\mathrm{v}}=\mathrm{v}_{0} \hat{\mathrm{j}} .\) If an electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{i}}\) and magnetic field \(\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{\mathrm{i}}\) act on the particle, its speed will double after a time:

The electric potential at the centre of two concentric half rings of radii \(R_1\) and \(R_2\), having same linear charge density \(\lambda\) is

The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is \(x: 4\) where \(x\) is ..... .

For a charged spherical ball, electrostatic potential inside the ball varies with \(r\) as \(V =2 ar ^2+ b\). Here, \(a\) and \(b\) are constant and \(r\) is the distance from the center. The volume charge density inside the ball is \(-\lambda a \varepsilon\). The value of \(\lambda\) is \(...........\). \(\varepsilon=\) permittivity of medium.

A big drop is formed by coalescing \(1000\) small identical drops of water. If \(E_1\) be the total surface energy of \(1000\) small drops of water and \(E_2\) be the surface energy of single big drop of water, the \(E_1\) : \(\mathrm{E}_2\) is \(\mathrm{x}: 1\) where \(x\) = _____.

Given is a thin convex lens of glass (refractive index \(\mu\) ) and each side having radius of curvature \(R\). One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself ?

A radioactive sample decays \(\frac{7}{8}\) times its original quantity in \(15\) minutes. The half-life of the sample is \(......min\)

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is \(p_d \) ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is \(P_c\). The values of \(P_d\) and \(P_c\) are respectively

The magnetic field in a travelling electromagnetic wave has a peak value of \(20\ n T\). The peak value of electric field strength is......\(Vm^{-1}\)