The magnetic flux \(\phi\) (in weber) linked with a closed circuit of resistance \(8\  \Omega\) varies with time (in seconds) as \(\phi=5 t^2-36 t+1\). The induced current in the circuit at \(t=2 \mathrm{~s}\) is _______ \(\mathrm{A}\).

For \(LED's\)  to emit light in visible region of electromagnetic light, it should have energy band gap in the range of

The energy released in the fusion of \(2 \mathrm{~kg}\) of hydrogen deep in the sun is \(\mathrm{E}_{\mathrm{H}}\) and the energy released in the fission of \(2 \mathrm{~kg}\) of \({ }^{235} \mathrm{U}\) is \(E_U\). The ratio \(\frac{E_H}{E_U}\) is approximately _______. (Consider the fusion reaction as \(4{ }_1^1 \mathrm{H}+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 \mathrm{v}+6 \gamma+26.7 \mathrm{MeV}\), energy released in the fission reaction of \({ }^{235} \mathrm{U}\) is \(200 \mathrm{MeV}\) per fission nucleus and \(\mathrm{N}_{\mathrm{A}}=6.023 \times 10^{23}\) )

A force \(\overrightarrow{ F }=4 \hat{ i }+3 \hat{ j }+4 \hat{ k }\) is applied on an intersection point of \(x =2\) plane and \(x\) -axis. The magnitude of torque of this force about a point \((2,3,4)\) is.......... . (Round off to the Nearest Integer)

Consider a situation in which reverse biased current of a particular \(P-N\) junction increases when it is exposed to a light of wavelength \(\le 621\, {nm}\). During this process, enhancement in carrier concentration takes place due to generation of hole-electron pairs. The value of band gap is nearly. (In \({eV}\))

A uniform cylinder of length \(L\) and mass \(M\) having cross-sectional area \(A\) is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density \(\sigma \) at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period \(T\) of the oscillations of the cylinder will be

A solid steel ball of diameter 3.6 mm acquired terminal velocity \(2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s}\) while falling under gravity through an oil of density \(925 \mathrm{~kg} \mathrm{~m}^{-3}\). Take density of steel as \(7825 \mathrm{~kg} \mathrm{~m}^{-3}\) and g as 9.8 \(\mathrm{m} / \mathrm{s}^2\). The viscosity of the oil in SI unit is

Figure shows a rod \({AB}\), which is bent in a \(120^{\circ}\) circular arc of radius \(R\). A charge \((-Q)\) is uniformly distributed over rod \({AB}\). What is the electric field \(\overrightarrow{{E}}\) at the centre of curvature \({O}\) ?

The output of the given combination gates represents

A charge \(Q\) is distributed over three concentric spherical shell of radii \(a, b, c (a < b < c)\) such that their surface charge densities are equal to one another. The total potential at a point at distance \(r\) from their common centre, where \(r < a\), would be