A nucleus with mass number \(242\) and binding energy per nucleon as \(7.6\,MeV\) breaks into fragment each with mass number \(121\) . If each fragment nucleus has binding energy per nucleon as \(8.1\,MeV\), the total gain in binding energy is \(........MeV\)

A body starts falling freely from height \(\mathrm{H}\) hits an inclined plane in its path at height \(\mathrm{h}\). As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of \(\frac{\mathrm{H}}{\mathrm{h}}\) for which the body will take the maximum time to reach the ground is _______.

As shown in the figure, the voltmeter reads \(2\,V\) across \(5\,\Omega\) resistor. The resistance of the voltmeter is \(.......\,\Omega\).

A string \(2.0\, m\) long and fixed at its end is driven by a \(240\, Hz\) vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

Two long straight wires \(P\) and \(Q\) carrying equal current \(10\,A\) each were kept parallel to each other at \(5\,cm\) distance. Magnitude of magnetic force experienced by \(10\,cm\) length of wire \(P\) is \(F_1\). If distance between wires is halved and currents on them are doubled, force \(F_2\) on \(10\,cm\) length of wire \(P\) will be :

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

A block of mass \(5 \mathrm{~kg}\) is placed on a rough inclined surface as shown in the figure.If \(\vec{F}_1\) is the force required to just move the block up the inclined plane and \(\vec{F}_2\) is the force required to just prevent the block from sliding down, then the value of \(\left|\vec{F}_1\right|-\left|\vec{F}_2\right|\) is _______. [Use \(g=10 \mathrm{~m} / \mathrm{s}^2\) ]

An \(AC\) source rated \(220\, V , 50\, Hz\) is connected to a resistor. The time taken by the current to change from its maximum to the rms value is

A time dependent force \(F = 6t\) acts on a particle of mass \(1\ kg\). If the particle starts from rest, the work done by the force during the first \(1\) secand will be ............... \(\mathrm{J}\)

An electric field \(\vec E\, = (25 \hat i + 30 \hat j)\,NC^{-1}\) exists in a region of space. If the potential at the origin is taken to be zero then the potential at \(x\, = 2\, m, y\, = 2\, m\) is......\(volt\)

The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index \(=1.7\)) are same. If the curvature of plano-concave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is ___________ .

A balloon filled with helium \(\left(32^{\circ} C \right.\) and \(1.7\; atm\).) bursts. Immediately afterwards the expansion of helium can be considered as