Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below: \({ }_{1}^{2} X +{ }_{1}^{2} X ={ }_{2}^{4} Y\) The binding energies per nucleon \({ }_{1}^{2} X\) and \({ }_{2}^{4} Y\) are \(1.1\,MeV\) and \(7.6\,MeV\) respectively. The energy released in this process is \(MeV\).

A vehicle of mass \(200\,kg\) is moving along a levelled curved road of radius \(70\,m\) with angular velocity of \(0.2\,rad / s\). The centripetal force acting on the vehicle is \(.........\,N\)

A convex lens, of focal length \(30\,cm,\)  a concave lens of focal length \(120\,cm,\) and a plane mirror are arranged as shown. For an object kept at a distance of \(60\,cm\)  from the convex lens, the final image, formed by the combination, is a real image, at a distance of

A gas mixture consists of \(3\) moles of oxygen and \(5\) moles of argon at temperature \(T\). Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of \(RT\) ) of the mixture is

If \(\overrightarrow{ P } \times \overrightarrow{ Q }=\overrightarrow{ Q } \times \overrightarrow{ P },\) the angle between \(\overrightarrow{ P }\) and \(\overrightarrow{ Q }\) is \(\theta\left(0^{\circ} < \theta < 360^{\circ}\right) .\) The value of \(\theta\) will be ........

In a series \(L-C-R\) circuit, \(C = 10^{-11}\,Farad.\) \(L = 10^{-5}\,Henry\) and \(R =100\,Ohm.\) when a constant \(D.C.\) voltage \(E\) is applied to the circuit, the capacitor acquires a charge \(10^{-9}\,C\) .The \(D.C.\) source is replaced by a sinusoidal voltage source in which the peak voltage \(E_0\) is equal to the constant \(D.C.\) voltage \(E.\) At resonance the peak value of the charge acquired by the capacitor will be

A small square loop of wire of side \(l\) is placed inside a large square loop of wire \(L(L \gg l)\). Both loops are coplanar and their centres coincide at point \(O\) as shown in figure. The mutual inductance of the system is.

In the given circuit, the breakdown voltage of the Zener diode is \(3.0 \mathrm{~V}\). What is the value of \(\mathrm{I}_z\) ?

The root mean square speed of smoke particles of mass \(5 \times 10^{-17}\,kg\) in their Brownian motion in air at NTP is approximately \(.......\,mm\,s ^{-1}\) [Given \(k =1.38 \times 10^{-23}\,J\,K ^{-1}\) ]

A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be.