In a nuclear fission process, a high mass nuclide \((A \approx 236)\) with binding energy \(7.6\  \mathrm{MeV} /\) Nucleon dissociated into middle mass nuclides \((A \approx 118)\), having binding energy of \(8.6 \ \mathrm{MeV} / \mathrm{Nucleon}\). The energy released in the process would be \(\mathrm{MeV}\).

If \(\vec{a}\) and \(\vec{b}\) makes an angle \(\cos ^{-1}\left(\frac{5}{9}\right)\) with each other, then \(|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|\) for \(|\vec{a}|=n|\vec{b}|\) The integer value of \(n\) is _______.

A sinusoidal voltage of peak value \(250\, V\) is applied to a series \(LCR\) circuit, in which \(R =8 \Omega, L =24\, mH\) and \(C =60 \mu F\). The value of power dissipated at resonant condition is \('x'\, kW\). The value of \(x\) to the nearest integer is .............

A body of mass \(2\) kg begins to move under the influence of time dependent force \(\vec{F} = (2t\hat{i} + 6t^2\hat{j})\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along \(x\) and \(y\)-axis respectively. The power produced by the force at \(t = 2\) s is _____ W.

In a Young's double slit experiment, a laser light of \(560\,nm\) produces an interference pattern with consecutive bright fringes' separation of \(7.2\,mm\). Now another light is used to produce an interference pattern with consecutive bright fringes' separation of \(8.1\,mm\). The wavelength of second light is \(......nm\)

A body of mass \(m\) is moving in a circular orbit of radius \(R\) about a planet of mass \(M\). At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius \(\frac{R}{2}\) , and the other mass, in a circular orbit of radius \(\frac{3R}{2}\). The difference between the final and initial total energies is

If \(50\) Vernier divisions are equal to \(49\) main scale divisions of a travelling microscope and one smallest reading of main scale is \(0.5 \mathrm{~mm}\), the Vernier constant of travelling microscope is _______.

An infinitely long wire has uniform linear charge density \(\lambda=2 \mathrm{nC} / \mathrm{m}\). The net flux through a Gaussian cube of side length \(\sqrt{3} \mathrm{~cm}\), if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be \(\mathrm{xNm}^2 \mathrm{C}^{-1}\), where x is :
[Neglect any edge effects and use \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\) SI units]

In the figure shown, after the switch \(‘S’\) is turned from position \(‘A’\) to position \(‘B’\), the energy dissipated in the circuit in terms of capacitance \(‘C’\) and total charge \(‘Q’\) is

A ring is hung on a nail. It can oscillate, without slipping or sliding \((i)\) in its plane with a time period \(T_{1}\) and, \((ii)\) back and forth in a direction perpendicular to its plane, with a period \(T _{2}\). the ratio \(\frac{ T _{1}}{ T _{2}}\) will be 

A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \(\omega_0\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

Some distant star is to be observed by some telescope of diameter of objective lens \(a\), at an angular resolution of \(3.0\times 10^{-7}\) radian. If the wavelength of light from the star reaching the telescope is \(500\) nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)