The energy released per fission of nucleus of \({ }^{240} X\) is \(200 MeV\). The energy released if all the atoms in \(120 g\) of pure \({ }^{240} X\) undergo fission is \(........\times 10^{25}\,MeV\).\(\left(\right.\) Given \(\left.N_A=6 \times 10^{23}\right)\)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet.
In the light of the above statements, choose the correct answer from the options given below :

A balloon and its content having mass \(M\) is moving up with an acceleration ' \(a\) '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' \(3 a^{\prime}\) will be
(Take ' g ' as acceleration due to gravity)

The angle between vector \(\vec{Q}\) and the resultant of \((2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})\) and \((2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})\) is _______.

A uniform disc of radius \(R\) and mass \(M\) is free to rotate only about its axis. A string is wrapped over its rim and a body of mass \(m\) is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

The dimensions of \(\left(\frac{ B ^{2}}{\mu_{0}}\right)\) will be. (if \(\mu_{0}\) : permeability of free space and \(B\) : magnetic field)

Let \(\left| {{{\vec A}_1}} \right| = 3,\,\left| {\vec A_2} \right| = 5\), and \(\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 5\). The value of \(\left( {2{{\vec A}_1} + 3{{\vec A}_2}} \right)\cdot \left( {3{{\vec A}_1} - 2{{\vec A}_2}} \right)\) is

A solid sphere of radius \(r\) made of a soft material of bulk modulus \(K\) is surrounded by a liquid in a cylindrical container. A massless piston of area \(a\) floats on the surface of the liquid, covering entire crosssection of cylindrical container. When a mass \(m\) is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \(\left( {\frac{{dr}}{r}} \right)\) is 

A sphere of capacitance \(100\) pF is charged to a potential of \(100\) V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is \(\alpha \times 10^{-7}\) J. The value of \(\alpha\) is __________. (combined capacitance of spheres is \(200\) pF)

Consider a n-type semiconductor in which \(\mathrm{n}_{\mathrm{e}}\) and \(\mathrm{n}_{\mathrm{h}}\) are number of electrons and holes, respectively.
(A) Holes are minority carriers
(B) The dopant is a pentavalent atom
(C) \(\mathrm{n}_{\mathrm{e}} \mathrm{n}_{\mathrm{h}} \neq \mathrm{n}_{\mathrm{i}}^2\)
(where \(n_i\) is number of electrons or holes in semiconductor when it is intrinsic form)
(D) \(\mathrm{n}_{\mathrm{e}} \mathrm{n}_{\mathrm{h}} \geq \mathrm{n}_{\mathrm{i}}^2\)
(E) The holes are not generated due to the donors Choose the correct answer from the options given below :

A capacitor has capacitance \(5 \mu F\) when it's parallel plates are separated by air medium of thickness \(d\). A slab of material of dielectric constant \(1.5\) having area equal to that of plates but thickness \(\frac{ d }{2}\) is inserted between the plates. Capacitance of the capacitor in the presence of slab will be \(..........\mu F\)