The r.m.s speed of oxygen molecules at \(47^{\circ} C\) is equal to that of the hydrogen molecules kept at _________ \({ }^{\circ} C\). (Mass of oxygen molecule/mass of hydrogen molecule \(=32 / 2\) )

The truth table for this given circuit is _______.

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is \(2000 Å\) and it becomes \(6000 Å\) when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is _______.

In the following circuit, the magnitude of current \(I _{ l }\), is \(............A\).

The magnetic field at the centre of a current carrying circular loop of radius \(R\) is 16 \(\mu\)T. The magnetic field at a distance \(x = \sqrt{3}R\) on its axis from the centre is ________ \(\mu\)T.

A solid sphere, of radius \(R\) acquires a terminal velocity \(\nu_1 \) when falling (due to gravity) through a viscous fluid having a coefficient of viscosity \(\eta \). The sphere is broken into \(27\) identical solid spheres. If each of these spheres acquires a terminal velocity, \(\nu_2\), when falling through the same fluid, the ratio \((\nu_1/\nu_2)\) equals

The atomic mass of \({ }_6 \mathrm{C}^{12}\) is \(12.000000\ \mathrm{u}\) and that of \({ }_6 \mathrm{C}^{13}\) is \(13.003354 \ \mathrm{u}\). The required energy to remove a neutron from \({ }_6 \mathrm{C}^{13}\), if mass of neutron is \(1.008665 \ \mathrm{u}\), will be :

A bead of mass \(m\) stays at point \(P ( a , b )\) on a wire bent in the shape of a parabola \(y=4 Cx ^{2}\) and rotating with angular speed \(\omega\) (see figure). The value of \(\omega\) is (neglect friction)

Keeping the significant figures in view, the sum of the physical quantities \(52.01 m, 153.2 m\) and 0.123 m is :

Given below are two statements:
Statement I: Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.
In the light of the above statements, choose the correct answer from the options given below.

For a nucleus \({ }_Z^A X\) having mass number \(A\) and atomic number \(Z\) \(A.\) The surface energy per nucleon \(\left(b_s\right)=a_1 A^{2 / 3}\) \(B.\) The Coulomb contribution to the binding energy \(b_c=-a_2 \frac{Z(Z-1)}{A^{4 / 3}}\) \(C.\) The volume energy \(b_v=a_3 A\) \(D.\) Decrease in the binding energy is proportional to surface area. \(E.\) While estimating the surface energy, it is assumed that each nucleon interacts with \(12\) nucleons, \(\left(a_1, a_2\right.\) and \(a _3\) are constants) Choose the most appropriate answer from the options given below: