Match List \(I\) with List \(II\) :

List \(I\)	List \(II\)
\(A\) Isothermal Process	\(I\) Work done by the gas decreases internal energy
\(B\) Adiabatic Process	\(II\) No change in internal energy
\(C\) Isochoric Process	\(III\) The heat absorbed goes partly to increase internal energy and partly to do work
\(D\) Isobaric Process	\(IV\) No work is done on or by the gas

Choose the correct answer from the options given below :

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, \(5 cm\). If the tube is dipped in a similar manner in another liquid \(B\) of surface tension and density double the values of liquid \(A\), the height of liquid column raised in liquid \(B\) would be \(........m\).

\(B _{ X }\) and \(B _{ Y }\) are the magnetic field at the centre of two coils of two coils \(X\) and \(Y\) respectively, each carrying equal current. If coil \(X\) has \(200\) turns and \(20 cm\) radius and coil \(Y\) has \(400\) turns and \(20 cm\) radius, the ratio of \(B _{ X }\) and \(B _{ Y }\) is

The position vectors of two 1 kg particles, (A) and (B), are given by
\(\overrightarrow{\mathrm{r}}_{\mathrm{A}}=\left(\alpha_1 \mathrm{t}^2 \hat{i}+\alpha_2 \mathrm{t} \hat{j}+\alpha_3 \mathrm{t} \hat{k}\right) \mathrm{m}\) and \(\overrightarrow{\mathrm{r}}_{\mathrm{B}}=(\beta_1 \mathrm{t} \hat{i}+\beta_2 \mathrm{t}^2 \hat{j}\) \(+\beta_3 \mathrm{t} \hat{k}) \mathrm{m}\), respectively; \((\alpha_1=1 \mathrm{~m} / \mathrm{s}^2, \alpha_2=3 \mathrm{n} \mathrm{m} / \mathrm{s},\) \(\alpha_3=2 \mathrm{~m} / \mathrm{s},\) \(\beta_1=2 \mathrm{~m} / \mathrm{s}, \beta_2=-1 \mathrm{~m} / \mathrm{s}^2, \beta_3=4 \mathrm{pm} / \mathrm{s})\), where t is time, n and p are constants. At \(t=1 \mathrm{~s},\left|\overrightarrow{V_A}\right|=\left|\vec{V}_B\right|\) and velocities \(\vec{V}_A\) and \(\vec{V}_B\) of the particles are orthogonal to each other. At \(t=1 \mathrm{~s}\), the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is \(\sqrt{\mathrm{L}} \mathrm{kgm}^2 \mathrm{~s}^{-1}\). The value of L is _______ .

Find the magnetic field at point \(P\) due to a straight line segment \(AB\) of length \(6\, cm\) carrying a current of \(5\, A\). (See figure) \((\mu _0 = 4p\times10^{-7}\, N-A^{-2})\)

A steel rod with \({y}=2.0 \times 10^{11} \,{Nm}^{-2}\) and \(\alpha=10^{-5}{ }^{\circ} {C}^{-1}\) of length \(4\, {m}\) and area of cross-section \(10\, {cm}^{2}\) is heated from \(0^{\circ} {C}\) to \(400^{\circ} {C}\) without being allowed to extend. The tension produced in the rod is \({x} \times 10^{5} \, {N}\) where the value of \({x}\) is ....... .

A container of fixed volume contains a gas at \(27^{\circ} \mathrm{C}\). To double the pressure of the gas, the temperature of gas should be raised to ______ \({ }^{\circ} \mathrm{C}\).

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across \(\mathrm{A}\) and \(B\), their readings are \(V_1, V_2\) and \(V_3\). Choose the correct option.

Let \(f(x)=a x^3+b x^2+c x+41\) be such that \(f(1)=40, f^{'}(1)=2\) and \(f^{''}(1)=4\). Then \(a^2+b^2+c^2\) is equal to :

Diameter of a plano-convex lens is \(6 \,cm\) and thickness at the centre is \(3\, mm\). If the speed of light in the material of the lens is \(2  \times  10^8 m/sec\), the focal length of the lens is.......\(cm\)

If \(C\) and \(V\) represent capacity and voltage respectively then what are the dimensions of \(\lambda,\) where \(\frac{ C }{ V }=\lambda ?\)

Suppose that intensity of a laser is \(\left(\frac{315}{\pi}\right)\, W / m ^{2} .\) The \(rms\) electric field, in units of \(V / m\) associated with this source is close to the nearest integer is \(\left(\epsilon_{0}=8.86 \times 10^{-12} C ^{2} Nm ^{-2} ; c =3 \times 10^{8} ms ^{-1}\right)\)

A diatomic gas \((\gamma=1.4)\) does \(100 \mathrm{~J}\) of work in an isobaric expansion. The heat given to the gas is _______.