If the average translational kinetic energy of a molecule in a gas is equal to the kinetic energy of an electron accelerating from rest through \(10 \mathrm{~V}\), then the temperature of the gas molecule is
\[
\left(\text { Boltzmann constant }=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right)
\]

The gravitational field in a region is given by \(\mathbf{E}=(5 \hat{\mathbf{i}}+12 \hat{\mathbf{j}}) \mathrm{Nkg}^{-1}\). If a particle of mass \(2 \mathrm{~kg}\) is moved from the origin to the point \((12 \mathrm{~m}\), \(15 \mathrm{~m}\) ) in this region, the change in gravitational potential energy is

It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point \(p\) at a horizontal distance \(r\) from the point of projection. If \(t_1\) and \(t_2\) are times taken to reach this point in two possible ways, then the product \(t_1 t_2\) is proportional to

If a resistor of resistance \(4 \Omega\), a capacitor of capacitive reactance \(6 \Omega\) and an inductor of inductive reactance \(9 \Omega\) are connected in series with an ac source, then the impedance of the circuit is

Two balls of charge \(q_1\) and \(q_2\) initially have a velocity of the same magnitude and direction. After a uniform electric field has been applied during a certain time, the direction of the velocity of the first ball changes by \(60^{\circ}\), and the velocity magnitude is reduced by half. The direction of the velocity of the second ball changes thereby by \(90^{\circ}\).
In what proportion will the velocity of the second ball change? Determine the magnitude of the charge-to-mass ratio for the second ball if it is equal to \(k_1\) for the first ball. The electrostatic interaction between the balls should be neglected.

A person climbs up a conveyor belt with a constant acceleration. The speed of the belt is \(\sqrt{\frac{g h}{6}}\) and coefficient of friction is \(\frac{5}{3 \sqrt{3}}\). The time taken by the person to reach from A to B with maximum possible acceleration is

If the emf of an AC source is given by \(6 \sin \omega t+4 \sin 2 \omega t \mathrm{~V}\), then the rms value of the emf is

Let 1 be the directrix of the parabola \(9 y^2+12 y+9 x-14=0\) and \(l_1\) be the line passing through the vertex of this parabola and the origin. If \((\mathrm{h}, \mathrm{k})\) is the point of intersection of \(l\) and \(l_1\), then \(\mathrm{h}+\mathrm{k}=\)

Match the following lists.
\begin{array}{|c|c|c|c|}
\hline & List I & & List II \\
\hline A & \begin{array}{l}\text { Zeroth law of } \\
\text { thermodynamics }\end{array} & 1 & \begin{array}{l}\text { Direction of flow of } \\
\text { heat }\end{array} \\
\hline B & \begin{array}{l}\text { First law of } \\
\text { thermodynamics }\end{array} & \| & Work done is zero \\
\hline\underline{\mathrm{C}} & Free expansion of a gas & III & Thermal equilibrium \\
\hline D & \begin{array}{l}\text { Second law of } \\
\text { Thermodynamics }\end{array} & IV & \begin{array}{l}\text { Law of conservation } \\
\text { of energy }\end{array} \\
\hline
\end{array}
The correct answer is
\(\begin{array}{lccccccccc} & \text { A } & \text { B } & \text { C } & \text { D } \end{array}\)

The area of the parallelogram, whose diagonals are $2\hat{i}-\hat{j}+\hat{k}$ and $\hat{i}+3\hat{j}-\hat{k},$ is equal to

\(\frac{\tan 52^{\circ}-\tan 38^{\circ}}{\tan 14^{\circ}}=\)

Which one of the following gives sooty flame on combustion?

The electrochemical equivalent of a metal is ' \(x\) ' \(g\) coulomb \({ }^{-1}\). The equivalent weight of metal is