A gas is governed by an equation \(\mathrm{V}=\frac{\mathrm{aT}^3}{\mathrm{P}}\) where \(\mathrm{P}, \mathrm{V}\) and \(\mathrm{T}\) are pressure, volume and temperature of the gas respectively and ' \(a\) ' is a constant. If the temperature of the gas is doubled at constant pressure then the workdone by the gas is

An explosion blows a stationary rock into three parts. Two parts of masses \(1 \mathrm{~kg}\) and \(2 \mathrm{~kg}\) moves at right angles to one another with velocities \(12 \mathrm{~ms}^{-1}\) and \(8 \mathrm{~ms}^{-1}\), respectively. If the velocity of third part is 4 \(\mathrm{ms}^{-1}\), the mass of the rock is

The shortest wavelength of $X$-rays emitted from an $X$-ray tube depends upon

A body of mass $10 \mathrm{kg}$ is attached to a wire of $0.3 \mathrm{m}$ length. The breaking stress is $4.8\times {10}^7 \mathrm{N} {\mathrm{m}}^{-2}$. The area of cross-section from the wire is ${10}^{-6}{ \mathrm{m}}^2$. The maximum angular velocity with which it can be rotated in a horizontal circle is

The value of shunt resistance, that allows only \(10 \%\) of main current through the galvanometer of resistance \(99 \Omega\) is

When an inductor of inductance \(\frac{6}{\pi} \mathrm{H}\), a capacitor of capacitance \(\frac{50}{\pi} \mu \mathrm{F}\) and resistor of resistance \(R\) are connected in series with an AC supply of rms voltage \(220 \mathrm{~V}\) and frequency \(50 \mathrm{~Hz}\), the rms current through the circuit is \(440 \mathrm{~mA}\). Match the inductive reactance, \(X_L\) the capacitive reactance, \(X_C\) the resistance \(R\) and the impedance \(Z\) of the circuit given in List-I with the corresponding values given in List-II.
\(\begin{array}{llll} \hline & \text { List- I } & & \text { List- II } \\ \hline \text {(A) } & X_L & \text { (i) } & 200 \Omega \\ \hline \text {(B) } & X_C & \text { (ii) } & 300 \Omega \\ \hline \text {(C) } & R & \text { (iii) } & 500 \Omega \\ \hline \text {(D) } & Z & \text { (iv) } & 600 \Omega \\ \hline \end{array}\)

The device used for voltage regulation is

Threshold frequency for photoelectric effect on sodium corresponds to a wavelength \(5000 Å\). Its work function is

In which of the following pairs, both molecules possess dipole moment?

Which of the following is an example for heterogeneous catalysis reaction?

If the median AD of the triangle ABC is bisected at E and BE meets AC in F, then \(\mathrm{AF}: \mathrm{AC}=\)

If \(P(-1,0), Q(0,0)\) and \(R(3,3 \sqrt{3})\) are three points, then the equation of the bisector of the \(\lfloor{P Q R}\) is

The number of five digit numbers that are divisible by 6 which can be formed by choosing digits from \(\{0,1,2,3,4,5\}\), when repetition is allowed, is