A body of mass \(2 \mathrm{~kg}\) is moving with a constant acceleration of \((2 \hat{i}+3 \hat{j}-\hat{k}) \mathrm{ms}^{-2}\). If the displacement made by the body is \((3 \hat{i}-\hat{j}+2 \hat{k}) \mathrm{m}\) then the work done is

A particle is executing simple harmonic motion with amplitude \(A\). The ratio of the kinetic energies of the particle when it is at displacements of \(\frac{A}{4}\) and \(\frac{A}{2}\) from the mean position is

When 40 J of heat is absorbed by a monatomic gas, the increase in the internal energy of the gas is

"The uniform motion is possible when no frictional forces oppose" is the concept of

The ends of an element of zinc wire are kept at a small temperature difference \(\Delta T\) and a small current \((I)\) is passed through the wire. Then, the heat developed per unit time

All electrons ejected from a metallic surface by incident light of wavelength \(400 \mathrm{~nm}\) travelled \(1 \mathrm{~m}\) in the direction of uniform electric field of \(2 \mathrm{NC}^{-1}\) and came to rest. The work function of the surface is

A radioactive element \(X\) converts into another stable element \(Y\). Half life of \(X\) is 2 hours. Initially only \(X\) is present. After a time \(t\), if the ratio of atoms of \(X\) to \(Y\) is \(1: 4\), then the value of \(t\) is

At \(T(K)\) for one mole of an ideal gas, the graph of \(P\) (on \(y\)-axis) and \(\mathrm{V}^{-1}\) (on \(x\)-axis) gave a straight line with slope of \(32.8 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1}\). What is the temperature (in K )? \(\left(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm}^{-1} \mathrm{Kol}^{-1}\right)\)

The least value of $n$ so that ${}^{\left(n-1\right)}C_3+{}^{\left(n-1\right)}C_4>{}^{n}C_3$

The ratio of kinetic energy of a diatomic gas molecule at a high temperature to that of NTP is

At \(300 \mathrm{~K}\), one mole of a gas present in a \(10 \mathrm{~L}\) flask exerted a pressure of \(2.706 \mathrm{~atm}\).
What is its compressibility factor \((\mathrm{Z})\) ?
(Given \(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) ).

In a transistor circuit, when the base current is increased by 50 micro-amperes keeping the collector voltage fixed at 2 volts, the collector current increases by \(1 \mathrm{~mA}\). The current gain of the transistor is

If \(E_1\) and \(E_2\) are two events of a random experiment such that \(P\left(E_1\right)=\frac{1}{8}, P\left(E_1 \mid E_2\right)=\frac{1}{3}\), \(P\left(E_2 \mid E_1\right)=\frac{1}{4}\), then match the items of List-I with the items of List-II.
\(\begin{array}{lllc}
\hline & \text { List-I } & & \text { List-II } \\
\hline \text { (A) } & P\left(E_2\right) & \text { I. } & \frac{3}{16} \\
\hline \text { (B) } & P\left(E_1 \cup E_2\right) & \text { II. } & \frac{3}{29} \\
\hline \text { (C) } & P\left(\bar{E}_1 \mid \bar{E}_2\right) & \text { III. } & \frac{3}{32} \\
\hline \text { (D) } & P\left(E_1 \mid \bar{E}_2\right) & \text { IV. } & \frac{26}{29} \\
\hline & & \text { V. } & \frac{13}{32} \\
\hline
\end{array}\)
The correct match is