In Bohr's theory the potential of an electron at a position is \(\frac{K r^2}{2}\), where \(K\) is a constant. Then, the quantised energy of the electron in \(n\)th orbit is

A metal block is made from a mixture of 2.4 kg of aluminium, 1.6 kg of brass and 0.8 kg of copper. The metal block is initially at \(20^{\circ} \mathrm{C}\). If the heat supplied to the metal block is 44.4 calories, find the final temperature of the block if specific heats of aluminium, brass and copper are \(0.216,0.0917,0.0931 \mathrm{cal} . \mathrm{kg}^{-1} \mathrm{C}^{-1}\) respectively.

If the ratio of the maximum and minimum amplitudes of an amplitude modulated wave is \(7: 3\), then the modulation index is

Names of units of some physical quantities are given in List-I and their dimensions formulae are given in List-Il. Match the correct pairs in the lists
\(\begin{array}{ll|ll}
\hline & \text{ List-I } & \text{ List-II } \\
\hline A. & \mathrm{Pa}-\mathrm{s} & (i) & {\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline B. & \mathrm{NmK}^{-1} & (ii) & {\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]} \\
\hline C. & \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1} & (iii) & {\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]} \\
\hline D. & \mathrm{Wm}^{-1} \mathrm{~K}^{-1} & (iv) & {\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline
\end{array}\)
\(\begin{array}{llll}A & B & C & D\end{array}\)

The work done by a force $\overrightarrow{F}=-5x^4 \hat{\mathrm{i}} \mathrm{N}$ in displacing a body from $x=2 \mathrm{m}$ to $x=-2 \mathrm{m}$ is

If \(A\) is the areal velocity of a planet of mass \(M\), its angular momentum is

The average translational kinetic energy of a molecule in a gas becomes equal to \(0.69 \mathrm{eV}\) at temperature about, [Boltzmann's constant \(=138 \times 10^{-23} \mathrm{~J} \mathrm{~K}^{-1}\) ]

An element occurs in the body centred cubic structure with edge length of 288 pm. The density of the element is \(7.2 \mathrm{~g} \mathrm{~cm}^{-3}\). The number of atoms present in 208 g of the element is nearly

The equation of the circle which cuts all the three circles \(4(x-1)^2+4(y-1)^2=1,4(x+1)^2+4(y-1)^2=1\) and \(4(x+1)^2+4(y+1)^2=1\) orthogonally is

100 mL of \(0.1 \mathrm{M} \mathrm{Fe}^{2+}\) solution was titrated with \(\frac{1}{60} \mathrm{MCr}_2 \mathrm{O}_7^{2-}\) solution in acid medium. What is the volume (in L ) of \(\mathrm{Cr}_2 \mathrm{O}_7{ }^{2-}\) solution consumed?

The integrating factor of the linear directional equation \(\frac{d y}{d x}+P(x) y=Q(x)\) is a solution of the differential equation

The apparent weight of a girl of mass 30 kg when she is in a lift moving vertically upwards with an acceleration of \(2 \mathrm{~ms}^{-2}\) is (Acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) )

If \(A=\left[\begin{array}{ccc}1 & 2 & -2 \\ 2 & -1 & 2 \\ -1 & 1 & -2\end{array}\right]\), then \(A+2 A^{-1}=\)