In hydrogen spectrum, the shortest and longest wavelengths of Balmer series are \(\lambda_1\) and \(\lambda_2\) respectively. The Rydberg constant of hydrogen is

An inductance \(1 \mathrm{H}\) is connected in series with an AC source of \(220 \mathrm{~V}\) and \(50 \mathrm{~Hz}\). The. inductive reactance (in ohm) is

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

Two sound waves each of intensity I are superimposed. If the phase difference between the waves is \(\frac{\pi}{2}\), then the intensity of the resultant wave is

In the arrangement of capacitors shown in the figure, if each capacitor is \(9 \mathrm{pF}\), then the effective capacitance between the points \(A\) and \(B\) is

A body of mass \(m\) rises to height \(h=R / 5\) from the earth's surface, where \(R\) is earth's radius. If \(g\) is acceleration due to gravity at earth's surface, the increase in potential energy is

A piece of copper and a piece of germanium are cooled from room temperature to \(80 \mathrm{~K}\). Then, which one of the following is correct?

An ideal gas in a cylinder is compressed adiabatically to one-third of its original volume. A work of \(45 \mathrm{~J}\) is done on the gas by the process. The change in internal energy of the gas and the heat flowed into the gas, respectively are

A Carnot engine whose efficiency is \(40 \%\), receives heat at \(500 \mathrm{~K}\). If the efficiency is to be \(50 \%\), the source temperature for the same exhaust temperature is

Two capacitors, $C_1=2\mathrm{mF}$ and $C_2=8\mathrm{mF}$ are connected in series across a $300 \mathrm{V}$ source. Then

An amplitude modulated signal consists of a message signal of frequency \(1 \mathrm{KHz}\) and peak voltage of \(5 \mathrm{~V}\), modulating a carrier frequency of \(1 \mathrm{MHz}\) and peak voltage of \(15 \mathrm{~V}\). The correct description of this signal is

A block of mass \(2 \mathrm{~kg}\) is connected to an ideal spring and is placed on a smooth horizontal surface. The spring is pulled to move the block and at an instant, the speed of end \(A\) of the spring and speed of the block were measured to be \(6 \mathrm{~m} / \mathrm{s}\) and \(3 \mathrm{~m} / \mathrm{s}\), respectively. At this moment the potential energy stored in the spring in increasing at a rate \(15 \mathrm{~J} / \mathrm{s}\). Find the acceleration of the block at this instant.

The relation between the current \(i\) (in ampere) in a conductor and the time \(t\) (in second) is \(i=12 i+9 t^2\). The charge passing through the conductor between the times \(t=2 \mathrm{~s}\) and \(t=10 \mathrm{~s}\) is