In an open organ pipe \(v_3\) and \(v_6\) are \(3^{\text {rd }}\) and \(6^{\text {th }}\) harmonic frequencies, respectively.
If \(v_6-v_3=2200 \) Hz then length of the pipe is ______ mm.
(Take velocity of sound in air is 330 m/s.)

Two wires \(A\) and \(B\) are carrying currents \(I_1\) and \(I_2\) as shown in the figure. The separation between them is \(d\). A third wire \(C\) carrying a current \(I\) is to be kept parallel to them at a distance \(x\) from \(A\) such that the net force acting on it is zero. The possible values of \(x\) are

A common emitter amplifier circuit, built using an \(npn\) transistor, is shown in the figure. Its \(dc\) current gain is \(250\), \(R_C = 1\,k\, \Omega \) and \(V_{CC} = 10\,V\). What is the minimum base current for \(V_{CE}\) to reach saturation?.........\(\mu A\)

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of \(0.8 \mathrm{~cm}^3\). If the bulk modulus of the liquid is 2 GPa , the initial volume of the liquid was _______ litre. \(\left(\right.\) Take \(\left.1 \mathrm{~atm}=10^5 \mathrm{~Pa}\right)\)

The amount of heat needed to raise the temperature of \(4\, moles\) of a rigid diatomic gas from \(0^{\circ} {C}\) to \(50^{\circ} {C}\) when no work is done is ......\({R}\) (\(R\) is the universal gas constant)

Given below are two statements : Statement\(-I:\) Acceleration due to gravity is different at different places on the surface of earth. Statement\(-II:\) Acceleration due to gravity increases as we go down below the earth's surface. In the light of the above statements, choose the correct answer from the options given below

A gas balloon is going up with a constant velocity of \(10\) m/s. When this balloon reached a height of \(75\) m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ________ m. (Take \(g=10\) m/s\(^2\))

Let \(\gamma_1\) be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \(\gamma_2\) be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, \(\frac{\gamma_1}{\gamma_2}\) is

The half-life of a radioactive nucleus is \(5\) years, The fraction of the original sample that would decay in \(15\) years is

In a typical combustion engine the work done by a gas molecule is given \(W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}\), where \(x\) is the displacement, \(k\) is the Boltzmann constant and \(T\) is the temperature. If \(\alpha\) and \(\beta\) are constants, dimensions of \(\alpha\) will be

Space between two concentric conducting spheres of radii \(a\) and \(b (b > a)\) is filled with \(a\) medium of resistivity \(\rho \). The resistance between the two spheres will be