A source emitting sound is tied to one end of a string of length \(50 \mathrm{~cm}\) and is rotated with an angular speed of 40 \(\mathrm{rad} \mathrm{s}^{-1}\) in the horizontal, plane. The ratio of the maximum and minimum frequencies of the sound heard by an observer standing at a distance of \(10 \mathrm{~m}\) from the fixed end of the string is (speed of sound in air \(=340 \mathrm{~ms}^{-1}\) )

In a photoelectric experiment three different lights are incident on a metal of work function \(1.5 \mathrm{eV}\). Light \(A\) is \(200 \mathrm{~nm}\) wavelength with intensity \(1.8 \mathrm{~W} / \mathrm{m}^2\), light \(B\) is \(400 \mathrm{~nm}\) with \(1 \mathrm{~W} / \mathrm{m}^2\) and light \(C\) is \(600 \mathrm{~nm}\) with \(0.5 \mathrm{~W} / \mathrm{m}^2\). The current versus voltage is measured. Which graphs correspond to which light?

Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of \(15 \mathrm{~m}\) a ball is projected vertically upwards with a velocity of \(30 \mathrm{~m} / \mathrm{s}\). If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is \(30 \%\). Statement (III) : The velocity acquired by a body of mass ' \(m\) ' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass ' \(\mathrm{m}\) '. Which of the following is correct?

A magnetic dipole is under the influence of two orthogonal magnetic fields, \(B_1=0.5 \times 10^{-3} \mathrm{~T}\) and \(B_2=0.866 \times 10^{-3} \mathrm{~T}\). If the dipole comes to stable equilibrium at an angle \(\theta\) with respect to \(B_2\) field, then the value of \(\theta\) is

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 current \(I\) flows in a straight wire bent in the shape of a quarter ring of radius \(R\) as shown in figure. The magnetic field induction \(B\) at point \(O\) is

A wire of resistance \(2 R\) is stretched such that its length is doubled. Then the increases in its resistance is

A water pump rated $600 \mathrm{W},$ has an efficiency of $95\%.$ If it is used to raise water through vertical distance of $60 \mathrm{m}.$ The volume of water drawn in $20$ minutes, is [Use density of water $=1000 \mathrm{kg}{ \mathrm{m}}^{-3}, g=10 \mathrm{m}/{\mathrm{s}}^2$]

Two parallel conductor each \(50 \mathrm{~m}\) long, separated by \(0.2 \mathrm{~m}\) experience a force of \(1 \mathrm{~N}\). If the current in the first conductor is twice that of the second conductor, then what is the current in the second conductor? \[ \left(\mu_o=4 \pi \times 10^{-7}\right) \]

A ball of mass $100 \mathrm{g}$ is dropped at time $t=0.$ A second ball of mass $200 \mathrm{g}$ is dropped from the same point at $t=0.2 \mathrm{s}$. The distance between the center of mass of two balls and the release point at $t=0.4 \mathrm{s}$ is: (Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The magnitude of acceleration and velocity of a particle moving in a plane, whose position vector $\overrightarrow{r}=3t^2\hat{\mathrm{i}}+2t\hat{\mathrm{j}}+\hat{\mathrm{k}}$ at $t=2 \sec .$ are, respectively

A particle of mass \(m=1 \mathrm{~kg}\) moves in the \(x y\)-plane. The force on it at time \(t\) is \(F(t)=[2 \sin (\alpha t) \hat{\mathbf{i}}+3 \cos (\alpha t) \hat{\mathbf{j}}] \mathrm{N}\), where \(\alpha=1 \mathrm{~s}^{-1}\). At time \(t=0\), the particle is at rest at the origin. Calculate the magnitude of its position vector \(\mathbf{r}\) (in \(\mathrm{m}\) ) and velcoity vector \(\mathbf{v}\) (in \(\mathrm{m} / \mathrm{s}\) ) at time \(t=\frac{\pi}{2} \mathrm{~s}\).

An ideal monoatomic gas of volume $V$ is adiabatically expanded to a volume $3V$ at $27°\mathrm{C}.$ The final temperature in Kelvins is
(use $\frac{C_P}{C_V}=\frac{5}{3}$)