$A$ sound source is moving towards a stationary observer with $(1/10)$ of the speed of sound. The ratio of apparent to real frequency is .........

$A$ body of mass $M \ kg$ is at the top point of a smooth hemisphere of radius $5 \ m$. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity is $5 \ m/s$. At this instant,the angle made by the radius vector of the body with the vertical is: (Acceleration due to gravity $g = 10 \ m/s^2$) (in $^{\circ}$)

An infinitely long straight conductor is bent into the shape as shown below. It carries a current of $I$ ampere and the radius of the circular loop is $R$ metre. Then,the magnitude of magnetic induction at the centre of the circular loop is

Reserpine is obtained from ...... .

The line passing through $\left(-1, \frac{\pi}{2}\right)$ and perpendicular to $\sqrt{3} \sin \theta + 2 \cos \theta = \frac{4}{r}$ is :

$A$ man measures the period of a simple pendulum inside a stationary lift and finds it to be $T \ s$. If the lift accelerates upwards with an acceleration $g/4$,then the period of the pendulum will be