The skull of a frog is:

If the curves $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $\frac{x^2}{25}+\frac{y^2}{16}=1$ cut each other orthogonally,then $a^2-b^2$ equals to

$A$ train moving at a speed of $220\, ms^{-1}$ towards a stationary object,emits a sound of frequency $1000\, Hz$. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is .... $Hz$ (speed of sound in air is $330\, ms^{-1}$)

Four thin rods of same mass $M$ and same length $l$ form a square as shown in the figure. The moment of inertia of this system about an axis passing through the centre $O$ and perpendicular to its plane is

Assertion $(A)$: Rapidly changing temperatures can be measured by thermocouples. Reason $(R)$: The thermal capacity of the junction of a thermocouple is very small.

$A$ simple pendulum performs simple harmonic motion about $x=0$ with an amplitude '$a$' and time period '$T$'. The speed of the pendulum at $x=\frac{a}{2}$ is