In the standing wave shown,particles at the positions $A$ and $B$ have a phase difference of

$A$ function $y = f(x)$ satisfies $(x + 1) f'(x) - 2(x^2 + x) f(x) = \frac{e^{x^2}}{x + 1}$ for all $x > -1$. If $f(0) = 5$,then $f(x)$ is:

If $f: R \rightarrow R$ is defined by $f(x) = 7 + \cos(5x + 3)$ for $x \in R$,then the period of $f$ is

The ratio of the magnetic field at the centre of a current-carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be

An alternating voltage $E = 200 \sqrt{2} \sin(100 t)$ is connected to a $1 \mu F$ capacitor through an $AC$ ammeter. The reading of the ammeter shall be: (in $\text{ mA}$)

The length of the chord intercepted by the circle $x^2 + y^2 = r^2$ on the line $\frac{x}{a} + \frac{y}{b} = 1$ is: