$A$ transition metal $M$ forms a volatile chloride with a vapor density of $94.8$. If it contains $74.75\%$ chlorine,what is the formula of the metal chloride?

A prism of angle $75^\circ$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index $1.5$ only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be . . . . . . .
$(\sin 15^\circ = 0.25$ and $\sin 25^\circ = 0.43)$

The pole of the straight line $x + 4y = 4$ with respect to the ellipse $x^2 + 4y^2 = 4$ is

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre,the ratio of $i_1: i_2$ is

$\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}$ is equal to :

An ideal coil of $10\,H$ is connected in series with a resistance of $5\,\Omega$ and a battery of $5\,V$. After $2\,s$ the connection is made,the current flowing in ampere in the circuit is