$A$ particle executes a simple harmonic motion of time period $T$. Find the time taken by the particle to go directly from its mean position to half the amplitude.

Total emf produced in a thermocouple does not depend on

If $a, b, c$ are in $AP$,and $b-a, c-b, a$ are in $GP$,then $a: b: c$ is

$A$ ray of light is incident normally on a glass slab of thickness $5 ~cm$ and refractive index $1.6$. The time taken by a ray to travel from the source to the surface of the slab is the same as the time taken to travel through the glass slab. The distance of the source from the surface is (in $~cm$)

$A$ cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of centre $O$ with angle $AOC = 60^{\circ}$. If $B_1$ and $B_2$ are the magnitudes of the magnetic fields at $O$ due to the currents in $ABC$ and $ADC$ respectively,the ratio $\frac{B_1}{B_2}$ is

$A$ circular disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is