$A$ body of mass $M$ at rest explodes into three pieces,two of which of mass $M/4$ each are thrown off in perpendicular directions with velocities of $3 \ m/s$ and $4 \ m/s$ respectively. The third piece will be thrown off with a velocity of.......... $m/s$.

The condition for a uniform spherical mass $m$ of radius $r$ to be a black hole is [$G$ = gravitational constant and $c$ = speed of light].

The primary and secondary coils of a transformer have $50$ and $1500$ turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi = \phi_0 + 4t$,where $\phi$ is in webers,$t$ is time in seconds,and $\phi_0$ is a constant,the output voltage across the secondary coil is ...... $volts$.

The area (in square units) of the region bounded by the curve $y=|\sin 2x|$ and the $X$-axis in the interval $[0, 2\pi]$ is:

Which of the following is a correct statement?

$A$ steel wire can withstand a load up to $2940 ~N$. $A$ load of $150 ~kg$ is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position,so that the wire does not break when the load passes through the position of equilibrium,is (in $^{\circ}$)