In how many ways can $6$ persons be selected from $4$ officers and $8$ constables,if at least one officer is to be included?

The equation $(2p-3)x^2 + 2pxy - y^2 = 0$ represents a pair of distinct lines:

Which of the following transitions in a hydrogen atom emits a photon of the highest frequency?

The perimeter of a $\triangle ABC$ is $6$ times the arithmetic mean of the sine of its angles. If its side $BC$ is of unit length,then $\angle A=$

$A$ 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 (in $m/s$)