The machine gun fires $240$ bullets per minute. If the mass of each bullet is $10 ~g$ and the velocity of the bullets is $600 ~ms^{-1}$,the power (in $kW$) of the gun is

From the top of a hill $h$ metres high,the angles of depression of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in metres) of the pillar is

In humans,which disorder is caused due to the absence of one of the $X$ chromosomes,i.e.,$45$ chromosomes with $XO$ genotype?

The eccentricity of the conic $\frac{5}{r}=2+3 \cos \theta+4 \sin \theta$ is

The bond angles of $NH_3$,$NH_4^+$,and $NH_2^-$ are in the order :-

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered $1$ to $6$) and let $E_k = \{(a, b) \in S : ab = k\}$ for $k \geq 1$. If $p_k = P(E_k)$ for $k \geq 1$,then which of the following is correct?