If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to

If $z=1+i\sqrt{3}$,then $|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|$ is equal to

$A$ uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended,with its length vertical,from a fixed point by a massless spring such that it is half-submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is:

Which of the following halides of group $13$ elements is the most acidic?

The Lassaigne’s extract is boiled with dil. $HNO_3$ before testing for halogens because

Which type of cartilage is found at the ends of long bones?