$1+\frac{2}{4}+\frac{2 \cdot 5}{4 \cdot 8}+\frac{2 \cdot 5 \cdot 8}{4 \cdot 8 \cdot 12}+\frac{2 \cdot 5 \cdot 8 \cdot 11}{4 \cdot 8 \cdot 12 \cdot 16}+\ldots \ldots$ is equal to :

Two identical short bar magnets,each having magnetic moment $M$,are placed a distance of $2d$ apart with their axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is:

Two identical charged spherical drops, each of capacitance $C$, merge to form a single drop. The resultant capacitance is:

Consider the following reaction,
$C_2H_5Cl + AgCN \xrightarrow{EtOH / H_2O} \underline{X} \text{ (major)}$
Which one of the following statements is true for $\underline{X}$?
$(I)$ It gives propionic acid on hydrolysis
$(II)$ It has an ester functional group
$(III)$ It has a nitrogen linked to ethyl carbon
$(IV)$ It has a cyanide group

The $K.E.$ and $P.E.$ of a particle executing $SHM$ with amplitude $A$ will be equal when its displacement is

For an electron with $n = 3$,there is only one radial node. The orbital angular momentum of the electron will be