The function $f(x) = x e^{-x}, \forall x \in R$ attains a maximum value at $x$ equal to

$2, 3$-dimethylhexane contains tertiary,secondary,and primary carbon atoms,respectively:

If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively,then

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$, then the position vector of $R$ is

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is (in $~K$)

Among the following series of transition metal ions,the one where all metal ions have $3d^2$ electronic configuration is