If $m \begin{bmatrix} -3 & 4 \end{bmatrix} + n \begin{bmatrix} 4 & -3 \end{bmatrix} = \begin{bmatrix} 10 & -11 \end{bmatrix}$,then $3m + 7n$ is equal to

The densities of a liquid at $0^{\circ} C$ and $100^{\circ} C$ are respectively $1.0127$ and $1$. $A$ specific gravity bottle is filled with $300 \ g$ of the liquid at $0^{\circ} C$ up to the brim and it is heated to $100^{\circ} C$. Then,the mass of the liquid expelled in grams is: (Coefficient of linear expansion of glass $= 9 \times 10^{-6} /^{\circ} C$)

The atomic weight of an element is $39$. The number of neutrons in its nucleus is one more than the number of protons. The number of protons,neutrons and electrons respectively in its atom would be

$A$ compound $X$ upon reaction with $H_{2}O$ produces a colorless gas $Y$ with a rotten fish smell. Gas $Y$ is absorbed in a solution of $CuSO_{4}$ to give $Cu_{3}P_{2}$ as one of the products. Predict the compound $X$.

The amplitude of vibration of a particle is given by $a_m = a_0 / (a\omega^2 - b\omega + c)$,where $a_0$,$a$,$b$,and $c$ are positive constants. The condition for a single resonant frequency is:

If $y = \sec(\tan^{-1}x)$,then $\frac{dy}{dx}$ at $x = 1$ is equal to: