$A$ particle is performing $SHM$ starting from the extreme position. The graphical representation shows that, between displacement and acceleration, there is a phase difference of:

Solid $NaCl$ is a bad conductor of electricity since

If $[x]$ denotes the greatest integer not exceeding $x$ and if the function $f$ defined by $f(x)= \begin{cases} \frac{a+2 \cos x}{x^2} & , x < 0 \\ b \tan \frac{\pi}{[x+4]} & , x \geq 0 \end{cases}$ is continuous at $x=0$,then the ordered pair $(a, b)$ is equal to

Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field. With like poles together,$12$ oscillations per minute are made,but for unlike poles together,only $4$ oscillations per minute are executed. The ratio of their magnetic moments is:

The solution of $\frac{dx}{dy} + \frac{x}{y} = x^2$ is:

At higher altitude,the boiling point of water is $95\,^{\circ}C$. The amount of $NaCl$ added to $1\, kg$ of water $(K_b = 0.52\, K\, kg\, mol^{-1})$ in order to raise the boiling point of the solution to $100\,^{\circ}C$ (assuming $90\%$ ionization of $NaCl$) is ........... $g$.