The logical statement $[ \sim ( \sim p \vee q) \vee (p \wedge r) ] \wedge ( \sim q \wedge r)$ is equivalent to

At higher altitude,the boiling point of water is $95\, ^oC$. 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 $100\, ^oC$ (assuming $90\%$ ionization of $NaCl$) is .......... $g$.

If $x=a\left[\cos \theta+\log \left\{\tan \left(\frac{\theta}{2}\right)\right\}\right]$ and $y=a \sin \theta$,then $\frac{dy}{dx}$ is equal to

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

The catalyst used for the polymerization of olefins is....

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction,when the angle of inclination of the plane is $60^{\circ}$,is