In a galvanometer,$5 \%$ of the total current in the circuit passes through it. If the resistance of the galvanometer is $G$,the shunt resistance $S$ connected to the galvanometer is

Two capillary tubes of same diameter are put vertically one each in two liquids whose relative densities are $0.8$ and $0.6$ and surface tensions are $60$ and $50 \, dyne/cm$ respectively. The ratio of the heights of the liquids in the two tubes $\frac{h_1}{h_2}$ is:

The equilibrium constant for the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2 NO_{(g)}$ at temperature $T$ is $4 \times 10^{-4}$. The value of $K_C$ for the reaction $NO_{(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + \frac{1}{2} O_{2(g)}$ at the same temperature is:

The ratio of the mass percentages of $C$ and $H$,and $C$ and $O$ of a saturated acyclic organic compound $X$ are $4:1$ and $3:4$ respectively. Then,the moles of oxygen gas required for the complete combustion of two moles of organic compound $X$ is:

Let $f(x)$ be a polynomial of degree $3$ such that $f(-1) = 10$,$f(1) = -6$,$f(x)$ has a critical point at $x = -1$,and $f'(x)$ has a critical point at $x = 1$. Then $f(x)$ has a local minima at $x =$

If $\frac{x}{(x - 1)(x^2 + 1)^2} = \frac{1}{4}\left[ \frac{1}{(x - 1)} - \frac{x + 1}{x^2 + 1} \right] + y$,then $y =$