If $\frac{4 + 3\sqrt{3}}{\sqrt{7 + 4\sqrt{3}}} = a + \sqrt{b}$,then $(a, b) = $

For preparing a $0.1 \, N$ solution of a compound from its impure sample,of which the percentage purity is known,the weight of the substance required will be

$A$ wall is made up of two layers $A$ and $B$. The thickness of the two layers is the same,but materials are different. The thermal conductivity of $A$ is double than that of $B$. In thermal equilibrium,the temperature difference between the two ends is $36\,^{\circ}C$. Then the difference of temperature at the two surfaces of $A$ will be......... $^{\circ}C$

When heat is supplied to a diatomic gas,it expands at constant pressure. What fraction of the heat supplied is converted into internal energy?

$(a+b) \cdot (b+c) \times (a+b+c)$ is equal to

An integrating factor of the differential equation $(1-x^2) \frac{dy}{dx} + xy = \frac{x^4}{(1+x^5)} (\sqrt{1-x^2})^3$ is