If $$\int \cos ^{\frac{3}{5}} x \cdot \sin ^3 x d x=\frac{-1}{m} \cos ^m x+\frac{1}{n} \cos ^n x+c$$, (where $$\mathrm{c}$$ is the constant of integration), then $$(\mathrm{m}, \mathrm{n})=$$

Let $$\mathrm{PQR}$$ be a right angled isosceles triangle, right angled at $$\mathrm{P}(2,1)$$. If the equation of the line $$\mathrm{QR}$$ is $$2 x+y=3$$, then the equation representing the pair of lines $$P Q$$ and $$P R$$ is

A uniform string is vibrating with a fundamental frequency '$$n$$'. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is

Let $$\gamma_1$$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $$\gamma_2$$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio $$\frac{\gamma_2}{\gamma_1}$$ is