If a convex lens of focal length $80 \ cm$ and a concave lens of focal length $50 \ cm$ are combined together,what will be their resulting power?

The first operation involved in a Carnot cycle is

The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

$\int \frac{dx}{(x+1) \sqrt{4x+3}}$ is equal to

An organic compound $X$ on treatment with pyridinium chlorochromate in dichloromethane gives compound $Y$. Compound $Y$ reacts with $I_2$ and alkali to form triiodomethane. The compound $X$ is

On heating one end of a rod,the temperature of the whole rod will be uniform when