Metamerism is a characteristic feature of which of the following?

Starting from rest,a body slides down a $45^{\circ}$ inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is:

Which of the following pairs is incorrectly matched?

$\sec ^2(\tan ^{-1} 2) + \operatorname{cosec}^2(\cot ^{-1} 3)$ is equal to

The solution of $\tan y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$ is

$A$ certain vector in the $xy$-plane has an $x$-component of $4 ~m$ and a $y$-component of $10 ~m$. It is then rotated in the $xy$-plane so that its $x$-component is doubled. Then its new $y$-component is (approximately) (in $~m$)