If the angle $2 \theta$ is acute,then the acute angle between the pair of straight lines $x^2(\cos \theta - \sin \theta) + 2xy \cos \theta + y^2(\cos \theta + \sin \theta) = 0$ is:

$\frac{\sin 5 \theta}{\sin \theta}$ is equal to

Which of the following is not a Lewis acid?

$A$ thin rod of length $L$ is bent to form a semicircle. The mass of the rod is $M$. What will be the gravitational potential at the centre of the circle?

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho_0 r^2$ (where $\rho_0$ is a constant and $r$ is measured from the centre). Consider two points $A$ and $B$ at distances $x$ and $y$ respectively from the centre,such that $x < R$ and $y > R$. If the magnitudes of the electric fields at points $A$ and $B$ are equal,then:

The focal length of a mirror is given by $\frac{2}{f} = \frac{1}{v} - \frac{1}{u}$. In finding the values of $u$ and $v$,the errors are equal to $p$. Then,the relative error in $f$ is