If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle $3\pi/4$ with the positive $x$-axis, then $f'(3)$ is

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

The incentre of the triangle with vertices $A(1, \sqrt{3})$,$B(0,0)$,and $C(2,0)$ is

Which insecticide is lipophilic in nature?

The arithmetic mean of a set of observations is $\bar{X}$. If each observation is divided by $\alpha$ and then increased by $10$,then the mean of the new series is:

$A$ screen is placed $50 \, cm$ from a single slit, which is illuminated with $6000 \, \mathring{A}$ light. If the distance between the first and third minima in the diffraction pattern is $3 \, mm$, the width of the slit is.....$mm$