If a force $F$ is applied on a body and it moves with a velocity $v$,the power will be

Two similar plano-convex lenses are combined together in three different ways as shown in the figure. The ratio of the focal lengths in the three cases will be

$\sum_{n=1}^{\infty} \frac{2n^2+n+1}{n!}$ is equal to

Which of the following is a latex-based alkaloid?

The pressure and density of a given mass of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$,then $\frac{P^{\prime}}{P}$ is $(\gamma = \text{ratio of specific heats})$

The equation of the plane passing through the line $\frac{x - 1}{5} = \frac{y + 2}{6} = \frac{z - 3}{4}$ and the point $(4, 3, 7)$ is