Let $a, b \in R$. If the mirror image of the point $P(a, 6, 9)$ with respect to the line $\frac{x-3}{7} = \frac{y-2}{5} = \frac{z-1}{-9}$ is $(20, b, -a-9)$,then $|a+b|$ is equal to:

The phosphate of a metal has the formula $MHPO_4$. The formula of its chloride would be

$A$ thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the centre of the shell is

If $\frac{4 + 3\sqrt{3}}{\sqrt{7 + 4\sqrt{3}}} = a + \sqrt{b}$,then $(a, b) = $

Which of the following taxonomical aids is being described by the given statements $(i-iv)$?
$(i)$. They are generally established in educational institutes.
$(ii)$. They have collections of preserved plant and animal specimens for study and reference.
$(iii)$. Insects are preserved in boxes after collecting,killing and pinning.
$(iv)$. They often have collections of skeletons of animals too.

The equation $x^2-5xy+py^2+3x-8y+2=0$ represents a pair of straight lines. If $\theta$ is the angle between them,then $\sin \theta$ is equal to