If the transverse and conjugate axes of a hyperbola are equal,then its eccentricity is

$A$ body is projected from the ground at an angle of $\tan ^{-1}(\sqrt{7})$ with the horizontal. At half of the maximum height, the speed of the body is '$n$' times the speed of projection. The value of '$n$' is

Consider the following anions:
$(I)$ $CF_{3}SO_{3}^{-}$
$(II)$ $C_{6}H_{5}SO_{3}^{-}$
$(III)$ $C_{6}H_{5}O^{-}$
$(IV)$ $CH_{3}COO^{-}$
When attached to $sp^{3}$-hybridized carbon,their leaving group ability in nucleophilic substitution reaction decreases in the order:

What is $X$ in the following reaction?
${}_{12}Mg^{26} + {}_{1}H^{2} \longrightarrow {}_{12}Mg^{27} + X$

The magnifying power of a telescope is $9$. When it is adjusted for parallel rays,the distance between the objective and the eye-piece is found to be $20\, cm$. The focal lengths of the two lenses are

An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is: