The famous botanical garden '$Kew$' is located in

The half-life period of a first-order chemical reaction is $6.93 \, \text{min}$. The time required for the completion of $99 \%$ of the chemical reaction will be .......... $\text{min}$ $(\log \, 2 = 0.301)$.

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

In an emission spectrum,the transitions $n_2 \to n_1, n_3 \to n_1, n_4 \to n_1, n_5 \to n_1$ result in the emission of energies $E_1, E_2, E_3, E_4$ respectively. What is the increasing order of these energies?

$A$ container is filled with water $(\mu = 1.33 \approx 4/3)$ up to a height of $33.25 \, cm$. $A$ concave mirror is placed $15 \, cm$ above the water level. The image of an object placed at the bottom is formed by the mirror at $25 \, cm$ below the water level. The focal length of the mirror is: (in $, cm$)

$A$ hyperbola passes through a focus of the ellipse $\frac{x^2}{169} + \frac{y^2}{25} = 1$. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse. The product of their eccentricities is $1$. Then,the equation of the hyperbola is: