The foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{b^2} = 1$ and the hyperbola $\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}$ coincide. Then the value of $b^2$ is -

$A$ particle is projected vertically upwards from a point $A$ on the ground. It takes $t_1$ time to reach a point $B$ but it still continues to move up. If it takes further $t_2$ time to reach the ground from point $B$,then the height of point $B$ from the ground is:

The number $\log_{2} 7$ is:

$A$ tuning fork of frequency $392 \ Hz$ resonates with $50 \ cm$ length of a string under tension $T$. If the length of the string is decreased by $2\%$,keeping the tension constant,the number of beats heard when the string and the tuning fork are made to vibrate simultaneously is:

Compared to other countries,which industry has received less attention for development in India?

The $pH$ of a buffer solution made by mixing $25 \ mL$ of $0.02 \ M \ NH_4OH$ and $25 \ mL$ of $0.2 \ M \ NH_4Cl$ at $25^{\circ}C$ is ($pK_b$ of $NH_4OH = 4.8$).