$11^2 + 12^2 + 13^2 + \dots + 20^2 = ?$

The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant,its length must be increased by ..... $\%$

Consider the two following statements $A$ and $B$,and identify the correct choice given in the answers: $(A)$ Duddell's thermo galvanometer is suitable to measure direct current only. $(B)$ Thermopile can measure temperature differences of the order of $10^{-3} {}^{\circ}C$.

$A$ gas mixture consists of $2$ moles of $O_2$ and $4$ moles of $Ar$ at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system is: (in $RT$)

If $f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x}$, for $x \in R$, then $f(2002)$ is equal to

The condition for a uniform spherical mass $m$ of radius $r$ to be a black hole is [$G$ = gravitational constant and $c$ = speed of light].