If $H$ is the harmonic mean between $p$ and $q$,then the value of $\frac{H}{p} + \frac{H}{q}$ is

Let $S_n = 1 + q + q^2 + ..... + q^n$ and $T_n = 1 + \left( \frac{q + 1}{2} \right) + \left( \frac{q + 1}{2} \right)^2 + ...... + \left( \frac{q + 1}{2} \right)^n$ where $q$ is a real number and $q \neq 1$. If $^{101}C_1 + ^{101}C_2 \cdot S_1 + ...... + ^{101}C_{101} \cdot S_{100} = \alpha \cdot T_{100}$,then $\alpha$ is equal to

If the third term of a $G.P.$ is $4$,then the product of its first $5$ terms is:

If $a, b, c, d, e, f$ are in $A.P.$,then the value of $e - c$ will be

The sum of the first $n$ natural numbers is:

If $a^2 + b^2 + 16c^2 = 2(3ab + 6bc + 4ac)$,where $a, b, c$ are non-zero numbers,then $a, b, c$ are in: