The structure of $H_2O_2$ is

If $|x| < 1$,then the sum of the series $1 + 2x + 3x^2 + 4x^3 + \dots \infty$ will be

The value of $k$,if $(1,2)$ and $(k,-1)$ are conjugate points with respect to the ellipse $2x^2 + 3y^2 = 6$ is:

Let $a, b, c \in R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f(x + y) = f(x) + f(y) + xy$ for all $x, y \in R$,then $\sum_{n=1}^{10} f(n)$ is equal to:

The radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is:

Two rain drops reach the earth with different terminal velocities having ratio $9:4$. Then the ratio of their volumes is