If the line $2x + 5y = 12$ intersects the ellipse $4x^2 + 5y^2 = 20$ in two distinct points $A$ and $B$,then the mid-point of $AB$ is

The function $f(x) = \log(1 + x) - \frac{2x}{2 + x}$ is increasing on

$A$ ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and each one is equal to $3/4$th the angle of the prism. The angle of deviation is (in $^{\circ}$)

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number,then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}$,$\lambda \vec{b}+4 \vec{c}$,and $(2 \lambda-1) \vec{c}$ are non-coplanar for:

Which method exhibits faster growth compared to callus culture?

$A$ bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively,until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is $14400$,then $n$ is equal to