Ravi obtained $70$ and $75$ marks in the first two unit tests. Find the minimum marks he should get in the third test to have an average of at least $60$ marks.

The value of the greatest integer $k$ satisfying the inequation $2^{n+4} + 12 \geq k(n+4)$ for all $n \in \mathbb{N}$ is

$A$ container is filled with $1120 \text{ litres}$ of a solution containing $40 \%$ acid. How many litres of acid must be added so that the resulting mixture contains more than $40 \%$ but less than $50 \%$ water?

$\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}$ is equal to

Let $m, n$ be real numbers such that $0 \leq m \leq \sqrt{3}$ and $-\sqrt{3} \leq n \leq 0$. The minimum possible area of the region of the plane consisting of points $(x, y)$ satisfying the inequalities $y \geq 0$,$y - 3 \leq mx$,and $y - 3 \leq nx$ is

The region formed by the inequalities $2x + 3y - 5 \leq 0$,$4x - 3y + 2 \leq 0$,and $x \geq 0$ is: