If $x$ is a solution of the equation $\sqrt{2x+1} - \sqrt{2x-1} = 1$ where $x \geq \frac{1}{2}$,then $\sqrt{4x^2-1}$ is equal to

The probability of a student qualifying for $IITJEE$ and $EAMCET$ are $\frac{1}{5}$ and $\frac{3}{5}$ respectively. The probability that the student qualifies for at least one of these tests is:

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/s}$ when the radius is $12 \text{ cm}$. Then, the rate at which the area increases, is

In an acute angled triangle,$\cot B \cot C + \cot A \cot C + \cot A \cot B$ is equal to

The basis of the quantum mechanical model of an atom is