If $a * b = 2a - 3b + ab$,then $3 * 5 + 5 * 3$ is

If $N = \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}},$ then what is the value of $N + \frac{1}{N} ?$

$(15 \times 0.40)^{4} \div (1080 \div 30)^{4} \times (27 \times 8)^{4} = (3 \times 2)^{?+5}$

$7 \frac{1}{2}-\left[2 \frac{1}{4} \div\left\{1 \frac{1}{4}-x\left(1 \frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]=3$. Find the value of $x$.

If $x = 3 - 2\sqrt{2}$,then $\sqrt{x} + \frac{1}{\sqrt{x}}$ is equal to

What least value should be added to $2505$ so that it becomes a perfect square?