$A$ person standing on a rotating platform has his hands lowered. He suddenly outstretches his arms. The angular momentum

The area (in square units) of the region bounded by $x^2=8y$,$x=4$ and the $X$-axis is:

In which of the following reactions,the concentration of the product is higher than the concentration of reactant at equilibrium? ($K =$ equilibrium constant)

The equation $12x^2 + 7xy + ay^2 + 13x - y + 3 = 0$ represents a pair of perpendicular lines. Then the value of $a$ is

If $\int \sec ^2 x \operatorname{cosec}^4 x \, dx = -\frac{1}{3} \cot ^3 x + k \tan x - 2 \cot x + C$, then $k$ is equal to

If the axes are rotated through an angle $45^{\circ}$ in the positive direction without changing the origin,then the coordinates of the point $(\sqrt{2}, 4)$ in the old system are