Let $\bar{a}, \bar{b}$ and $\overline{\mathrm{c}}$ be three vectors having magnitude 1,1 and 2 respectively. If $\overline{\mathrm{a}} \times(\overline{\mathrm{a}} \times \overline{\mathrm{c}})+\overline{\mathrm{b}}=\overline{0}$, then the acute angle between $\overline{\mathrm{a}}$ and $\overline{\mathrm{c}}$ is

The area bounded between the curves $y=a x^2$ and $x=a y^2(a>0)$ is 1 sq. units, then the value of a is

The integral $\int \sec ^{\frac{2}{3}} x \cdot \operatorname{cosec}^{\frac{4}{3}} x \mathrm{~d} x$ is equal to

If sum of two numbers is 3 , then the maximum value of the product of first number and square of the second number is