Express the following in the exponential form :

$2\times 2\times a\times a$

Q. Write the element $a_{21}$ of the matrix $A=[a_{ij}{]}_{2\times 2}$ whose elements $a_{ij}$ are given by $a_{aj}=e^{2ix}\cos jx$

Q. Express the following in exponential form:
$512$

Q. The incircle of a scalene triangle $ABC$ touches side $AB,BC$ and $AC$ at $P,Q$ and $R$ respectively. If $O$ is the incentre of triangle $ABC,$ then which of the following statements is (are) correct?

$\text{I.}$ Area of $△OBC$ is $\frac{1}{2}\times BC\times \text{radius of incircle}$
$\text{II.}$ $AB+CQ=BQ+AC$
$\text{III.}$ Area of $△ABC$ is $\frac{1}{2}\times \text{perimeter of}△ABC\times \text{radius of incircle}$

Q.

The speed of a projectile at the highest point becomes $\frac{1}{\sqrt{2}}$times its initial speed. The horizontal range of the projectile will be

Q. If the mass of earth and radius suddenly become $2times$ and $1/4^{th}$ of the present value, the length of the day becomes: