Which of the following methods uses a rotary shaker?

The circumcentre of the triangle formed by the lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is:

If $\log_e \left( \frac{a + b}{2} \right) = \frac{1}{2}(\log_e a + \log_e b)$,then the relation between $a$ and $b$ is:

If the volume of a parallelepiped with coterminous edges $4 \hat{i} + 5 \hat{j} + \hat{k}$,$-\hat{j} + \hat{k}$,and $3 \hat{i} + 9 \hat{j} + p \hat{k}$ is $34$ cubic units,then $p$ is equal to:

Two equally charged metal spheres $A$ and $B$ repel each other with a force of $4 \times 10^{-5} ~N$. Another identical uncharged sphere $C$ is touched to $A$ and then placed at the midpoint of the line joining the spheres $A$ and $B$. The net electric force on the sphere $C$ is

$\int_{-1}^1 \frac{\cosh x}{1+e^{2 x}} d x$ is equal to :