Which one of the following is a correct set?

$A$ coil of $50$ turns and $4\,cm$ radius carries $2\,A$ current. The magnetic field at its centre is......$mT$.

Let $\overrightarrow{a}=\hat{i}-2 \hat{j}+3 \hat{k}$,$\overrightarrow{b}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\overrightarrow{c}=\lambda \hat{i}+\hat{j}+(2 \lambda-1) \hat{k}$. If $\overrightarrow{c}$ is parallel to the plane containing $\overrightarrow{a}$ and $\overrightarrow{b}$,then $\lambda$ is equal to

If the kinetic energy of a body is directly proportional to time $t$,the magnitude of force acting on the body is
$(i)$ directly proportional to $\sqrt{t}$
$(ii)$ inversely proportional to $\sqrt{t}$
$(iii)$ directly proportional to the speed of the body
$(iv)$ inversely proportional to the speed of the body

Which of the following fluorides does not exist?

$\int_0^\pi \frac{1}{1+\sin x} \, dx$ is equal to