$A$ body of mass $2 \, kg$ slides down a curved track which is a quadrant of a circle of radius $1 \, m$. All the surfaces are frictionless. If the body starts from rest,its speed at the bottom of the track is ................. $m/s$.

Which of the following statements is correct?

The half-life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$,which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1:15$ in a sample of a given rock. The age of the rock was estimated to be ......... years.

Which of the following is an oxidizing agent?

The normal to the curve $x^{2}=4y$ passing through $(1,2)$ is

$A$ vector $n$ of magnitude $8$ units is inclined to $x$-axis at $45^\circ$,$y$-axis at $60^\circ$ and an acute angle with $z$-axis. If a plane passes through a point $(\sqrt{2}, -1, 1)$ and is normal to $n$,then its equation in vector form is