If $A = \begin{bmatrix} 1 & 0 & 1 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix}$,then $\det(A)$ is equal to

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $\frac{-2q}{3}$ placed at points $A, B$ and $C$,respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $\angle CAB = 60^{\circ}$.

Which of the following statements are true about acceleration due to gravity $(g)$ of the earth (where $r$ is distance from the centre of the earth and $R$ is the radius of the earth)?
$(a)$ $g$ decreases in moving away from the centre,if $r > R$.
$(b)$ $g$ decreases in moving away from the centre,if $r < R$.
$(c)$ $g$ is zero at the centre of the earth.
$(d)$ $g$ at the equator decreases,if the earth stops rotating about its axis.

Which of the following is known as the pitcher plant?

Among the following series of transition metal ions,the one where all metal ions have $3d^2$ electronic configuration is

$\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}$ is equal to :