Cinnabar is the ore of

The following are some statements related to $VA$ group hydrides:
$I$. Reducing property increases from $NH_3$ to $BiH_3$.
$II$. Tendency to donate lone pair decreases from $NH_3$ to $BiH_3$.
$III$. Thermal stability of hydrides decreases from $NH_3$ to $BiH_3$.
$IV$. Bond angle of hydrides decreases from $NH_3$ to $BiH_3$.
The correct statements are:

Along the $X$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at $x=a+r$ (if $a \ll r$) is: ($\varepsilon_0$ is the permittivity of free space)

$A$ rocket with a lift-off mass $2 \times 10^4 \ kg$ is blasted upwards with an initial acceleration of $5 \ m \ s^{-2}$. The initial thrust of the blast is (Take $g = 10 \ m \ s^{-2}$)

Let $f(x)$ be a polynomial of degree $3$ such that $f(-1) = 10$,$f(1) = -6$,$f(x)$ has a critical point at $x = -1$,and $f'(x)$ has a critical point at $x = 1$. Then $f(x)$ has a local minima at $x =$

If $f(x)=(x-1)(x-2)(x-3)$ for $x \in[0,4]$,then the value of $c \in(0,4)$ satisfying Lagrange's mean value theorem is: