If $P(n,r) = 1680$ and $C(n,r) = 70$,then $69n + r! = $

If $P=(0,1,0)$ and $Q=(0,0,1)$, then the length of the projection of the line segment $PQ$ on the plane $x+y+z=3$ is

Which one of the following is not a biopolymer?

Which of the following statements are correct?
$I$. $P_4$ molecule is very reactive because of angular strain.
$II$. The basicity of $H_3PO_3$ is $3$.
$III$. In gas phase,all $P-Cl$ bonds of $PCl_5$ have same bond length.
$IV$. In solid state,$PCl_5$ exists as an ionic solid,in which anion $[PCl_6]^-$ has octahedral and cation $[PCl_4]^+$ has tetrahedral shape.

$\left|\begin{array}{ccc}x+2 & x+3 & x+5 \\ x+4 & x+6 & x+9 \\ x+8 & x+11 & x+15\end{array}\right|$ is equal to

Observe the following reaction: $2 A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?