If the vectors $a \hat{i}+\hat{j}+\hat{k}$,$\hat{i}+b \hat{j}+\hat{k}$,and $\hat{i}+\hat{j}+c \hat{k}$ $(a \neq 1, b \neq 1, c \neq 1, a \neq b \neq c)$ are coplanar,then the value of $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is:

Four particles $A, B, C$ and $D$ of equal mass $m$ are placed at the four corners of a square. They move with equal uniform speed $v$ towards the intersection of the diagonals. After the collision,particle $A$ comes to rest,particle $B$ traces its path back with the same speed $v$,and particles $C$ and $D$ move with equal speeds $v'$. What is the velocity of particle $C$ after the collision?

Which one of the following is an artificial sweetening agent?

Which part of the tobacco plant is infected by the nematode $Meloidogyne \ incognita$?

Which of the following acts as a rocket propellant?

If $x = \log_a(bc)$,$y = \log_b(ca)$,and $z = \log_c(ab)$,then which of the following is equal to $1$?