$A$ polygon has $54$ diagonals. Then,the number of its sides is

Given the circle $C$ with the equation $x^2+y^2-2x+10y-38=0$. Match the List-$I$ with the List-$II$ given below concerning $C$.

$A$. The equation of the polar of $(4, 3)$ with respect to $C$	$I$. $y + 5 = 0$
$B$. The equation of the tangent at $(9, -5)$ on $C$	$II$. $x = 1$
$C$. The equation of the normal at $(-7, -5)$ on $C$	$III$. $3x + 8y = 27$
$D$. The equation of the diameter passing through $(1, -5)$ and $(1, 3)$	$IV$. $x = 9$

Three numbers are chosen at random from $1$ to $20$. The probability that they are consecutive is

Which of the following elements is a constituent of biotin?

With what minimum velocity should a block of mass $m$ be projected from the left end $A$ towards end $B$ such that it reaches the other end $B$ of a conveyor belt of length $L$ moving with a constant velocity $v$ in the opposite direction? The friction coefficient between the block and the belt is $\mu$.

The perimeter of the triangle with vertices at $(1,0,0), (0,1,0)$ and $(0,0,1)$ is