Reduction of nitrobenzene with $Zn$ and alcoholic $KOH$ solution results in the formation of the following compound:

If $X$ is a Poisson variate such that $P(X=1)=P(X=2)$,then $P(X=4)$ is equal to

The distance between the foci of the hyperbola $x^2 - 3y^2 - 4x - 6y - 11 = 0$ is

Considering only the Principal values of inverse functions,the set $A = \{x \geq 0 \mid \tan^{-1}(2x) + \tan^{-1}(3x) = \frac{\pi}{4}\}$

As shown in the figure,a block of mass $10 \, kg$ lying on a horizontal surface is pulled by a force $F$ acting at an angle of $30^{\circ}$ with the horizontal. For $\mu_{s} = 0.25$,the block will just start to move for the value of $F$ in $N$ is: [Given $g = 10 \, ms^{-2}$]

If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2 + y^2 + 4x - 6y = 12$ externally at the point $(1, -1)$,then the radius of $C$ is