If $\frac{x^3}{(2 x-1)(x+2)(x-3)} = A+\frac{B}{2 x-1}+\frac{C}{x+2}+\frac{D}{x-3}$,then $A$ is equal to

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

The value of $\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$ is equal to:

If $\sin {\theta _1} + \sin {\theta _2} + \sin {\theta _3} = 3,$ then $\cos {\theta _1} + \cos {\theta _2} + \cos {\theta _3} = $

When a person dies after being stung by a bee followed by the administration of penicillin,death may be due to:

There are two holes,one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is $0.01 ~m^2$ and the vertical distance between the holes is $1 ~m$. The tank is filled with water. The net force on the tank in newtons when the water flows out of the holes is (Density of water $= 1000 ~kg/m^3$,$g = 10 ~m/s^2$):