In the reaction $A + 2B \rightleftharpoons 2C + D$,the initial concentration of $B$ was $1.5$ times that of $[A]$. At equilibrium,the concentrations of $A$ and $B$ became equal. The equilibrium constant $K_c$ for the reaction is:

The product $(A)$ is:

The area (in sq. units) of the triangle formed by the lines $x^2-3xy+y^2=0$ and $x+y+1=0$ is

The value of $x$ for which $\sin (\cot^{-1} (1 + x)) = \cos(\tan^{-1} x)$ is

$A$ rifle of $20 ~kg$ mass can fire $4$ bullets per second. The mass of each bullet is $35 \times 10^{-3} ~kg$ and its final velocity is $400 ~ms^{-1}$. What force must be applied on the rifle so that it does not move backwards while firing the bullets (in $~N$)?

$A$ force acts on a $3\, g$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^2 + t^3$,where $x$ is in $meters$ and $t$ is in $seconds$. The work done during the first $4\, seconds$ is .............. $mJ$.