If $f(x) = x^3 - 6x^2 + 9x + 3$ is a decreasing function,then $x$ lies in

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

$A$ magnetic needle lying parallel to a magnetic field is turned through $60^{\circ}$. The work done on it is $W$. The torque required to maintain the magnetic needle in the position mentioned above is

If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

Identify the major product of the following reaction:

In the circuit element given here,if the potential at point $B$,$V_B = 0$,then the potentials of $A$ and $D$ are given as