$A$ stone of mass $m$ is tied to a string and is moved in a vertical circle of radius $r$ making $n$ revolutions per minute. The total tension in the string when the stone is at its lowest point is

A short bar magnet placed with its axis at $30^{\circ}$ with an external field of $800$ $Gauss$, experiences a torque of $0.016 ext{ N.m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} ext{ J}$. The value of $\alpha$ is . . . . . . . . . .

In a circuit,$L$,$C$,and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^{\circ}$. The value of $C$ is

In $\triangle ABC$,with usual notation,observe the two statements given below:
$(I)$ $r r_1 r_2 r_3 = \Delta^2$
$(II)$ $r_1 r_2 + r_2 r_3 + r_3 r_1 = s^2$
Which of the following is correct?

If $EAN$ of central metal cation $M^{2+}$ in a non-chelating complex is $36$ and atomic number of metal $M$ is $26$,then the number of monodentate ligands in this complex is:

The moment of inertia of a sphere (mass $M$ and radius $R$) about its diameter is $I$. Four such spheres are arranged as shown in the figure. The moment of inertia of the system about the axis $XX'$ will be (in $,I$)