$A$ rod of mass $M$ and length $l$ is suspended by two wires $P$ and $Q$. $A$ uniform magnetic field $B$ is directed into the page. When current $I$ flows through the rod,the tension in each supporting wire is:

Let $a, b$ and $c$ be distinct and none of them is equal to $1$. If the lines $x+ay+a=0$,$bx+y+b=0$ and $cx+cy+1=0$ are concurrent,then the value of $\frac{a}{a-1}+\frac{b}{b-1}+\frac{c}{c-1}$ is

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to the disc and passing through the centre),and rotating with angular speed $\omega_1$ and $\omega_2$ are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the system in the process?

Two spheres $S_{1}$ and $S_{2}$ have the same radii but temperatures $T_{1}$ and $T_{2}$ respectively. Their emissive power is the same and their emissivity is in the ratio $1: 4$. Then the ratio of $T_{1}$ to $T_{2}$ is:

If a body is projected with an angle $\theta$ to the horizontal,then

$(b \times c) \times (c \times a) = $