Two spheres each of mass $M$ and radius $\frac{R}{2}$ are connected at their centres with a massless rod of length $2R$. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod?

If the best and the worst paper never appear together,then in how many ways can six examination papers be arranged?

Condenser $A$ has a capacity of $15 \mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity of $1 \mu F$ with air between the plates. Both are charged separately by a battery of $100 V$. After charging,both are connected in parallel without the battery and the dielectric material being removed from condenser $A$. The common potential now is.......$V$

Senescence as an active developmental cellular process in the growth and functioning of a flowering plant,is indicated in

Five very long,straight wires are bound together to form a small cable. Currents carried by the wires are $I_1 = 20\ A, I_2 = -6\ A, I_3 = 12\ A, I_4 = -7\ A, I_5 = 18\ A$. The magnetic induction at a distance of $10\ cm$ from the cable is

The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is