A sphere has the equation |r-a|^2+|r-b|^2=72, where a=hat(i)+3hat(j)-6hat(k) and b=2hat(i)+4hat(j)+2hat(k) Find (i) The centre of sphere (ii) The radius of sphere (iii) Perpendicular distance from the centre of the sphere to the plane rcdot(2hat(i)+2hat(j)-hat(k))+3=0 .

Fill in the blanks. Cylinder has ______ faces.

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine P(2)

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number '3’. If die is rolled once, determine : P(2).

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number '3’. If die is rolled once, determine : P(1 or 3) .

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number '3’. If die is rolled once, determine : P (not 3).

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine P(1 or 3)

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine P(not 3)

Consider two conducting spheres of radii of R_1 and R_2 with R_1 > R_2 . If the two are at the same potential the larger sphere has more charge than the smaller spheres. State whether the charge density of the smaller sphere is more or less than that of the larger one.

The electric force of repulsion on a tiny charged conducting sphere A as a function of its separation form a large conducting sphere B. The sphere B has 10 times the charge on the sphere A. Explain the behaviour of the force between separation 2 cm and 1 cm.