After rotating by 60 about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

An ellipse x^2+4y^2 =4 is rotated anticlockwise through a right angle in its own plane about its centre. If the locus of the point of intersection of a tangent to ellipse in its origin position with the tangent at the same point of the ellipse in its new position is given by the curve (x^2+y^2)^2=lambda(x^2+y^2)+mu xy where lambda and mu are positve integers. Find the value of (lambda+mu)

What is the rotational symmetry about the point O and line of symmetry of the given figure?

A vector of length l is turned through the angle theta about its tail. What is the change in the position vector of its head ?

A rod and a block are of same mass. Initially rod is in horizontal position. What will be acceleration of tip of the rod just after the system is released from this position shown in figure.

Three dipoles each of dipole moment of magnitude p are placed tangentially on a circle of radius R in its plae positioned at equal angle from each other as shown in the figure. Then the magnitude of electric field intensity at the centre of the circle will be :

A ring of radius R rotates about its diameter while a disc of the same radius rotates about the transeverse axis through its centre. The respective radii of gyrations are

Figure shows the circular motion of a particle. The radius of the circle, the period, same of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector the rotating particle P is

The earth makes a complete rotation about its axis in 24h. What angles will it turn in 3h 20 min ?