At a height 'R' above the earth's surface the gravitational acceleration is (R = radius of earth, g = acceleration due to gravity on earth's surface)

Two rings of radius 'R' and 'nR' made of same material have the ratio of moment of inertia about an axis passing through its centre and perpendicular to the plane is $$1: 8$$. The value of '$$n$$' is (mass per unit length $$=\lambda$$)

'$$n$$' waves are produced on a string in 1 second. When the radius of the string is doubled, keeping tension same, the number of waves produced in 1 second for the same harmonic will be

the magnetic flux (in weber) in a closed circuit of resistance $$20 \Omega$$ varies with time $$t$$ second according to equation $$\phi=5 t^2-6 t+9$$. The magnitude of induced current at $$t=0.2$$ second is