The series combination of two batteries, both of the same emf 10 V, but different internal resistance of 20$$\Omega $$ and 5$$\Omega $$, is connected to the parallel combination of two resistors 30$$\Omega $$ and R $$\Omega $$. The voltage difference across the battery of internal resistance 20$$\Omega $$ is zero, the value of R (in $$\Omega $$) is : _______

An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s) ? Give your answer to the nearest integer in kilometer/s _____.

The first member of the Balmer series of hydrogen atom has a wavelength of 6561 Å. The wavelength of the second member of the Balmer series (in nm) is:

A ball is dropped from the top of a 100 m high tower on a planet. In the last $${1 \over 2}s$$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in ms^–2) near the surface on that planet is _____.