JEE (Advanced) 2010 Paper-1

A binarystar consists of two stars A (mass 2.2 $$M_s$$) and B (mass 11 $$M_s$$). where $$M_s$$ is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binarystar to the angular momentumof star B about the centre of mass is

Gravitational acceleration on the surface of a planet is $$\frac{\sqrt{6}}{11} g$$, where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is $$\frac{2}{3}$$ times that of the earth. If the escape speed on the surface of the earth is taken to be 11 $$kms^{-1}$$, the escape speed on the surface of the planet in $$kms^{-1}$$ will be

A piece of ice (heat capacity = 2100 J $$kg^{-1} {^\circ}C^{-1}$$ andlatent heat = $$3.36 \times 10^5 J kg^{-1}$$) of mass m grams is at $$-5 ^\circ C$$ at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gmof ice has melted. Assuming there is no other heat exchange in the process, the value of m is

A stationary source is emitting sound ata fixed frequency $$f_0$$, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of $$f_0$$. What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is 330 $$ms^{-1}$$.