KVPY Government Jobs Exams

A small asteroid is orbiting around the sun in a circular orbit of radius r0 with speed V0. A rocket is launched from
the asteroid with speed V = αV0 , where V is the speed relative to the sun. The highest value of α for which the
rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effects of other planets

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KVPY Other Question
The total energy of a black body radiation source is collected for five minutes and used to heat water. The
temperature of the water increases from 10.0º C to 11.0ºC. The absolute temperature of the black body is doubled
and its surface area halved and the experiment repeated for the same time. Which of the following statements
would be most nearly correct ?
(A) The temperature of the water would increase from 10.0º C to a final temperature of 12º C
(B) The temperature of the water would increase from 10.0º C to a final temperature of 18º C
(C) The temperature of the water would increase from 10.0º C to a final temperature of 14ºC
(D) The temperature of the water would increases from 10.0º C to a final temperature of 11º C A radioactive nucleus A has a single decay mode with half life τA. Another radioactive nucleus B has two decay
modes 1 and 2. If decay mode 2 were absent, the half life of B would have been τA/2. If decay mode 1 were absent,
the half life of B would have been 3τA, then the ratio τB/τA is