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
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
Let
x 1
f (x) x 1
−
+
= for all x ≠ 1. Let
f 1(x) = f (x),f 2 (x) = f (f (x)) and generally
f n (x) = f (f n−1(x)) for n > 1
Let P = f1(2)f2(3)f3(4)f4(5)
Which of the following is a multiple of P –
(A) 125 (B) 375 (C) 250 (D) 147
A man tosses a coin 10 times, scoring 1 point for each head and 2 points for each tail. Let P(K) be the probability
of scoring at least K points. The largest value of K such that P(K) > ½ is
Suppose a, b, c are real numbers, and each of the equations x^2 + 2ax + b2= 0 and x^2 + 2bx + c2 = 0 has two distinct
real roots. Then the equation x2 + 2cx + a2 =0 has–
(A) Two distinct positive real roots (B) Two equal roots
(C) One positive and one negative root (D) No real roots
For a one-electron atom, the set of allowed quantum numbers is –
(A) n = 1, l = 0, m1 = 0, ms = +½ (B) n = 1, l = 1, m1 = 0, ms = +½
(C) n = 1, l = 0, m1 = –1, ms = –½ (D) n = 1, l = 1, m1 = 1, ms = –½