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Frequently Asked KVPY Exam Pattern, KVPY Questions with Answers Page 34

(#M40027011) KVPY QUESTION General Ability Test Keep an EYE

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

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(#M40027010) KVPY QUESTION General Ability Test Keep an EYE

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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(#M40027009) KVPY QUESTION General Ability Test Keep an EYE

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

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(#M40027008) KVPY QUESTION General Ability Test Keep an EYE

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

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(#M40027007) KVPY QUESTION General Ability Test Keep an EYE

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

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(#M40027006) KVPY QUESTION General Ability Test Keep an EYE

A polynomial P(x) with real coefficients has the property that P''(x) ≠ 0 for all x. Suppose P(0) = 1 and P'(0) = –1.
What can you say about P(1)

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(#M40027004) KVPY QUESTION General Ability Test Keep an EYE

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

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(#M40027002) KVPY QUESTION General Ability Test Keep an EYE

Typical electronic energy gaps in molecules are about 1.0 eV. In terms of temperature, the gap is closed to

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(#M40026998) KVPY QUESTION General Ability Test Keep an EYE

An unpolarized beam of light of intensity I0 passes through two linear polarizers making an angle of 30º with
respect to each other. The emergent beam will have an intensity

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(#M40026997) KVPY QUESTION General Ability Test Keep an EYE

A parent nucleus X is decaying into daughter nucleus Y which in turn decays to Z. The half lives of X and Y are
40000 years and 20 years respectively. In a certain sample, it is found that the number of Y nuclei hardly changes
with time. If the number of X nuclei in the sample is 4 × 1020, the number of Y nuclei present in its is

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