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Frequently Asked KVPY Exam Pattern, KVPY Questions with Answers Page 23

(#M40027213) KVPY QUESTION Mental Ability Keep an EYE

The maximum possible value of x^2 + y^2 – 4x – 6y, x, y real, subject to the condition | x + y | + | x – y | = 4
(A) is 12 (B) is 28 (C) is 72 (D) does not exist

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(#M40027212) KVPY QUESTION Mental Ability Keep an EYE

Let f(x) = x^12 – x^9 + x^4 – x + 1. Which of the following is true ?
(A) f is one-one
(B) f has a real root
(C) f ′ never vanishes
(D) f takes only positive values

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(#M40027211) KVPY QUESTION Mental Ability Keep an EYE

The smallest possible positive slope of a line whose y-intercept is 5 and which has a common point with the
ellipse 9x^2 + 16y^2 = 144 is-

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(#M40027210) KVPY QUESTION Mental Ability Keep an EYE

Let A and B be any two n × n matrices such that the following conditions hold : AB = BA and there exist
positive integers k and l such that Ak = I (the identity matrix) and Bl = 0 (the zero matrix). Then-
(A) A + B = I (B) det (AB) = 0
(C) det (A + B) ≠ 0 (D) (A + B)m = 0 for some integer m

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(#M40027209) KVPY QUESTION General Ability Test Keep an EYE

The locus of the point P = (a, b) where a, b are real numbers such that the roots of x^3 + ax^2 + bx + a = 0 are in
arithmetic progression is-
(A) an ellipse
(B) a circle
(C) a parabola whose vertex in on the y-axis
(D) a parabola whose vertex is on the x-axis

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(#M40027208) KVPY QUESTION General Ability Test Keep an EYE

An electrode is placed in the axioplasm of a mammalian axon and another electrode is placed just outside the
axon. The potential difference measured will be-
(A) 0 (B) –70 mV
(C) –70 μV (D) +70 μV

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(#M40027204) KVPY QUESTION General Ability Test Keep an EYE

Puffs in the polytene chromosomes of Drosophila melanogaster salivary glands represent-
(A) transcriptionally active genes
(B) transcriptionally inactive genes
(C) heterochromatin
(D) housekeeping genes

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(#M40027203) KVPY QUESTION General Ability Test Keep an EYE

Soon after the three germ layers are formed in a developing embryo, the process of organogenesis starts. The
human brain is formed from the-
(A) ectoderm
(B) endoderm
(C) mesoderm
(D) partly endoderm and partly mesoderm

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(#M40027201) KVPY QUESTION General Ability Test Keep an EYE

Circadian Rhythm is an endogenously driven cycle for biochemical, physiological and behavioral processes.
In humans, the approximate duration of this 'biological clock' is-
(A) 1 Hour (B) 6 Hours (C) 12 Hours (D) 24 Hours

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(#M40027200) KVPY QUESTION General Ability Test Keep an EYE

A water molecule can from a maximum of ………. hydrogen bonds.
(A) 1 (B) 2 (C) 3 (D) 4

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