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Frequently Asked KVPY Exam Pattern, KVPY Questions with Answers Page 21

(#M40027254) KVPY QUESTION General Ability Test -2010 Keep an EYE

A charge +q is placed somewhere inside the cavity of a thick conducting spherical shell of inner radius R1
and outer radius R2. A charge – Q is placed at a distance r > R2 from the centre of the shell. Then the electric
field in the hollow cavity-
(A) depends on both +q and – Q (B) is zero
(C) is only that due to – Q (D) is only that due to +q

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(#M40027253) KVPY QUESTION General Ability Test -2010 Keep an EYE

A comet (assumed to be in an elliptical orbit around the sun) is at a distance of 0.4 AU from the sun at the
perihelion. If the time period of the comet is 125 years, what is the aphelion distance ? AU : Astronomical
Unit.
(A) 50 AU (B) 25 AU (C) 49.6 AU (D) 24.6 AU

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(#M40027246) KVPY QUESTION Mental Ability -2010 Keep an EYE

Let kˆ jˆ iˆ u = 2 − + r , kˆ v = −3ˆj + 2 r be vectors in R3 and w r be a unit vector in the xy-plane. Then the maximum
possible value of | (u r × v r ) .w r | is-

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(#M40027245) KVPY QUESTION Mental Ability -2010 Keep an EYE

Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability
that they form the vertices of an isosceles triangle is-

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(#M40027243) KVPY QUESTION Mental Ability -2010 Keep an EYE

The roots of (x – 41)^49 + (x – 49)^41 + (x – 2009)^2009 = 0 are -
(A) all necessarily real
(B) non-real except one positive real root
(C) non-real except three positive real roots
(D) non-real except for three real roots of which exactly one is positive

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(#M40027241) KVPY QUESTION Mental Ability -2010 Keep an EYE

The product (1 + tan 1º) (1 + tan 2º) (1 + tan 3º) …. (1 + tan 45º) equals-

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(#M40027240) KVPY QUESTION Mental Ability -2010 Keep an EYE

The number of roots of the equation cos^7θ – sin^4θ = 1 that lie in the interval [0, 2π] is-
(A) 2 (B) 3 (C) 4 (D) 8

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(#M40027238) KVPY QUESTION Mental Ability -2010 Keep an EYE

A circle touches the parabola y^2 = 4x at (1, 2) and also touches its directrix. The y-coordinates of the point of
contact of the circle and the directrix is-

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(#M40027233) KVPY QUESTION Physical Ability Test Keep an EYE

Nocturnal animals have retinas that contain-
(A) a high percentage of rods to increase sensitivity to low light conditions
(B) a high percentage of cones so that nocturnal color vision can be improved in low light conditions
(C) an equal number of rods and cones so that vision can be optimized
(D) retinas with the photoreceptor layer present in the front of the eye to increase light sensitivity

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(#M40027231) KVPY QUESTION Physical Ability Test Keep an EYE

Increasing the number of measurements of an experimental variable will-
(A) increase the standard error of the sample (B) increase the mean of the sample
(C) decrease the standard error of the sample (D) result in all of the above

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