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Frequently Asked KVPY Exam Pattern, KVPY Questions with Answers Page 33

(#M40027023) KVPY QUESTION Mental Ability Keep an EYE

In the xy-plane, three distinct lines l1, l2, l3 concur at a point (λ, 0). Further the lines l1, l2, l3 are normals to the
parabola y^2 = 6x at the points A = (x1, y1), B = (x2, y2), C = (x3, y3) respectively. Then find λ

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(#M40027022) KVPY QUESTION Mental Ability Keep an EYE

In a rectangle ABCD, the coordinates of A and B are (1, 2) and (3, 6) respectively and some diameter of the
circumscribing circle of ABCD has equation 2x – y + 4 = 0. Then the area of the rectangle is

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(#M40027019) KVPY QUESTION Mental Ability Keep an EYE

Consider the cubic equation x^3 + ax^2 + bx + c = 0, where a, b, c are real numbers. Which of the following
statements is correct ?
(A) If a^2 – 2b < 0, then the equation has one real and two imaginary roots
(B) If a^2 – 2b ≥ 0, then the equation has all real roots
(C) If a^2 – 2b > 0, then the equation has all real and distinct roots
(D) If 4a^3 – 27b^2 > 0, then the equation has real and distinct roots

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(#M40027018) KVPY QUESTION Mental Ability Keep an EYE

Let P be an m × m matrix such that P2 = P. Then (1 + P^)n equals

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(#M40027017) KVPY QUESTION Mental Ability Keep an EYE

Suppose n is a natural number such that| i + 2i2 + 3i3 + ... + nin |=18 2 , where i is the square root of – 1.
Then n is

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(#M40027016) KVPY QUESTION General Ability Test Keep an EYE

Suppose logab + logba = c. The smallest possible integer value of c for all a, b > 1 is

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(#M40027015) KVPY QUESTION General Ability Test Keep an EYE

A standing wave in a pipe with a length L = 1.2 m is described by
y (x,t)= y0 sin [(2π/L)x] sin [(2π/L)x + π/4]
Based on above information, which one of the following statements is incorrect.
(Speed of sound in air is 300 m s–1)–
(A) The pipe is closed at both ends
(B) The wavelength of the wave could be 1.2 m
(C) There could be a node at x = 0 and antinode at x = L/2
(D) The frequency of the fundamental mode of vibrations is 137.5 Hz

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(#M40027014) KVPY QUESTION General Ability Test Keep an EYE

On a bright sunny day a diver of height h stands at the bottom of a lake of depth H. Looking upward, he can see
objects outside the lake in a circular region of radius R. Beyond this circle he sees the image of objects lying on
the floor of the lake. If refractive index of water is 4/3, then the value of R is

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(#M40027013) KVPY QUESTION General Ability Test Keep an EYE

Consider three concentric metallic spheres A, B and C of radii a, b, c respectively where a < b < c, A and B are
connected whereas C is grounded. The potential of the middle sphere B is raised to V then the charge on the sphere
C is–

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(#M40027012) KVPY QUESTION General Ability Test Keep an EYE

A stream of photons having energy 3 eV each impinges on a potassium surface. The work function of potassium is
2.3 eV. The emerging photo-electrons are slowed down by a copper plate placed 5 mm away. If the potential
difference between the two metal plates is 1 V, the maximum distance the electrons can move away from the
potassium surface before being turned back is

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