KVPY Government Jobs Exams

arithmetic mean and the geometric mean of two distinct 2-digit numbers x and y are two integers one of
which can be obtained by reversing the digits of the other (in base 10 representation). Then x + y equals-
(A) 82 (B) 116 (C) 130 (D) 148

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KVPY Other Question

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
The surface of a planet is found to be uniformly charged. When a particle of mass m and no charge is thrown
at an angle from the surface of the planet, it has a parabolic trajectory as in projectile motion with horizontal
range L. A particle of mass m and charge q, with the same initial conditions has a range L/2. The range of
particle of mass m and charge 2q with the same initial conditions is-
(A) L (B) L/2 (C) L/3 (D) L/4