KVPY Government Jobs Exams

Let a0 = 0 and ax = 3an–1 + 1 for n ≥ 1. Then the remainder obtained dividing a2010 by 11 is-
(A) 0 (B) 7 (C) 3 (D) 4

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KVPY Other Question

The number of natural numbers n in the interval [1005, 2010] for which the polynomial 1 + x + x^2 + x^3 + …. x^n–1
divides the polynomial 1 + x^2 + x^3 + x^4 + …. + x^2010 is-
(A) 0 (B) 100 (C) 503 (D) 1006 A pen of mass 'm' is lying on a piece of paper of mass M placed on a rough table. If the coefficient of
friction between the pen and paper, and, the paper and table are μ1 and μ2, respectively, then the minimum
horizontal force with which the paper has to be pulled for the pen to start slipping is given by-
(A) (m + M) (μ1 + μ2) g (B) (mμ1 + Mμ2)g
(C) {mμ1 + (m + M) μ2} g (D) m(μ1 + μ2) g