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MATHEMATICS
SECTION - III
PART - A
Straight Objective Type:
This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. The order and degree of the differential equations of the family of hyperbolas centred at origin; principal axis along co-ordinate axis and of length √(a2+λ) and √(b2+λ) where a, b are fixed real numbers and λ is a real parameter is (A) 1, 1 (B) 2, 1 (C) 1, 2 (D) 3, 2 8. Let f: [k, k + 1, …, 2007] ® [1, 2, 3, …, n] be defined by f(x) = [ 2007 / x ] (where [.] denotes the greatest integer function). The maximum value of k such that it is not possible to make f an onto function for any vale of n is (A) 50 (B) 40 (C) 51 (D) none of these 9. Let f and g be continuous and differentiable functions. If f(0) = f(2) = f(4); f(1) + f(3) = 0; g(0) = g(2) = g(4) = 0 and if f(x) = 0 and g’(x) = 0 do not have a common root, then the minimum number of zeros of f’(x)g’(x) + f(x) g”(x) in [0, 4] is (A) 3 (B) 4 (C) 5 (D) 2
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