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IIT JAM 2021 : Mathematics (with Answer Keys)

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JAM 2021 MATHEMATICS - MA N = {1, 2, . . .}. Z = {. . . , 2, 1, 0, 1, 2, . . .}. Q = the set of rational numbers. R = the set of real numbers. Rn = the n-dimensional real space with the Euclidean topology. C = the set of complex numbers. Cn = the n-dimensional complex space with the Euclidean topology. Mn (R), Mn (C) = the vector space of n n real or complex matrices, respectively. f , f = the first and second derivatives of the function f , respectively. f (n) = the nth. derivative of the function f . R C stands for the line integral over the curve C. In = the n n identity matrix. A 1 = the inverse of an invertible matrix A. Sn = the permutation group on n symbols. i = (1, 0, 0), j = (0, 1, 0) and k = (0, 0, 1). ln x = the natural logarithm of x (to the base e). |X| = the number of elements in a finite set X. Zn = the additive group of integers modulo n. arctan(x) denotes the unique ( /2, /2) such that tan = x. All vector spaces are over the real or complex field, unless otherwise stated. MA 1/1

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