jam.iitm.ac.in Mathematics Question Paper Sample : Indian Institute of Technology Madras
Name of the Organisation : Indian Institute of Technology Madras
Name of the Exam : JAM Exam
Document Type : Sample Question Paper
Name of the Subject : Mathematics (MA)
Website : jam.iitm.ac.in
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IITM JAM Mathematics Sample Questions
Section – A :
Q.1 Suppose N is a normal subgroup of a group G. Which one of the following is true?
(A) If G is an infinite group then G/N is an infinite group
Related : Indian Institute of Technology Madras Geology Question Paper Sample : www.pdfquestion.in/7708.html
(B) If G is a nonabelian group then G/N is a nonabelian group
(C) If G is a cyclic group then G/N is an abelian group
(D) If G is an abelian group then G/N is a cyclic group
Q.3 Let a,b,c,d be distinct non-zero real numbers with a+b=c+d. Then an eigenvalue of the
Let S be a nonempty subset of R. If S is a finite union of disjoint bounded intervals, then which one
of the following is true?
(A) If S is not compact, then sup SeS and inf SES
(B) Even if sup SeS and inf SeS, S need not be compact
(C) If sup SeS and inf SeS then S is compact
(D) Even if S is compact, it is not necessary that sup SeS and inf SES
Q.9 An integrating factor of the differential equation
Let A be a nonempty subset of A. Let A denote the set of interior points of A. Then A can be
(A) empty
(B) singleton
(C) a finite set containing more than one element
(D) countable but not finite
Let S3 be the group of permutations of three distinct symbols. The direct sum S3+S3 has an element of order
(A) 4 (B) 6 (C) 9 (D) 18
Which one of the following statements is true for the series
(A) The series converges conditionally but not absolutely
(B) The series converges absolutely
(C) The sequence of partial sums of the series is bounded but not convergent
(D) The sequence of partial sums of the series is unbounded
The sequence
(A) monotone and convergent
(B) monotone but not convergent
(C) convergent but not monotone
(D) neither monotone nor convergent
JAM 2014 Mathematics :
Let f (x) = ‘x2 —25l for all x e R. The total number of points of R at which f attains a local extremum (minimum or maximum) is
(A) 1 (B) 2 (C) 3 (D) 4
For a, b, c e R , if the differential equation (ax2 +bxy+y2)dx+(2×2 +cxy+y2)dy=0
Let G be a group of order 17. The total number of non-isomorphic subgroups of G is
(A) l (B) 2 (C) 3 (D) 17
Which one of the following is a subspace of the vector space R ?
(A) {(x,y,z) 5R3 :x+2y=0, 2x+3z =0
Let A: 0 b 7 be a matrix with real entries. If the sum and the product of all the eigenvalues of A are 10 and 30 respectively, then a2 + b2 equals
(A) 29 (B) 40 (C) 58 (D) 65
The equation of the curve passing through the point (g, I] and having slope each point (x, y) with x i 0 is
The value of a e R for which the curves at2 +0zy2 =1 and y I x2 intersect orthogonally is
Let {Xn} be a sequence of real numbers such that lim (er+1 —x” )= c , where c is a positive real number. Then the sequence n
A) is NOT bounded
(C) converges to c
(B) is bounded but Not convergent
(D) converges to 0
Let f (x) = x3 +x and g(x) = x3 —x for all x e R. If f _1 denotes the inverse function of f ,then the derivative of the composite function g o f _’ at the point 2 is
2 1 11 1
For all (x, y)e]R2, let f(x,y)= lxl
(A) —l (B) 0 (C) 1 (D) 2