IIT Joint Admission Test previous year question papers in PDF format
 

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An abeliari group of order 24 has
(A) exactly one subgroup of order 3
(B) exactly two subgroups of order 3
(C) no subgroup of order 3
(D) more than two subgroups of order 3

Let A be an n x n matrix such that xTAx > 0 for every non zero vector x in R’. Which of the following is true?
(A) All eigen values of A are negative
(B) All eigen values of A are positive
(C) Exactly one eigen value of A is zero
(D) More than one eigen values of A are zero

Which of the following is not true?
(A) The order of the subgroup of a finite group divides the order of the group
(B) Every group of finite order is cyclic
(C) Every cyclic group is abelian
(D) If k is a divisor of the order of a group G, then G must have a subgroup of order k

Which of the following is true?
(A) The set of all 2×2 real matrices forms a group under matrix multiplication
(B) A finite abelian group of order 6 has exactly two non-trivial subgroups
(C) Every finite group is always cyclic
(D) The set of all 2×2 real non-singular matrices forms an abelian group under matrix multiplication

Let F be a field. Given below are six statements about F.
1. F is a skew field
2. F is a group with respect to multiplication
3. Fis an integral domain
4. F has zero divisors
5. Fhas no zero divisors
6. Only ideals ofF are {O} and itself

In which of the following options all the statements are correct?
(A) 1,2,3
(B) 1,3,5
(C) 2,4,6
(D) 4,5,6

Consider the statements
(P) If a linear programming problem has only one optimal solution, then this solution is an extreme point of the feasible region.
(03 A linear programming problem either is infeasible or has at least one optimal solution.
(R) A linear programming problem can have exactly two optimal solutions.
(S) A feasible linear programming problem has an optimal solution or unbounded solution.

Let be the set of all planes in G3. The nonrepresentational inPis
(A) symmetric and transitive
(B) symmetric and reflexive
(C) symmetric but not transitive
(D) transitive but not reflexive

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IIT Joint Admission Test previous year question papers in PDF format

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