Math Chapter Wise

EnglishJSSC PGT 2018

Q41.Which of the following is a non-abelian group?

AThe set of non-zero real number under multiplication. BThe real number under addition. CThe set of 2 by 2 matrices under addition. DThe set of 2 by 2 matrices with determinant 1 under matrix multiplication.

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EnglishJSSC PGT 2018

Q42.What is the order of (2, 6) in Z6 × Z12?

A1 B6 C10 D2

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EnglishJSSC PGT 2018

Q43.GLn (R) denotes the group of n × n non- singular matrices under the operation of matrix multiplication. Which one of the following gives an Abelian (commutative) subgroup?

ASet of all non-singular upper triangular matrices. BSet of all non-singular matrices with positive trace. CSet of all matrices with positive determinant. DSet of all non-singular diagonal matrices.

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EnglishJSSC PGT 2018

Q44.What is the order of an element g of a cyclic group G?

AThe smallest integer r such that gr is identity. BThe order axioms imposed on the group. CThe number of elements in the group. DThe number of element a ∈ G such that a2 = e, the identity.

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EnglishOPSC PGT 2017

Q45.The set of non-zero complex numbers form a group under:

AAddition BMultiplication CAddition as wall as multiplication DNone of the above

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EnglishOPSC PGT 2017

Q46.A ideal P is a prime ideal, if:

AOrder of P is prime Bab P a,b P Cab P (a,b) 1 Dab P either a P or b P

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EnglishOPSC PGT 2017

Q47.M is a maximal ideal of the commutative ring R if and only if:

AR/M is normal subgroup BR∩M is an ideal CR/M is a field DR∩M is a proper ideal

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EnglishOPSC PGT 2017

Q48.If f ∈ F[X] and degree of f is n, then f has a splitting field K over F with:

A[K: F] < n! B[K: F] < n C[K: F] ≤ n! D[K: F] ≤ n

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EnglishOPSC PGT 2017

Q49.For integers a, b & m, a b(modm) f(a) f(b)(modm), when f() is:

AA function over set of integers BA polynomial CA polynomial with integer coefficients DA continuous function

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EnglishOAVS TGT 2018

Q50.Find the rank of the following matrix: 1 2 1 2 2 2 3 1 4

A0 B3 C2 D1

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EnglishOAVS TGT 2018

Q51.For what values of p and q will the following pair of linear equations have infinitely many solutions? 4x 5y 2 (2p 7q)x (p 8q)y 2q p 1

Ap = 1, q = 2 Bp = –1, q = –2 Cp = 1, q = –2 Dp = –1, q = 2

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EnglishOAVS TGT 2018

Q52.The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is:

ANo value B3 C–10 D–12

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EnglishOAVS TGT 2018

Q53.For the given equation, find the values of a and b such that infinite solutions are obtained. 2x 3y 7 (a b)x (2a b)y 21

Aa = 5, b = 1 Ba = 5, b = 5 Ca = 1, b = 5 Da = 1, b = 1

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EnglishOAVS TGT 2018

Q54.Which of the following represents the dimension of the vector space of all matrices of the order m × n if the sum of each row is 0?

Amn – m Bmn + m Cmn + n Dmn – n

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EnglishOAVS TGT 2018

Q55.The number of dimensions of a surface is:

A2 B3 C1 D0

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EnglishOAVS TGT 2018

Q56.If in a pair of linear equations, the equations are consistent, then their corresponding lines will be:

Aalways coincident Bparallel Calways intersecting Dintersecting or coincident

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EnglishJSSC PGT 2018

Q57.Consider the following real-valued maps defined over the vector space of 2 × 2 real- valued matrices. Which one of the following is not linear?

AImage/formula option A (see source) BT CT DT

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EnglishJSSC PGT 2018

Q58.A is a square matrix with each row sum equal to 1. Which one of the following statements regarding the eigenvalues of A is always true?

A0 is an eigenvalue of A. B1 is an eigenvalue of A. CBoth 0 and 1 are eigenvalues of A. DNo statement can be made on eigenvalue of A based on given information.

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EnglishJSSC PGT 2018

Q59.Which of the following is true?

AEvery permutation can be written as a product of intersecting cycles. BEvery permutation can be written as a product of cycles of length 1. CEvery permutation can be written as a product of disjoint cycles. DEvery permutation can be written as a product of cycles that do not commute.

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EnglishJSSC PGT 2018

Q60.Obtain the dimension of the dual space for {(x, y, z):x + 2y + 3z = 0}.

A3 B2 C4 D1

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