Math Chapter Wise

EnglishRPSC PGT 2022

Q21.Total number of subgroups of the symmetric group of permutations S3 is-

A3 B4 C5 D6

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EnglishRPSC PGT 2022

Q22.Oder of element a4 in the group G = ({a, a2, a3, a4, a5, a6 = e},x)is -

A6 B3 C2 D4

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EnglishRPSC PGT 2022

Q23.If α = 1 2 3 4 5 6 7 8 9 7 8 9 6 4 5 2 3 1, then order of α is

A6 B5 C4 D3

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EnglishRPSC PGT 2022

Q24.Let N be normal subgroup of a group G and f: G → G N is a mapping defined by f(x) = xN ∀ x∈G, then f is

AMonomorphism BEpimorphism CIsomorpism DAutomorpism

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EnglishRPSC PGT 2022

Q25.Every infinite cyclic group has -

AOne and only one generator BTwo and only two generator CInfinite generator DNo generator

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EnglishRPSC PGT 2022

Q26.Incorrect statement is -

ASet (–2z) is an ideal of ring (Z, +, •) BSet 2z and 3z are ideals of ring (Z, +, •) but (2z ∪ 3z) is not ideal CThere is no proper ideal of the ring (Z5, +5, ×5) DSets 4Z and 5Z are ideals of the ring (Z, +, •) but (4z ∩ 5z)

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EnglishRPSC PGT 2022

Q27.If F is homomorphism of a group G into another group G’ with kernel k, then which of the following is true?

Ak is a normal subgroup of G Bk is a normal subgroup of G' Ck is not a normal subgroup of G Dk is complex of G

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EnglishDSSSB PGT 2021

Q28.How many elements (Permutations) in S6 commutes with σ = (123)(34) ∈ S6?

A2 B5 C8 D6

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EnglishDSSSB PGT 2021

Q29.The order of the permutation 1 2 3 4 5 6 4 6 3 5 1 2, is -

A8 B4 C6 D12

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EnglishOAVS TGT 2021

Q30.The value of 337 (mod 7) is:

A3 (mod 7) B2 (mod 7) C4 (mod 7) D1 (mod 7)

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EnglishOAVS TGT 2019

Q31.Let φ(n) denotes the Euler totient function, then the value of φ(15) is equal to:

A8 B2 C12 D4

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EnglishOAVS TGT 2019

Q32.Which of the following is true?

A126/mod 7 ≡ 1 B146/mod 7 ≡ 1 C167/mod 8 ≡ 1 D188/mod 9 ≡ 1

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EnglishOAVS TGT 2019

Q33.If a ≠ 0 or b ≠ 0, then gcd(a, b) exists and satisfying from the following condition:

A{ } 0 gcd(a,b) min a, b > > B{ } 0 gcd(a,b) min a, b > < Cgcd(a,b) 0 < D{ } 0 gcd(a,b) min a, b < <

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EnglishOAVS TGT 2019

Q34.If in a class, 40% of the student study math and science and 60% of the student study math, then the probability of a student studying science given that he/she is already studying math is:

A0.55 B0.63 C0.47 D0.07

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EnglishOAVS TGT 2018

Q35.If a and b are real numbers such that ab ≠ 0, then which of the following statements is true?

AAll of the given options BBoth a and b must be zero CBoth a and b must be non-zero DEither a or b must be non-zero.

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EnglishOAVS TGT 2018

Q36.The inverse of 19 mod 141 is:

A51 B55 C52 D50

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EnglishOAVS TGT 2018

Q37.For x,y,z, if x > y, y > z and x > z, then this property is said to be:

AAdditive BTransitive CMultiplicative DDistributive

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EnglishJSSC PGT 2018

Q38.The set of units is Z14 (under the usual operation modulo 14 addition and multiplication) is given by:

AZ14 B{1} C{1, 13, 3, 5, 11, 9} D{1, –1, 3, 5, 2, 7}

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EnglishJSSC PGT 2018

Q39.Which one of the following is a group?

AThe set of all 2 by 2 matrices under multiplication. B(R+, ×) where a×b = ab for all a, b ∈ R+. C(C[0,1],×) where (f × g) (x) = f(x)g(x). (C[0,1] denotes the set of continuous functions defined over [0,1]) DThe set of odd integers under addition.

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EnglishJSSC PGT 2018

Q40.Which one of the following group is cyclic?

A(Q, +) B(Q+,.) CGLn (R) under the operation of matrix multiplication D1 n: n Z 0 1 ∈ under the operation of matrix multiplication

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