Math Chapter Wise

EnglishUPPSC Polytechnic Lecturer 2021(II) UP PGT 2016

Q121.If 'G' is a cyclic group of order 30, then total number of subgroups of G is –

A6 B7 C9 D8

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q122.Let 'S' be the set of all 2 × × × 2 matrices of the form a 0 b 0 where a, b are integers. Let 'R' be the ring of 2 × × × 2 matrices with elements as integers. Then -

AS is a left ideal of R BS is a right ideal of R CS is a left as well as a right ideal of R DS is neither a left nor a right ideal of R

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q123.If H is a p - sylow subgroup of G and x∈G, then x–1 Hx is also a -

Aand BImage/formula option B (see source) Cboth DNone of these

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EnglishUP PGT 2021, 2016

Q124.Statement A: Every isomorphic image of a cyclic group is cyclic. Statement B: Every cyclic group is abelian. Then

ABoth A and B are true BBoth A and B are false CA is true only DB is true only

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EnglishUP PGT 2021

Q125.Let G be a cyclic group of order 6. Then, the number of elements g ∈ G, such that G = <g> is

A2 B3 C4 D5

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EnglishUP PGT 2021 UPPSC GIC 2015 UP TGT 2004

Q126.Let 'a' be an element of a group and O(a) = 30, O(a18) is equal to –

A2 B5 C6 D10

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EnglishUP PGT 2021, 2016 UPPCS (Pre) 2006

Q127.Let (Z, o), where a o b def = a + b + 1, a, b ∈ Z, is a commutative group. Let a–1 be inverse of a, then a–1 is equal to –

A–a + 1 B–a –1 C–a –2 D–a + 2

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EnglishUP PGT 2021, 2016

Q128.If H and K are subgroups of a group G such that O(H) = 3 and O(K) = 5, then what will be O(H∩ ∩ ∩K)?

A1 B3 C5 D15

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EnglishUP PGT 2021

Q129.In the group (Z, +), the subgroup generated by 2 and 7 is –

A9Z B14Z CZ D5Z

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EnglishUP PGT 2021

Q130.If (G, *) is a group and x * y = x + 2y – 3 ∀ ∀ ∀ x, y ∈ G, then inverse of x in the group is

A2 9 4 + x B9 – 2 4 x C– 3 4 x D2 4 + x

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EnglishUP PGT 2021 LT 2018 UPPSC GIC 2015 UPPCS (Pre) 2003

Q131.A non commutative group has at least

A2 elements B3 elements C5 elements D6 elements

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EnglishUP PGT 2021

Q132.Let G be a group of order 30 and let A, B be normal subgroups of orders 2 and 5 respectively. Then G O AB is –

A2 B3 C5 D10

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q133.The relation of isomorphism in the set of all groups is-

ASymmetric and transitive, but not reflexive BReflexive and transitive, but not symmetric CReflexive and symmetric, but not transitive DReflexive, symmetric and transitive

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q134.In the group {a, a2, a3, a4, a5, a6 = e} the order of a5 is-

A5 B6 C2 D3

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q135.For the multiplicative group of residue classes () {1, 2, 3, 4,5, 6, mod7 }, generating element is-

A2 B3 C4 D6

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q136.The alternating group A3 on 3 symbols 1,2,3 is-

A{I, (1 2)} B{I, (1 3)} C{I, (2 3)} D{I, (1 2 3), (1 3 2)}

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q137.Let Z be the additive group of integers and E the additive subgroup of even integers with zero, then the number of distinct cosets of E in Z is-

A2 B3 C1 D∞

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q138.Let R+ be the multiplicative group of positive real numbers and R be the additive group of real numbers, then the mapping f: R+ → → R given by f(x) = logx ∀ ∀ ∀ x∈R+ is-

AOne - one and onto, but not homomorphism BOne-one and homomorhism, but not onto COnto and homomorphism, but not one-one DOne-one, onto and homomorphism

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EnglishUP TGT 2021

Q139.The number of generators of a cyclic group of order 10 is

A2 B3 C4 D5

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EnglishUP TGT 2021

Q140.The order of the element (–i) of the multiplicative group G = {1, –1, i, –i} is

A4 B3 C2 D1

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