Math Chapter Wise

EnglishUKPSC Lecturer (Mains) 2020

Q161.If N is a set of natural numbers, '*' is an operation such that a*b = a + b + ab ∀ a, b N, ∈ then identity element for * is:

A1 B0 C2 DNon-existent

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EnglishUKPSC Lecturer (Mains) 2020

Q162.In the group S3 of all permutations on the set of 3 elements, the maximum number of permutations y satisfying y3 = e (the identity permutation) is:

A4 B3 C2 D1

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q163.In Ring of real quaternion, (1–2i–3j–2k)–1 =......

A(1–2i–3j–2k) ÷18 B(1–2i–3j–2k) ÷6 C(–1+2i+3j+2k) ÷18 D(1+2i+3j+2k) ÷18

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q164.Let ∗ ∗ ∗ be a group action of G on X. For x∈X. let Gx denote the subset {g∗ ∗ ∗x:g∈G} of X. Define an equivalence relation ~ on X by setting x ~ y iff Gx=Gy. The equivalence class of X is known as the_______

Aspace of orbits Ox Borbit and stabilizer of x Corbit Ox of x Ddisjoint union of X

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q165.Let Q be the field of rational number. Find the Galois group order of f (x) = x2 – 2 over Q.

A2 B3 C4 D1

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q166.If G is a finite group of order 217. Find out the number of generators of the group G.

A180 B188 C181 D182

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q167.Calculate the number of elements of order 7 in Z (49)⊕ ⊕ ⊕Z (7).

A56 B48 C49 D51

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q168.Let X be a set and G be a group. A group action of G on X is a map *: G ×X → X given by (g,x) → g ∗ ∗ ∗x such that (1) (gh) ∗ ∗ ∗x = g∗ ∗ ∗ (h ∗ ∗ ∗ x) for all g, h∈G and x ∈ X.. (2) e∗ ∗ ∗x = x for all x∈X If this happens then we say that G acts on X and X is a

AG- Bijection BG- isomorphism CG- set DG- homomorphism

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q169.Let G be a group we know that G is the internal direct product of two subgroups of H and K. It is not true when:

AH ∩ K = {e} BH and K are normal subgroups of G CH ∪ K= G DHK= G

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q170.If G be a group of order 57. Assume that G is not a cyclic group. Then what is the number of elements in G of order 3?

A32 B85 C38 D36

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EnglishUK SSSC LT 2020

Q171.A ring (R, +, ⋅) is said to be Boolean ring if R ∀α∈ ∀α∈:

Aa = e Ba–1 = a Ca2 = a Da3 = a

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EnglishUK SSSC LT 2020

Q172.The generators of a group G = {a, a2, a3, a4, a5, a6 = e} are:

Aa and a5 Ba2/and a4 Ca3/and a5 Da2/and a3

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EnglishUK SSSC LT 2020

Q173.The order of the group S4 (Symmetric group) is:

A12 B16 C20 D24

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EnglishHaryana PGT 2020

Q174.Let G be an infinite cyclic group, then:

AG has infinitely many generators BG has one generator CG has two generators DG has three generators

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EnglishHaryana PGT 2020

Q175.G = ({0, 1, 2, 3, 4, 5}, +6) is a group. Order of 5 is:

A1 B3 C5 D6

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EnglishUP TGT-2016 (08-03-2019)

Q176.If the mapping f and g are given by f = {(1, 2), (3, 5), (4, 1)} g = {(2, 3), (5, 1), (1, 3)} then gof is

A{(2, 5), (5, 2), (1, 5)} B{(1, 2), (3, 5), (4, 1)} C{(1, 3), (3, 1), (4, 3)} D{(2, 3), (5, 1), (1, 3)}

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EnglishUP TGT-2016 (08-03-2019)

Q177.The value of 9 2 r 1 r sin 18 = π ∑ ∑ is

A1 B0 C5 Dπ

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EnglishUP TGT-2016 (08-03-2019)

Q178.Given: Statement A: All cyclic groups are abelian group. Statement B: The order of the cyclic group is same as the order of its generator.

AA and B are false BA is true, B is false CB is true, A is false DA and B both are true

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EnglishUP TGT-2016 (08-03-2019)

Q179.If G is a group of even order, then it has an element a≠e, satisfying

Aa2 =e Ba3 =e Ca5 =e Da7 =e

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EnglishNVS PGT 10-06-2019

Q180.Let a and b two positive integers. Then gcd(a,b). lcm(a,b) equals:

Aab Ba–b Ca/b Da+b

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