Math Chapter Wise

EnglishRajasthan TGT 2011

Q241.Let (R,+) be the additive group of real numbers and let (R,) + i i be the multiplicative group of positive real numbers, then mapping F: R R+ + → → defined by x f(x) e x R = ∀ ∈ = ∀ ∈ = ∀ ∈ = ∀ ∈ is.

AOnly homomorphism BOnly monomorphism COnly epimorphism DAn isomorphism

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EnglishRajasthan TGT 2011

Q242.Which one of the following statements is correct?

AEvery finite integral domain is a field BIn a ring a – b = 0 ⇒ either a = 0 or b = 0 CEvery finite ring is an integral domain DThe set of natural numbers N is a ring with respect to binary compositions usual addition and multiplication

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EnglishRajasthan TGT 2011

Q243.The set 4 Z {0,1,2,3}, = under binary compositions addition and multiplication modulo 4 is

AA field BA division ring CA ring without zero divisor DA ring with zero divisor

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EnglishRajasthan TGT 2011

Q244.Total number of ideals of the ring 5 Z = {0,1,2, 3,4},+5, 5 × is

A1 B2 C3 D4

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EnglishTGT 2011

Q245.A subset H of a group (G, *) is a group if and only if.

Aa, b∈H ⇒a*b∈H Ba∈H ⇒a–1/∈H Ca, b∈H ⇒a*b–1 ∈H DH ceW FkeâeF& DeJeÙeJe nw

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EnglishTGT 2011

Q246.In a group the number of improper subgroups is

A2 B3 CGroup on dependent D1

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EnglishTGT 2011

Q247.The number of generator in a finite cyclic group (order 28) will be.

A10 B8 C12 D14

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English(GIC) Lecture Exam, 2015

Q248.If 250 is divided by 7, then remainder is

A2 B4 C6 D3

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EnglishUP PCS (Pre) 2003

Q249.The set 5,15,25,35 under the binary operation of multiplication of residue classes modulo 40 is–

Anot a group Ba group with identity 5 Ca group with identity 25 Da group with identity35

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EnglishUP PCS (Pre) 2003

Q250.Which one of the following groups is non- abellian:

AThe additive group of integers BThe multiplicative group of non-zero rational numbers CKlein’s four group DHamiltonian group

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EnglishUP PCS (Pre) 2004

Q251.In the group 5 Z 0,1,2,3,4 of residue classes modulo 5, with respect to the operation of addition of residue classes modulo 5, the inverse of 2 is–

A1 B2 C3 D4

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EnglishUP PCS (Pre) 2004/ PGT 2013

Q252.Let H and K be two subgroups of a group G, then HK = {hk: h∈h, k∈K} is a subgroup of G iff–

AHK = KH BHK = G CH ∪ K = G Dnone of the above

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EnglishUP PCS (Pre) 2004

Q253.For the multiplicative group 2 1,,, where is one of the complex roots of unity the order of 2 is–

A0 B1 C2 D3

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EnglishUP PCS (Pre) 2004, 2005

Q254.{1, -1, i, –i} forms a group with respect to the operation of–

Amultiplication of complex numbers Baddition of complex numbers Csubtraction of complex numbers Dnone of the above

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EnglishUP PCS (Pre) 2004

Q255.If S denotes the set of all rational numbers except 1 and ‘*’ is defined on S as: a*b = a + b – ab, then the solution of the equation 2* x* 7 = 13

A1 B2 C3 D7

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EnglishUP PCS (Pre) 2005

Q256.The order of the element-i of the multiplicative group G = {1, –1, i, –i},

A4 B3 C2 D1

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EnglishUP PCS (Pre) 2006

Q257.Consider the group (z,*), where Z is the set of all integers and * is defined by a*b=a+b+1, a, b∈z The inverse of a∈Z is:

A2+a B–2+a C3–a D–2–a

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EnglishUP PCS (Pre) 2006

Q258.Let H be a subgroup of a group (G,.). Consider the following statements: (i) a,b ∈H⇒ ⇒ ⇒aob ∈ H (ii) a∈H⇒ ⇒ ⇒a–1 ∈ H Of these statements

Aboth (i) and (ii) are correct B(i) is correct, but (ii) is incorrect C(ii) is correct, but (i) is incorrect Dboth (i) and (ii) are incorrect

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EnglishUP PCS (Pre) 2006

Q259.If every element of a group G is its own inverse, then G is:

Aof even order Bof odd order Cabelian Dnon-abelian

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EnglishUP PCS (Pre) 2006

Q260.The set {1, –1, i, –i} is a multiplicative finite group of order:

A3 B4 C1 D2

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