Math Chapter Wise

English(GIC) Lecture Exam, 2015

Q281.A homomorphism of a group into itself is called a/an–

Aisomorphism Bmonomorphism Cepimorphism Dendomorphism

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English(GIC) Lecture Exam, 2015

Q282.Let (R, +,.) be a ring in which a2 = a, ∀ ∀ ∀a∈R Then the incorrect statement for a, b∈R is–

Aa. b = 2 (b.a) Bab + ba =0 Ca + a = 0 Da. b = b. a

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English(GIC) Lecture Exam, 2015

Q283.A subgroup H of a group G is called a normal subgroup if and only if–

AaH Ha a H/∨ ∈ BaH Ha a G/∨ ∈ CaHa H a G/∨ ∈ DaHa H a H/∨ ∈

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English(GIC) Lecture Exam, 2015

Q284.The number of elements in the cyclic subgroup of Z30 generated by 25 is–

A5 B10 C6 D15

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English(GIC) Lecture Exam, 2015

Q285.The roots of the equation 2 x 5 0 in the ring Z6 are–

A1,4 B1,5 C2,4 DDo not exist

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English(GIC) Lecture Exam, 2015

Q286.If y = sin (5 – 3x), the yn is–

An n 5 sin 5 3x 2 Bn n 3 sin 5 3x 2 Cn n (3) sin 5 3x 2 Dn n (3) cos 5 3x 2

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EnglishTGT 2010

Q287.How many generators does a cyclic group of order n have?

An–1 Bn Cm, where m is total number of relatively prime number between 0 and n DNone of the above

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EnglishTGT 2010

Q288.Which of the following sets is bounded below but not bounded above?

AN BZ CQ DR

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EnglishTGT 2010

Q289.If H1 and H2 are two subgroups of a group G, then H1 ∩ ∩ ∩ H2 is

Acyclic groups of G Bnormal subgroup Csubgroups of G DNone of these

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EnglishTGT 2010

Q290.If axb = b,a,x, ∈G (group), then the value of x is

Aa–1/ba–1 Bab C1/ba− DNone of these

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EnglishTGT 2010

Q291."Every bounded infinite subset of R has at least one limit point." This result is known as

ADedekind-Cantor theorem BCantor theorem CBolzano-Weierstrass theorem DBolzano theorem

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EnglishTGT 2009

Q292.If G is a group of order n and H is of order m be a subgroup then

An = m Bn divides m Cm divides n DNone of these

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EnglishTGT 2009

Q293.Every cyclic group

AGroup BSub Group CAbelian group DNone of these

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EnglishTGT 2004

Q294.The digit in the unit place of (237)610 is:

A9 B7 C3 D1

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EnglishTGT 2004

Q295.Let S be a set of two elements. The number of different binary compositions that can be defined is:

A16 B8 C4 D2

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EnglishTGT 2004/ GIC 2015

Q296.In a group (G, o), a is an element of order 30. The order of a18 is–

A30 B6 C5 D12

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EnglishTGT 2004

Q297.In a group (G, o) if n is the order of an element a, where a∈G, and p is prime to 'n' then the order of ap is.

Anp Bnp Cp Dn

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EnglishPGT 2003

Q298.Which one of these statements is false?

A(zz,+) is cyclic group B(zz4+) is a cyclic group C{ } 1,, 1, s i i = − − Then (),* S is a cyclic group DKlein’s 4– group is a cyclic group

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