Math Chapter Wise

EnglishUP PCS (Pre) 2007

Q261.Which one of the following is not a Klein's four group?

AMultiplicative (modulo 8) group { } 1,3,5,7 BMultiplicative (modulo 40) group { } 5,15,25,35 CMultiplicative group 1 0 1 0 1 0 1 0,,, 0 1 0 1 0 1 0 1 − − − DMultiplicative group { } 1, 1,i, i − −

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EnglishUP PCS (Pre) 2007

Q262.The set A = { } 1,-1,i,- i is a group with usual multiplication as binary operation. In the following which is a subgroup of A?

A{1, i} B{1, –1, i} C{1, i, –i} D{1, –1}

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EnglishUP PCS (Pre) 2007

Q263.If a, b, c are elements of a group (G, o), then (), –1 a b c is equal to

A1 1 1 a b c − − − B1 1 1 b c a − − − C1 1 1 c a b − − − D1 1 1 c o b o a − − −

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EnglishUP PCS (Pre) 2007

Q264.In a finite group having 15 elements the number of elements which are their own inverse is–

A5 B3 C1 Dnone of the above

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EnglishUP PCS (Pre) 2008

Q265.The set Z of all integers with addition operation is

Aan abelian group Bnot an abelian group Ca semi- group Dnot a semi-group

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EnglishUP PCS (Pre) 2008

Q266.The set of all vectors with respect to vector addition is

Aa semi- group Bnot an abelian group Can abelian group Dnot a semi-group

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EnglishUP PCS (Pre) 2008

Q267.If x and y are two positive rational numbers, then there exists a positive integer z such that zy>x. This property is known, as

ADensity of rational numbers BArchemedian property CEuclidem algorithm DDivision algorithm

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EnglishUP PCS (Pre) 2008

Q268.Which of the following sets with given operation is not a group?

AThe set of all integers with respect to addition. BThe setofall even integers with respect to addition. CThe set of all cube roots of unity with respect to multiplication. DThe set of all odd integers with respect to addition.

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EnglishUP PCS (Pre) 2008

Q269.Consider the following statements: I. { { { } } } 10 G 1,3,7,9 = ⊂ = ⊂ ℤ ℤ is a group with respect to multiplication of residue classes modulo 10. II. 10 ℤ ℤ is a group with respect to multiplication of residue classes modulo 10. of these statements.

AI is correct, and II is not correct BII is correct, and I is not correct Cboth I and II are correct Dboth I and II are not correct

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EnglishUP PCS (Pre) 2008

Q270.A real skew-symmetric matrix of odd order is

Ainvertible matrix Bnon-invertible matrix CHermitian matrix Dorthogonal matrix

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English(GIC) Lecture Exam, 2015

Q271.Choose the incorrect statement from the following statements: S1: Every field is an integral domain S2: Every integral domain is a field. S3: Every finite integral domain is a field S4: Every finite field is an integral domain.

AS1 BS2 CS3 DS4

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English(GIC) Lecture Exam, 2015

Q272.For a group G the factor group G/H is defined when the subgroup H is

Anormal Bcyclic Cfinite Dcommutative

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English(GIC) Lecture Exam, 2015

Q273.(Zp,+,.) is a field if

Ais a positive integer Bp is even integer Cp is odd integer Dp is a prime

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English(GIC) Lecture Exam, 2015

Q274.The number of generators of a cyclic group of order 10 is equal to

A2 B3 C4 D6

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English(GIC) Lecture Exam, 2015

Q275.The set of all positive rational numbers G form an Abelian group under the operation defined by ∀ ∈ ab a*b =, a,b G. 2 Identify element of this group is

A0 B1 C2 D3

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English(GIC) Lecture Exam, 2015/ PGT 2013

Q276.The least order of a non-abelian group is equal to

A1 B3 C4 D6

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English(GIC) Lecture Exam, 2015

Q277.In the multiplicative group G = ({1, –1, i, –i}, ●) The order of the element i is equal to

A3 B1 C4 D2

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English(GIC) Lecture Exam, 2015

Q278.An infinite cyclic group has–

Aan element of order 2 Bonly one generator Conly two generators Dinfinitely many generators

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English(GIC) Lecture Exam, 2015

Q279.If G is a finite group and o(a) denotes the order of a∈G, then for nay m∈Z.

Am/o(a ) o(a) Bm/o(a ) o(a) Cm/o(a ) o(a) DNone of the above

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English(GIC) Lecture Exam, 2015

Q280.With respect to multiplication of residue classes modulo a prime p the set of non-zero residue classes modulo p forms a commutative group of order–

Ap Bp 2 Cp + 1 Dp – 1

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