Math Chapter Wise

EnglishPGT 2000

Q301.Let A and B be two sets having 5 common elements. Then number of elements common to A × × ×B and B× × ×A is:

A25 B52 C0 DNone of these

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EnglishPGT 2000

Q302.Let f: R → → → R be a function defined by x m f(x), x n − = − where m≠n. Then:

Af is one - one into Bf is one-one on to Cf is many -one into Df is many- one on to

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EnglishPGT 2000

Q303.Zn = {0, ± ± ±1, ± ± ±2,.........(n–1)} fails to be a group under multiplication modulo n because:

AThere is no identity BClosure hold but not associatively CThere is no inverse for an elements of the set. DClosure property fails

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EnglishPGT 2000

Q304.In a group G if a2 =e for all a∈G. Then:

AThe order of G is only 2 BG is not abelian CG is abelian DNone of these

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EnglishPGT 2000

Q305.If (k, +......) is a division ring centuining a element Then:

Aaq = a Baq = 1 Caq–1 = a DNone of these

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EnglishPGT 2000

Q306.The dimension of the vector space of complex number over the field of Real number is:

A1 B3 C2 DNone of these

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EnglishPGT 2000/ PCS 1998

Q307.If Z denotes the set of integers and A, B, C are its subset given by: A= {x∈z:x is divisible by 2} B= {x∈z:x is divisible by 4} C= {x∈z:x is divisible by 6} Then A ∩ ∩ ∩B∩ ∩ ∩C is:

A{x∈z:x is divisible by 4} B{x∈z:x is divisible by 12} C{x∈z:x is divisible by 24} DNone of these

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EnglishPGT 2000

Q308.If f(x)= cos2 x+sec2 x, its value always will be:

Af(x)<1 Bf(x)=1 C2>f(x)>1 Df(x)≥2

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EnglishPGT 2000

Q309.If a<0 and b≥0 then:

Aab≤0 Bab≥0 Cab> 0 DNone of these

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EnglishPGT 2000

Q310.The number of rational numbers existing between two unequal rational numbers is:

A10 B1 C0 DInfinite

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EnglishPGT 2000

Q311.Let f, g: R → → → R be given by (f(x) = 2x–3 and g(x)=x2 +5, then g{f (2)} is equal to:

A2 B6 C–2 D0

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EnglishPGT 2000

Q312.If A={2,6}, B={10,9} and C={1,9} then the value of A× × ×(B∪ ∪ ∪C) is:

A{(2,1) (2,9), (2,10), (6,1), (6,9), (6, 10)} B{(2,0), (2,1), (6,0)} C{(3,4), (3,1)} D{(3,1), (3,4)}

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EnglishPGT 2000

Q313.If A={1} and B={1,2,3} then (A× × ×B) is:

A{(1,1), (1,2), (1,3)} B{(1,2), (3,1), (2,1)} C{(2,1), (1,1), (3,1)} DNone of these

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EnglishPGT 2000

Q314.If x={a,b,c,d} and y={4,5,6,7} the x∪ ∪ ∪y is:

A{a,b,c,3,7} B{a,b,4,5} C{a,b,c,d, 4,5,6,7} DNone of these

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EnglishRajasthan TGT 2016

Q315.A mapping f from a group (G,o) to a group (G',*) is group homomorphism from G to G' if

A* f-1 B∀a, b∈G Cf-1 (a*b) = f-1 Df(a o b) = f(a) *f-1

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EnglishRajasthan TGT 2016

Q316.Every subgroup with index 2 is

AQuotient group BNormal sub group CCyclic group DNone of these

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EnglishRajasthan TGT 2016

Q317.Let f be a homomorphism from a group G into a group G'. Then which of the following is not true?

Af(e)=e', where e and e' are identities of G, G' respectively Bf(a–1)=[f(a)]–1, ∀ a∈G Cf(G) is a subgroup of G' DAll of these

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EnglishRajasthan TGT 2016

Q318.The intersection of two convex sets is

Aalways a convex set Bnot always a convex set Cnot a convex set Dnull set

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EnglishRajasthan TGT 2016

Q319.If A= {1,2,3,4,5}, then the number of subsets of A which contain element 2 but not 4, is

A2 B4 C6 D8

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EnglishRajasthan TGT 2016

Q320.If R be the set of real numbers and f:R→ → →R is defined by f(x)=ex, then f is

Asurjective only Binjective only Cbijective DNeither surjective nor injective

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