Math Chapter Wise

EnglishPGT 2004

Q281.If G is the additive group of residue classes modulo 10, then the order of the residu class [3] is?

A8 B10 C6 D4

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EnglishPGT 2004

Q282.Which of the following is false?

AThe intersection of two equivalence relations a set is an equivalence resation to the set BThe inverse of an equivalence relation is an equivalence relation CThe union of two equivalence relation on a set is not necessarily an equivalence DThe reflexive relation on a set is necessarily the indemnity relation on the set

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EnglishPGT 2004

Q283.If E = {1, 2, 3, 4} and F = {1, 2}, then the total number of onto functions from E to F is?

A14 B16 C9 D4

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EnglishPGT 2004

Q284.Image of the open interval (0, 1) under the continuous mapping y = x – x2 is

Aopen interval 1 0, 4 Bsemi open interval 1 0, 4 Csemi-closed interval 1 0, 4 Dclosed interval 1 0, 4

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EnglishPGT 2004

Q285.If a finite set S has n elements, then the total number of binary operations which are possible over it will be?

An B2/n C3/n D2n

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EnglishPGT 2004

Q286.The generators of the cyclic group{: } ∈ 6n n Z are

A1 and -1 B6 and -6 C6 and 1 6 DNone of the above

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EnglishPGT 2004

Q287.If g(x)= x2 + x–2 and 2 1 ()() 2 5 2, 2 gof x x x = − + = − + = − + = − + then f(x) is equal to

A2x - 3 B2x + 3 C2x2/+ 3x + 1 D2x2/- 3x - 1

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EnglishPGT 2004

Q288.Range of the function 2 (), 1 x x f x x x x + + = − ∞ < < ∞ = − ∞ < < ∞ = − ∞ < < ∞ = − ∞ < < ∞ + + is?

A(1,∞) B1 1, 2 C7 1, 5 D7 1, 3

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EnglishPGT 2004

Q289.If f ' (x) = g(x) and g' (x) = –f(x) for all values of x, and f(2) = 4 = f' (2), then f2 (16) + g2 (16) is equal to

A16 B32 C64 D128

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EnglishPGT 2004

Q290.The number of real solutions of the equation tan-1 1 2 (1) sin 1 2 x x x x π − + + + + = + + + + = + + + + = + + + + = is

Atwo Bone Czero Dinfinite

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EnglishPGT 2004

Q291.If solution of the equation 7 cos x + 5 sin x = 2k + 1 is possible, then the number of integral values of k is

A4 B8 C10 D12

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EnglishPGT 2003

Q292.Index of every element of a finit group is

Afinite BInfinite CZero DOne

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EnglishPGT 2003

Q293.Which of the following statement is false?

A() A B A B ∪ ⊂ ∪ B() A B A B ∪ ⊃ ∪ C() A B A B ∪ = ∪ D() A B A B ∪ ≠ ∪

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EnglishPGT 2003

Q294.Let { { { } }: 1 1 = ∈ − < < = ∈ − < < = ∈ − < < = ∈ − < < S x IR x and: f IR S → be defined by ((()):,, 1 x f x x IR x = ∈ + then

Af is only injective Bf is only surjective Cf is only bijective DNone of the above

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EnglishPGT 2003

Q295.Set H be a sub–group of a group G and, a b G ∈ aH is a sub–group of G if

Aa is non–empty Ba H/∉ Ca H/∈ DNone of the above

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EnglishPGT 2003

Q296.aH bH φ ∩ =

Ab aH/∉ Bb H/∉ Cb=a DNone of these

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EnglishPGT 2003

Q297.A,B,C are subsets of a universal set S then () () A C B C − ∪ − =

A() A B C ∪ − B() A C B ∪ − C() A B C ∩ ∪ DNone of these

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EnglishPGT 2003

Q298.() () − ∪ − A B B A is equal to

A() A B ∪ B() A B ∩ C() () A B A B ∪ − ∩ DNone of these

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EnglishPGT 2002

Q299.Let F: R→ → →R be defined by f(x)= 3x–4. Then f–1 (x) is:

A() x 4 3 + B−x/3 4 C3x+4 DNone of these

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EnglishPGT 2002

Q300.If a<b, then the solution of the inequation x2 +(a+b) x+ab < 0 is given by:

Aa<x<b B–b<x<–a Cx<a or x>b Dx<–b or x>–a

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