Math Chapter Wise

EnglishUP PCS (Pre) 2007

Q421.Consider the following two statements for four non-empty sets A, B, C and D I. (A∩ ∩ ∩B) × × × (C∩ ∩ ∩D) = (A× × ×C) ∩ ∩ ∩ (B× × ×D) II. (A ∪ ∪ ∪ B) × × × (C ∪ ∪ ∪D) = (A × × × C) ∪ ∪ ∪ (B × × × D)

Aboth I and II are correct. BI is correct, but II is not correct. CII is correct, but I is not correct. Dboth I and II are incorrect.

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EnglishUP PCS (Pre) 2007

Q422.If A = {x: x2 + 6x – 7 =0 x ∈ IR} and B = {x: x2 + 9x + 14 = 0 x ∈ IR}, then the number of elements in the intersection set of power set of A and power set of B is

A2 B1 C0 Dnone of these

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EnglishUP PCS (Pre) 2007

Q423.Number of equivalance relation defined in the sets S = {a, b, c, d) is

A42 B42/– 1 C4 D5

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EnglishUP PCS (Pre) 2008

Q424.Let an equivalence relation R defined in the set S = {1, 2, 3, 4} be given by R = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)}. Then the number of equivalence classes of S determined by R is:

A1 B2 C3 D4

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EnglishUP PCS (Pre) 2008

Q425.The power set P(X) of a set X is a group under the law of composition of:

Adifference of sets '∼' Bsymmetric difference '∆' Cunion '∪' Dintersection '∩'

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EnglishUP PCS (Pre) 2008

Q426.Which one in the following relation in the set of real numbers is an equivalence relation?

Aa R b if a b = Ba R b if a b/≥ Ca R b if a b 0/− ≥ Da R b if a b 0/− ≤

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EnglishUP PCS (Pre) 2009

Q427.If f(x+1)+f(x–1) = 2 f(x) and f(0) = 0, then for n∈ ΙN the value of (n) is

An f(1) B(f(1))2 Cn Dn f(1) 2

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EnglishUP PCS (Pre) 2009

Q428.The relation defined by "is perpendicular to" in the set of straight lines in a plane, is

Areflexive Btransitive Csymmetric DNone of the above

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EnglishUP PCS (Pre) 2009

Q429.A relation R on a set A is symmetric, if and only if

AR–1/⊂R BR⊂ R–1 CR= R–1 DNone of the above

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EnglishUP PCS (Pre) 2009

Q430.The number of symmetric relations on A set with 5 elements is

A25 B210 C215 D225

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EnglishUP PCS (Pre) 2009

Q431.If X and Y be two non-empty sets then X∩ ∩ ∩(Y∪ ∪ ∪X)' equals

AX BY Cφ D(X∩Y)'

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EnglishUP PCS (Pre) 2009

Q432.If A={(x,y):y = e', x∈ R}and B={(x,y):y = x, x∈ R}, then

AA⊂B BB⊂C CA∩B=φ DA∪B=A

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EnglishUP PCS (Pre) 2009

Q433.Let be the set of integers. Then the function f: → × ℤ ℤ ℤ ℤ ℤ ℤ ℤ ℤ ℤ ℤ ℤ ℤ defined by f(x)= (x-1, 1) x ∀ ∈ ∀ ∈ ℤ ℤ ℤ is

Aone-one onto Bone-one into Cmany one onto Dmany one onto

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EnglishUP PCS (Pre) 2009

Q434.If 1 f(x) g(x) f[f(x)] 1 x = − and h(x)=f[g(x)], then f(x). g(x). h(x) is equal to

A–1 B0 C1 D2

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EnglishUP PCS (Pre) 2009

Q435.For three sets A, B and C the correct statement is

AA∪B=A∪C⇒B=C BA∩B=A∩C⇒B=C CA∪B=A∪C and A∩B=A∩C ⇒B=C DA–B=A–C⇒B=C

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EnglishUP PCS (Pre) 2009

Q436.If R is a symmetric relation in a set, then the incorrect statement is

AR∪R–1 =R BR∩R–1 =R–1 CRοR–1/is symmetric DRοR–1 =R

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EnglishUP PCS (Pre) 2009

Q437.Let R = {(1, 2), (2, 3)} be a relation in a set S = {1, 2, 3}. Then how many number of elements of S× × ×S are added to R make the enlarged relation an equivalence relation in the set S?

A9 B7 C4 D3

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EnglishUP PCS (Pre) 2009

Q438.The number of reflexive relations on a set containing 4 elements is

A24 B28 C212 Dnone of the above

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EnglishUP PCS (Pre) 2009

Q439.If 2 z 6, z − = then the greatest value of z is

A36 B11 C3 11 D3 11/+

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English(GIC) Lecturer exam, 2015

Q440.The relation S in the set R of real numbers defined by S = {(a, b):a, b∈R and a≤b3 is

Areflexive Bsymmetric Ctransitive DNone of the above

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