Math Chapter Wise

EnglishUP PCS (Pre) 1996

Q381.A function f is defined for all real x > 0 by f (x2) = x3. Then the value of f ′ ′ ′(4), is:

A3 B2 2 C6 D8

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EnglishUP PCS (Pre) 1996

Q382.Let f, g: ΓR → → → ΓR be given by f(x) = 2x – 3, and g(x) = x2 + 5, then g (f(2)) is equal to:

A9 B6 C25 DNone of these

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EnglishUP PCS (Pre) 1999

Q383.Let x, y be any two elements of a group (G, o). Then (x o y)–1 equals:

Ax–1/o y–1 Bx–1/o y Cx o y Dy–1/o x–1

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EnglishUP PCS (Pre) 1999

Q384.Let be a group and a be an element of order 12 in G. Then the order of a8 is:

A3 B4 C12 D24

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EnglishUP PCS (Pre) 1999

Q385.If G is the multiplicative group of non–zero residue classes modulo 7, then the order of the element residue class [4] of G is:

A2 B3 C4 D6

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EnglishUP PCS (Pre) 1999

Q386.The total number of subgroups of the group Z11 is:

A2 B211/–11 C3 D7

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EnglishUP PCS (Pre) 1999

Q387.Let X and Y be two sets such that X and Y have n elements in common. The number of elements common X× × ×Y and Y× × ×X is:

An Bn2 C2n Dn3

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EnglishUP PCS (Pre) 1999

Q388.The relation {(a, a), (a, b)} on the set {a, b, c} is:

Areflexive and transitive Breflexive and symmetric Ctransitive Dreflexive

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EnglishUP PCS (Pre) 2000

Q389.If < G, θ > be a group, then for a, b ∈ G, (a θ b)–1 is equal to:

Aa–1/θ b Bb–1/θ a Ca–1/θ b–1 Db–1/θ a–1

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EnglishUP PCS (Pre) 2000 TGT 2003

Q390.If f (x) = cos (log x), then ((()) x f f xy y + is:

A() f x f y B() 2f x f y Cf (x) f (y) D2f (x) f (y)

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EnglishUP PCS (Pre) 2000

Q391.The number of proper subsets of a set containing n elements is:

An B2n C2n–1 D2n/–2

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EnglishUP PCS (Pre) 2000 PGT 2003

Q392.If the complement of the set A be A', then (()) A B ' ∩ ∩ is equal to:

AA B/∪ BA' B'/∪ CA' B'/∩ DB'/A'

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EnglishUP PCS (Pre) 2000

Q393.A relation in the set of natural numbers N is defined as follows: a < b if a + x = b has a solution in N. Then the relation < is:

Areflexive Bsymmetric Ctransitive Dan equivalence relation

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EnglishUP PCS (Pre) 2000

Q394.The relation x y ≤ on the set Z of integrers is:

Areflexive and transitive but not symmetric Breflexive and symmetric but not transitive Csymmetric and transitive but not reflexive Dneither reflexive nor symmetric but transitive

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EnglishUP PCS (Pre) 2001

Q395.On the class of all sets define the relation '≤' by A≤B if A∪ ∪ ∪B≤B. Then the relation '≤' is:

Areflexive and symmetric but not transitive. Bsymmetric and transitive but not reflexive Creflexive and transitive but not symmetric. Dan equivalence relation.

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EnglishUP PCS (Pre) 2001

Q396.The product of any two different irrational numbers is always:

Aa rational number other than an integer. Ba primer number. Can irrational number Dnone of these is true

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EnglishUP PCS (Pre) 2002

Q397.The set (1, –1, i, –i) is a multiplicative finite group of order:

A1 B2 C3 D4

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EnglishUP PCS (Pre) 2002

Q398.If R1 = {(1, 1), (2, 2), (1, 2), (2, 1), (3, 3)} and R2 = {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3)} are two relations in the set S = (1, 2, 3), the incorrect statements is:

AR1 and R2 both are equivalent relations in S. BR1 ∩ R2 is an equivalent relation in CR1∪ R2 is an equivalent relation in D1 1 1 2 R R − − ∩ is an equivalent relations in S

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EnglishUP PCS (Pre) 2002

Q399.Total number of equivalence relations defined in the set S = {a, b, c} is:

A5 B3! C23 D33

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EnglishUP PCS (Pre) 2002

Q400.Consider the following two statement for four set A, B, C and D: I. A⊆ ⊆ ⊆B and C⊆ ⊆ ⊆D⇒ ⇒ ⇒A× × ×C⊆ ⊆ ⊆B× × ×D II. A× × ×C⊆ ⊆ ⊆B× × ×D ⇒ ⇒ ⇒A⊆ ⊆ ⊆B and C⊆ ⊆ ⊆D

ABoth I and II are correct BI is correct but II is not correct CI is not correct but II is correct DBoth I and II are incorrect

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