Math Chapter Wise

EnglishPGT 2013

Q261.Let R be the set of all real numbers. Then f:R→ → →R is not a mapping if it is defined by:

Af (x) = log x Bf (x) = ex Cf (x) = Sin x Df (x)=x2

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EnglishPGT 2013

Q262.Let R, be the set of real number, aRb if and only if 1 2 a b − ≥ − ≥ any defined by is a relation then the relation R is:

AAn equivalence relation BSymmetric but not reflexive and transitive CReflexive and symmetric but not transitive DSymmetric and transitive but not reflexive

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EnglishPGT 2010

Q263.A relation R in the set of natural numbers defined by aRb, if a and b are Co-prime, then R is

Areflexicve and symmetric Btransitive and symmetric Creflexive and transitive Dan equivalence relation

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EnglishPGT 2010

Q264.Let R be a relation of the set of natural numbers N be defined by (()) { { } } x,y: x,y N,2x y 41 ∈ + = ∈ + = ∈ + = ∈ + = then R is

Areflexive Bsymmetric Ctransitive DNone of these

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EnglishPGT 2010

Q265.If A={x:f(x)=0} and B={x:g(x)=0}, then A∩ ∩ ∩B will be the set of roots of equation

A() () 2 2 0 f x g x + = B() f x g x C() g x f x DNone of these

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EnglishPGT 2010

Q266.Root(s) of the equation 9x2 –18|x|+5=0 belonging to the domain of function (())) (((()))) 2 log 2 = − − = − − = − − = − − f x x x is (are)–

A5 1, 3 3 − − B5 1, 3 3 C−5/3 D−1/3

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EnglishPGT 2010

Q267.A and B are two independent sets then P(Ac ∩ ∩B) is equal to

AP(A) P(B) BP(Ac/) P(B) CP(A) P(Bc/) DNone of these

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EnglishPGT 2010

Q268.If f '(x) =2x∀ ∀ ∀x and f (0)=0 then the value of f(2) will be

A16 B2 C6 D4

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EnglishPGT 2010

Q269.If f(x) = loge (loge x), then f'

A1/e Be C1 D0 Eis

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EnglishPGT 2010

Q270.If the set A has p elements and set B has q elements, then the number of elements in A×B is

Ap+q Bp+q+1 Cpq Dp2/q2

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EnglishPGT 2010

Q271.If f: R→ → →R and g: R→ → →R are two mappings defined as f(x) = x2 and g(x) = x2 +2, then

Afog≠ gof Bfog = gof Cfog is one mapping DNone of these ****

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EnglishPGT 2009, 2010

Q272.Let A, B, C be three sets, then (A – B) ∩ ∩ ∩(A – C) is equal to

A() ∪ ∪ A B C B() ∩ − A B C C() ∪ − A B C D() − ∪ A B C

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EnglishPGT 2009

Q273.In a city, 20% of the population travel by car, 50% travel by bus and 10% travel by both car and bus. Then persons travelling by car or bus is

A80% B40% C60% D70%

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EnglishPGT 2009

Q274.Following are the relations in a set of real numbers. What of them is equivalence relation?

A| | | | ⇔ = aRb a b B| | | | ⇔ ≥ aRb a b C0 ⇔ − ≥ aRb a b D0 ⇔ − ≤ aRb a b

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EnglishPGT 2005

Q275.A relation R is defined on the set of positive integers N by a R b if ab = ba. Then R is

Areflexive and symmetric, but not transitive Bnot symmetric Cnot reflexive Dan equivalence relation

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EnglishPGT 2005

Q276.If 2 (), 3 3 + = ≠ − x f x x x then 1 () − f x is equal to

A1 3 2 x − + B3 2 1 x + − C3 2 x − + D2 3 x − +

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EnglishPGT 2005

Q277.If the equation a b 1 x a x b + = − − has two roots equal in magnitude and opposite in sign, then the value of a + b is

A0 B1 C–1 DNone of these

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EnglishPGT 2005

Q278.If the roots of the equation ax2 +bx+c=0 are of the form 1 k + and 2 1 k + then the value of (a+b+c)2 is

Ab2/–4ac Bb2/–2ac C2b2/–ac DΣa2

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EnglishPGT 2005

Q279.Range of the function (()) f(x) 1/ 2 sin3x, x = − −∞ < < ∞ = − −∞ < < ∞ = − −∞ < < ∞ = − −∞ < < ∞ is

A1 1, 3 2 B1,1 3 C1 1, 3 DNone of these

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EnglishPGT 2004

Q280.If,,, a b c d are positive real number such that a + b + c + d = 2, then M = (a + b) (c + d) satisfies the following relation

A0 1 M ≤ B1 2 M ≤ C2 3 M ≤ D3 4 M ≤

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