Math Chapter Wise

EnglishOPSC PGT 2017

Q101.In minimal form, the function f(x,y,z) = xyz + xy′ ′ ′z + x′ ′ ′yz + x′ ′ ′y′ ′ ′z is written as:

Af = z′ Bf = z Cf = x + z Df = y + z

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EnglishUPPSC GDC 2021

Q102.The set of points in the interval [2, 4] and in interval (1, 2) are

AFinite BCardinally equivalent CCardinally unequivalent DNone of the above

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EnglishUPPSC GIC 2021

Q103.Let a relation R be defined on the set of non- zero rational number Q* by aRb. If 1 a b =, then this relation R over Q* is

Areflexive, but not symmetric and transitive Bsymmetric, but not reflexive and transitive Ctransitive, but not reflexive and symmetric Dreflexive and transitive, but not symmetric

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EnglishUPPSC GIC 2021

Q104.Let R be a relation on a set A such that R = R-1, then R is-

AReflexive BSymmetric CTransitive DNone of these

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EnglishUP Higher Asst. Prof. 2021

Q105.Let a and b belong to set S, Let R be an equivalence relation on S. Then aRb if and only if

A[a]R ≠ [b]R B[a]R ⊆ [b]R C[a]R ⊂ [b]R D[a]R = [b]R

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EnglishUPPSC Ashram Paddhati 2021

Q106.Let a relation r be defined over the set of non- zero real numbers R* by arb if a = 2 b, then over R* this relation r is

Areflexive, but not symmetric and transitive Bsymmetric, but not reflexive and transitive Ctransitive, but not reflexive and symmetric Dreflexive and transitive, but not symmetric

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EnglishUP PGT 2021

Q107.If X = (1, 2, 3, 4) then the relation R = {(1, 1), (2, 2), (3, 3), (4, 4), (3, 2), (2, 3), (2, 1), (1, 2)} defined on X is –

Areflexive symmetric and transitive Breflexive, symmetric but not transitive CSymmetric, transitive but not reflexive Dreflexive, transitive but not symmetric

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EnglishUP TGT 2021

Q108.In a group of 300 people, 150 speak Hindi and 200 can speak English. How many can speak both Hindi and English?

A40 B50 C60 D85

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EnglishUPPSC GDC 2021

Q109.Which of the following statement is/are true? I: If B is countable subset of an uncountable set A, then A – B is countable. II: Every countable union of countable sets is countable.

AOnly I BOnly II CBoth I and II DNeither I nor II

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q110.Which of the following functions is not a function of bounded variation?

A2 f(x) x x,x [–1,1] = + ∈ Bx f(x) tan,x [–1,1] 2 π = ∈ Cx f(x) sin,x [–1,1] 2 = ∈ DNone of the above

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EnglishUP PGT 2021

Q111.If A and B are two sets such that n(A) = 4, n(B) = 3 then maximum of n(A ∩ B) is –

A0 B1 C4 D3

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EnglishUP PGT 2021 LT 2018

Q112.The composite mapping fog(x) of the maps f: R → → R, f(x) = sinx; g: R → → → R, g(x) = x2, is–

Asin x + x2 B(sin x)2 Csin x2 Dx2/sin x

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EnglishUP PGT 2021

Q113.If f(x) = ax + b and f(f(f(x))) = 8x + 21 and if a, b are real numbers then a + b is equal to–

A2 B3 C5 D7

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EnglishUP PGT 2021

Q114.If N is the set of natural numbers then the mapping f: N → → → N defined by () x 1 if xisodd f x,is x –1 if xiseven + =

Aone-one and onto Bmany to one and onto Cone-one and into Dmany to one and into

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EnglishUPPSC GIC 2021

Q115.Let R be the set of real numbers, if f: R → → → R is given by f (x) = x2 + 2 and g:R → → → R is given by g (x) = x x 1 −, then the value of (gof) (x) is –

A2 x 2 x 1 + B() 2 x 2 x 1 + − C2 x 1 x 2 + D() 2 x 2 x 1 +

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q116.A binary operation on a non-empty set G is a mapping-

Afrom G to G Bfrom G × G to G Cfrom R × G to G Dfrom R × G to R, where R is the set of real numbers.

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EnglishUPPSC GIC 2021

Q117.If f(x) () 1 4 5 6 − + = ≠ − − x,x,thenf x isequalto x

A5x 6,x 4 x 4 + ≠ − + B5x 6,x 4 x 4 + ≠ − C6x 5,x 4 x 4 + ≠ − D6x 5,x 4 x 4 + ≠ − +

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EnglishUPPSC GIC 2021

Q118.If R be the set of real numbers, which of the following is one- one?

Af: R→ R, f (x) = sin x Bg: R →R, g (x) = cos x Ch: R→R, h (x) = ex Df1: R → R, f1 (x) = a, where 'a' is a constant

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EnglishUP TGT 2021

Q119.Which of the following is an open set?

A1 1 S 1,,,...... 2 3 = BN CZ D{ } S x R:1 x 3 = ∈ < <

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EnglishUP TGT 2021

Q120.If 3 1 1 f x + = x +, x x then () f 3 is equal to

A0 B1 C3 D3 3

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