Math Chapter Wise

EnglishUPPSC Ashram Paddhati 2021

Q101.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

Q102.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

Q103.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

Q104.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)

Q105.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

Q106.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

Q107.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

Q108.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

Q109.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

Q110.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

Q111.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

Q112.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

Q113.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

Q114.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

Q115.If 3 1 1 f x + = x +, x x then () f 3 is equal to

A0 B1 C3 D3 3

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EnglishSection B PGT TIER-I 31.11.2014 UP PCS (Pre) 2006 UP TGT 2021, 2003

Q116.Two finite sets have m and n elements respectively. The number of subsets of the first set is greater than the number of the subsets of the second by 56. Then the value of m2 + n2 is equal to

A40 B38 C42 DNone of the above

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EnglishUP TGT 2021

Q117.For any two sets A and B, A– (A – B) equals

AA – B BB CA ∪ B DA ∩ B

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EnglishUP TGT 2021

Q118.If f(x) = tan–1 x and g(x) = sinx, then (gof) (x) is equal to

A2/x 1– x B2 x 1 x + C2 1 x x + D1

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EnglishUPPSC Ashram Paddhati 2021

Q119.The function f: R→ → →R defined by f(x) = cosx ∀ ∀ x∈R is

Aone-one, but not onto Bonto, but not one-one Cboth one-one and onto Dneither one-one nor onto

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EnglishUPPSC Ashram Paddhati 2021

Q120.If f: R→ → →R is defined by f(x) = 8x3 and g: R→ → →R is defined by g(x) = x1/3, then the value of (gof) (x) is

A8x B2x C– 2x D4x

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