Math Chapter Wise

EnglishKVS PGT 2022

Q41.Which one of the functions ex, x3, sinx and 2x+3 is not a monotonic function on R?

Aex Bsinx C2x + 3 Dx3

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EnglishKVS PGT 2022

Q42.A and B are two sets such that n(A)=4 and the number of non - empty relations from A to B is 4095. Then n(B) is equal to:

A4 B5 C3 D2

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EnglishOAVS TGT 2022

Q43.Let f: X→ → →Y when X and Y are finite sets |X| = m, |Y| = and m > n, then there exist at least two distinct elements x1 and x2 in X such that:

A() () 1 2 x x > f f B() () 1 2 x x f < f C() () 1 2 x x = f f DNo relation

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EnglishOAVS TGT 2022

Q44.The set of natural numbers has:

Aa lower bound Ba minimal element Can upper bound Da maxima element

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EnglishRPSC PGT 2022

Q45.Which of the following is an odd function?

A[x] Bcoshx Cx sinhx Dx e 1 − + −

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EnglishRPSC PGT 2022

Q46.If A = {1,2,3,}, B = {3,4} and C = {4,5,6}, then (A × B) ∩ ∩ ∩ (A ×C) is -

A{(1,4), (1,5), (1,6)} B{(2,4), (2,5), (2,6)} C{(3,4), (3,5), (3,6)} D{(1,4), (2,4), (3,4)}

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EnglishRPSC PGT 2022

Q47.If f(x) is an odd differentiable function defined on set R such that f"(5) = –3, then f"(–5) is equal to -

A–3 B0 C3 DDoes not exist

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EnglishRPSC PGT 2022

Q48.If g(x) is the inverse function of an invertible function f(x) which is differentiable at x = –1 then g′ ′ ′ {f(–1)} is equal to -

A−1/f '( 1) Bf '(1) C−1/f '( 1) D−1/f ( 1)

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EnglishRPSC PGT 2022

Q49.Incorrect statement is -

AIf S1 and S2 are two convex sets in Rn then S1+S2 is also convex set BIf S1 and S2 are two convex sets in Rn then S1–S2 is also convex set CIf S1= a1x+b1y+c1z+d1= 0 and S2 = a2x + b2y + c2z + d2 = 0 are two planes in Rn, then (S1∪S2) is a convex set. DIf S1= a1x+b1y+c1z+d1= 0 and S2 = a2x + b2y + c2z + d2 = 0 are two planes in Rn, then (S1∩S2) is a convex set.

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EnglishRPSC PGT 2022

Q50.Under relation S, xSy iff xy is irrational ∀ x, y ∈R, then S is -

AReflexive BSymmetric CAntisymmetric DTransitive

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EnglishRPSC PGT 2022

Q51.If function f: R → R, where R is the set of real numbers and f(x) = 1 – |x – 2|, then the range of f(x) is -

A(– ∞, 2) B1 1, 2 2 − C[–2, 4) D(– ∞, 1]

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EnglishDSE TGT 2022

Q52.If A = {1,2,3,4} and B = {a,b,c} then total number of relations between A and B is ____.

A212 B214 C218 D25

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EnglishDSE TGT 2022

Q53.Which of the following is true

AA ∪ B = A – B B(A ∪ b)' = A' B' C(A ∪ b)' = A' U B' DA ∪ B = B – A

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EnglishDSE TGT 2022

Q54.The inverse function for f(x) = 3x + 5 is _____.

A1 x 5 f (x) 3 B1 2x 3 f (x) 5 C1 4x 5 f (x) 4 D1 4x 9 f (x) 15

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EnglishDSE TGT 2022

Q55.If A = {1,2,3,5} B={5,6,7} then A–B = ______

A{2,3} B{1,2,3,5} C{1,2,3} D{6,7}

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EnglishDSE TGT 2022

Q56.If A and B are two sets such that A×B = φ, then which of the following must be true?

AA= φ and B= φ BA= φ and B≠ φ CA≠ φ and B= φ DA= φ and/or B= φ

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EnglishDSE TGT 2022

Q57.Let A and B be sets with |B|=3. If there are 4096 relations from A to B, then |A|=

A5 B4 C6 D3

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EnglishDSE TGT 2022

Q58.If n(A)=38, () () n B 42,n A B 60 = ∪ () ∩ then n A B is

A10 B14 C18 D20

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EnglishDSSSB PGT 2021

Q59.If A∩ ∩ ∩B = B holds for all sets B of the universal Set S, then

AA' = B BA = S CA = B DA = φ

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EnglishDSSSB PGT 2021

Q60.Let f: R – {1} → → → R – {1} defined by f(x) = x +1 x –1', x ∈ R – {1}, then f–1 is -

A() –1 x 1 f x,x R x 1 + = ∈ + B() –1 x –1 f x,x R x 1 = ∈ + –{1} C() –1 x 1 f x,x R x –1 + = ∈ –{1} D() –1 x 1 f x,x R x –1 + = ∈

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