Math Chapter Wise

EnglishDSSSB PGT 2021

Q61.A, B, C are sub-sets of the universal set S and if A ∪ ∪ ∪ B = A ∪ ∪ ∪ C and A'∪ ∪ ∪ B = A' ∪ ∪ ∪ C then -

AB = C BA = B CB' = C DA' = B

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EnglishDSSSB PGT 2021

Q62.A relation ρ is defined on a set N by "aρb if and only if a is divisible by b" for all a, b ∈ N. Then ρ is -

AReflexive and transitive BReflexive and systematic CEquivalence DSystematic and transitive

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EnglishDSSSB PGT 2021

Q63.Let f: A → → → B and g: B → → → C be both injective mapping such that gof: A → → → C is injective, then

Ag is injective but f need not be Bf is injective but g need not be Cboth f and g are injective Dboth f and g are not injective

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EnglishDSSSB PGT 2021

Q64.The function f: R → → 1 1 –,, 2 2 defined as f(x) = 2 x 1+ x, is -

ASurjective but not injective BInjective but not surjective CNeither injective nor surjective DInvertible

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EnglishDSSSB PGT 2021

Q65.If A, B, C, are three sets, then the Set A – (B – C) is equal to

A(A–B)∪(A∩C) B(A–B)∩C C(A–B)∩(B–C) DA ∩ (B–C)

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EnglishDSSSB PGT 2021

Q66.The function f: [0, 3] → → → [1, 29] defined by f(x) = 2x3 - 15x2 + 36x + 1, is

AOne-one but not onto BOne-one and onto COnto but not One-one DNeither One-one nor onto

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EnglishDSSSB PGT 2021

Q67.Let A be a set of n elements and B be a set of m elements, then the total number of mapping from A to B is

Anm Bmn Cn/Cm Dmn

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EnglishDSSSB PGT 2021

Q68.Let A be a set of 4 elements and B be a set of 3 elements, then the total number of surjective mappings from A to B is

A36 B12 C72 D144

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EnglishDSSSB PGT 2021

Q69.If f: R → → → R be defined by f(x) = x2, x∈R then f is

ABijective BInjective CSurjective DNot Bijective

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EnglishDSSSB PGT 2021

Q70.If f: A → → → B be a mapping and P ⊂ ⊂ ⊂ A, then which of the following is true?

Aff–1(P) ⊂ P ff–1(P) = P if f is injective Bff–1(P) = P if f is injective Cf–1(Pc/)⊂[f–1(P)]c D[f(P)c ⊂ f(Pc)]

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EnglishDSSSB PGT 2021

Q71.Which one of the following in not a convex set?

AX = {(x, y): x ≥ 3, y ≤ 5} BX = {(x, y): x2 + y2 < 9} CX = {(x, y): 4 ≤ x2 + y2 ≤ 9} DX = {(x, y): x2 + y2 ≤ 9}

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EnglishDSE TGT 2019

Q72.If f: ℝ ℝ ℝ → ℝ ℝ ℝ, g: ℝ ℝ ℝ → ℝ ℝ ℝ are defined by f(x) = 4x – 1 and g(x) = x2 + 2, then fof(x) =

A16x – 5 B27 Ca2/+ 2 D16x2/– 8x + 3

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EnglishDSE TGT 2019

Q73.A set S has 3 elements. The number of elements in power set of S is

A64 B8 C24 D256

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EnglishDSE TGT 2019

Q74.If A and B are countable sets, then A × B is

AUncountable BInfinite CFinite DCountable

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EnglishOAVS TGT 2021

Q75.In a class of 60 students, 30 students passed in Mathematics and 40 passed in Science. At least how many students passed in both Mathematics and Science?

A10 B9 C11 D0

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EnglishOAVS TGT 2019

Q76.The domain of 2 x x f(x) 2sin((1 x)) e 2 is:

Ax > 1 BR CR – {0} D–1 ≤ x ≤ 1

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EnglishOAVS TGT 2019

Q77.If 1 f(x) 1, x then the value of 1 f f x is:

Ax/x 1 Bx Cx 2/x 1 Dx/x 1

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EnglishDSE TGT 2019

Q78.Let E ⊆ ⊆ ⊆ℝ and f, g, h are the functions from E into ℝ. Suppose a ∈ E and f, g, h are continuous at 'a', then for h(

Abijection Bnot continuous at a Csurjection Dcontinuous at a

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EnglishOAVS TGT 2018

Q79.For two different finite sets A and B, Inclusion- Exclusion relation states that:

An(AUB) n(A) n(B) n(A B) ∩ Bn(AUB) n(A) n(B) n(A B) ∩ Cn(AUB) n(A) n(B) n(A B) ∩ Dn(AUB) n(A) n(B) n(A B) ∩

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EnglishOAVS TGT 2017

Q80.A B B – A _____. + = ∩

AB BA CAUB Dφ

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