Math Chapter Wise

EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q221.Choose the correct set of function which are linearly dependent.

A2 2 {sin x,sin x,cos x} B{cos x,sin x,tan x} C2 2 {cos2x,sin x,cos x} D{cos2x,sin x,cosx}

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q222.Which of the following is a subspace of the vector space 3 IR?

A3 {(x,y,z) IR: x 1 0, y 0} B3 {(x, y,z) IR: x 0, y 0} C3 {(x, y,z) IR: 2x 3y 4z 3 0,z 0} D3 {(x, y,z) IR: x 2y 0,2x 3z 0}

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q223.If 14 = 172 (modx), then x can take the value–

A38 B54 C66 D79

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q224.The least positive integer to which 79×101×125 is congruent mod 11 is–

A5 B6 C4 D8

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q225.If 7x = 13(mod 11) then the value of x is–

A3 B–2 C5 DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q226.The supremum of the set { { { } } 2 A P Q:P 2 = ∈ < = ∈ < = ∈ < = ∈ < in Q is

A2 B2 Cexists, but not 2 Ddoes not exist

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q227.lf x 3 10,then + ≥ + ≥ –

A() x 13,7 ∈ − B[ ] x 13,7 ∈ − C(][) x, 13 7, ∈ −∞ − ∞ DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q228.Let 2 A X: X 5X 6 0 ℝ ℝ The infimum and supremum of A are–

A1 and 2 B2 and 3 C2 and 5 Dnone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q229.lf x 2 A x R: 4, x 1 + = ∈ < = ∈ < = ∈ < = ∈ < − then–

A() () x,1 2, ∈ −∞ ∪ ∞ B() x, ∈ −∞ ∞ C() () x,2 2, ∈ −∞ ∪ ∞ Dnone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q230.The limit points of the following subset of (()) n 1 R 1 1: n N is n + − ∈ + − ∈ + − ∈ + − ∈ –

A0 B1 Cinfinitely many points Dnone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q231.Which of the following is uncountable set?

AThe set of all algebraic numbers BThe set of all rational numbers CThe set of all subsets of natural numbers DEvery subset of a countable set

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q232.lf the set A and B are defined by x A x,y: y e,x R and B x,y: y x,x R then –

AA B/⊆ BB A/⊆ CA B A ∪ = DA B ∩ = φ

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q233.Every non empty set of real number which is bounded below has–

Aa supremum Ban infimum Cneither infimum nor supremum Dnone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q234.If x and y are real number with x>0 then there exists a positive integer such that nx is–

Ay/< By/> Cy = DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q235.The union of any collection of open set–

Aclosed only Bboth open and closed Copen only Dneither open nor closed

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q236.The total number of injective functions from a set having m elements to a set having n elements where m>n, is equal to –

A0 B() n! n m! − C() m! m n! − DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q237.For any two real number, an operation defined by a*b=1+ab is–

Aneither commutative nor associative Bcommutative but not associative Cboth commutative and associative Dassociative but not commutative

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q238.Which of the following is the empty set?

A{x x is a real number and x2 –1 = 0} B{x x is a real number and x2 +1 = 0} C{x x is a real number and x2 –9 = 0} D{x x is a real number and x2 = x +2}

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q239.lf ((()) f x sin x cos x, = + = + ((())) 2 g x x 1 = − then ((()) (()) g f x is invertible in the domain–

A0, 2 π B, 4 4 −π C, 2 2 −π D[ ] 0,π

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q240.lf ((()) g x 1 x = − = − and ((()) x h x x 1 = − the (()) (()) (()) (()) g h x h g x is–

A() h x g x B−1/x C() g x h x D()2 x 1 x −

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