Math Chapter Wise

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

Q221.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

Q222.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

Q223.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

Q224.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

Q225.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

Q226.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

Q227.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

Q228.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

Q229.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

Q230.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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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q231.A function f(x) is linear and has a value of 29 at x= –2 and 39 at x=3, Then value of f(x)atx = 5 is

A59 B45 C43 D35

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

Q232.Let function f: R R → → be defined by ((()) f x 2x sin x = + = + for all x R, ∈ Then f is–

Abijective Bone-one but not onto Conto but not one-one Dneither one-one nor onto

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

Q233.The domain of ((())) 2 f x 16 x = − = − is–

AR B[–4, 4] C[0, ∞) D[0, 4)

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

Q234.lf f: R R → → is defined by ((()) f x x, = then–

A() 1 1 f x x − = B() 1 f x x − = − C() 1 1 f x x − = Dthe function () 1 f x − does not exist

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

Q235.ln the set { { { } } A 1,2,3,4,5, = a relation R is defined by ((()) { R X,Y: X,Y A = ∈ = ∈ and } } X Y, < Then R is-

Areflexive Bsymmetric Ctransitive Dnone of these

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

Q236.Let A = {p, q, r, s} B= {1, 2, 3}. Then which of the following relations from A to B is not a function?

A1 R {(p,1),(q,2),(r,1),(s,2)} = B2 R {(p,1),(q,1),(r,1),(s,1)} = C3 R {(p,1),(q,1),(p,2),(s,3)} = D4 R {(p,2),(q,3),(r,2),(s,2)} =

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EnglishTGT 2003

Q237.The domain of the function f(x)= 2 (2 2x x) − − − − is

A–1– 3 ≤ x≤ –1+ 3 B3/− ≤ x ≤ 3 C–2 ≤ x ≤ 2 D–2+ 3 ≤ x ≤ – 3

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EnglishTGT 2003

Q238.The domain of the function 1 f(x) x x = − is

A(–∞, 0) B(∞, 0] C(–∞, –1) D(–∞,∞)

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EnglishTGT 2001

Q239.Coefficients of odd power in the expansion of (1+x) 50 is the sum of?

A0 B249 C250 D251

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EnglishTGT 2001

Q240.If { { { } } 1,2,3,4,5,6 ∪ = ∪ = and { { { } } A 1,3,6, = { { } } 5,6 = B then ((()) A B ' ∩ ∩ will be:

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

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