Math Chapter Wise

English(GIC), 2015

Q41.If the vectors (0, 1, a), (1, a, 1) and (a, 1, 0) of a vector space V3(R) are linearly dependent, then the values of a are

A1, 2, 3 B0, i 3 ± C0, i 2 ± D0,3 2 ±

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English(GIC) 2015

Q42.If T:R3 → →R2 is a linear transformation defined by T(x, y, z)= (x+y, y+z), then nullity of T is

A0 B1 C2 D3

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English(GIC) 2015

Q43.Which of the following functions T:R2 → →R2 is a linear transformation?

AT(x1, x2)= (x1 –x2, 0) BT(x1, x2)= (x1 2, –x2) CT(x1, x2)= (1+x1, x2) DT(x1, x2)= (x1, 1+x2)

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English(GIC) 2015

Q44.The dimension of the smallest vector space is equal to

A0 B1 C2 D3

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English(GIC) 2015

Q45.If W1 and W2 are subspaces of a finite dimensional vector space V, then– Dim (W1 + W2) =

Adim w1 + dim w2 Bdim (w1∩ w2) Cdim w1 + dim w2 + dim (w1 ∩ w2) Ddim w1 + dim w2 – dim (w1 ∩ w2)

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English(GIC) 2015

Q46.Let T: V→ → →V be a linear transformation such that T2 –T+ IV = 0 (zero linear transformation), Then T–1 is equal to –

AIv + T BIv – T CIv + 2T DIv – 2T

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English(GIC) 2015

Q47.If W1 and W2 are subspaces of a vector space V, then the subspace generated by W1 ∪ ∪ ∪W2 is–

A1 2/W W B1 2/W W C1 2/W W DNone of the above

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English(GIC) 2015

Q48.The number of symmetric relations on a set with five elements is–

A25 B210 C215 D225

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English(GIC) 2015

Q49.Let f(x+y) = f(x) + f(y), x, y ∈ R and f(1) = k, then f(n) is equal to–

Ank Bkn C(2k) n D(k)2n

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English(GIC) 2015

Q50.Let f: X → → →Y be a map. If a map g: Y→ → → X such that gof = Ix and fog = Iy, then–

Af is one-one onto Bf is one-one but not onto. Cf is onto but not one-one Df is neither one-one nor onto

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English(GIC) 2015

Q51.If set X = {1,2,3}, then the relation R = {(1,1), (2,2), (3,3), (1,2), (2,1)} on set X is–

Aonly reflexive Bonly symmetric Can equivalence relation Donly transitive

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English(GIC) 2015

Q52.Given Statement A: T: R3 →R2 defined by T(a,b,c) = (a,0), is linear Statement B: T: R3 →R3 defined by T(a,b,c) = (a+1, b + c, 0) is linear Which one of the following is correct?

AA is true and B is false. BB is true and A is false CA and B both are true DA and B both are false.

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English(GIC) 2015

Q53.Let u (1, 2,k),v (3,0, 2) = − = − = − = − = − = − = − = − and w (2, 1, 5) then the value of k, for which vectors u, v, w are linearly dependent, is–

A8 B–10 C12 D–8

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English(GIC) 2015

Q54.The co-ordinates of the vector (2,1,–6) in R3 relative to the basis {(1,1,2), (3,–1,0), (2,0,–1)} of R3 (R) are given by–

A7 15 17,, 8 8 4 B7 15 17,, 8 8 4 C7 15 17,, 8 8 4 D7 15 17,, 8 8 4

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English(GIC) 2015

Q55.The matrix of the linear transformation T on R3 defined as T(x,y,z) (2y z,x 4y,3x) with respect to standard basis or R3 is–

A3 0 0 1 4 0 0 2 1 B1 4 0 0 2 1 3 0 0 C0 1 3 2 4 0 1 0 0 D0 2 1 1 4 0 3 0 0

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English(GIC) 2015

Q56.Let T be the linear transformation from R3 into R3 defined by T (x,y,z) = (x–y+2z, 2x+y, –x–2y+2z) then rank and nullity of T are respectively–

A3, 0 B0, 3 C2, 1 D1, 2

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EnglishKVS PGT 23-12-2018

Q57.Let C[0, 1] be the set of all continuous functions defined in the interval [0, 1]. If on this set + and • • • are defined, then C[0, 1] is:

Aa field Ban integral domain but not field Ca group but not a ring Da ring but not an integral domain

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EnglishKVS PGT 23-12-2018

Q58.On the number line, the solution of system of inequalities 5 x 3x 7 11 5x 1 + > − + > − + > − + > − − ≤ is represented by:

AImage/number-line option A BImage/number-line option B CImage/number-line option C DImage/number-line option D

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EnglishUP PGT-2016 (02-02-2019)

Q59.Vectors x = (1,0,1), y = (–4, a, 4) and z = (a, –1,– a) are linearly dependent in R3, if a equal to

A2 only B–2 only C± 2 both D0

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EnglishUP PGT-2016 (02-02-2019)

Q60.If T: U → → → V be a linear transformation then Kernel T is a subspace of

AU∩V BU CV DU/V

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