Math Chapter Wise

EnglishOAVS TGT 2022

Q41.Which of the following is the inconsistent equation to 2x + 3y - 5 = 0?

A4x + 6y -11 = 0 B4x - 6y -11 = 0 Cx + 3y = 5 D2x + y - 5 = 0

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EnglishOAVS TGT 2022

Q42.If the system of equations λx + y + z =0, x + λy + z = 0, x + y + λz =0 have non-zero solutions, then λ =?

A1 or –2 B–2 C4 D1

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EnglishOAVS TGT 2022

Q43.The solution of the system of equations 2x 5y 6 xy + = and 4x 5y 3 0 xy − + = is:

Ax = 1, y = 2 Bx = 1, y = –2 Cx = –1, y = –2 Dx = –1, y = 2

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EnglishOAVS TGT 2022

Q44.The rank of 1 2 3 2 1 0 0 1 2 is:

A0 B3 C2 D1

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EnglishOAVS TGT 2022

Q45.The standard basis of V3 (F) is:

A{(1, 1, 0), (0, 1, 0), (0, 0, 1)} B{(1, 0, 0), (0, 1, 0), (0, 1, 1)} C{(1, 0, 0), (0, 1, 0), (0, 0, 1)} D{(1, 0, 0), (1, 1, 0), (0, 0, 1)}

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EnglishOAVS TGT 2022

Q46.If one equation of a pair of dependent linear equations is –5x + 7y = 2, then the second equation would be:

A–10x – 14y + 4 = 0 B10x + 14y + 4 = 0 C–10x +14y + 4 = 0 D10x –14y = –4

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EnglishOAVS TGT 2022

Q47.A subset of a vector space containing zero vector is:

Alinearly independent Beither linearly dependent or linearly independent Cneither dependent nor linearly independent Dlinearly dependent

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EnglishRPSC PGT 2022

Q48.If S and T are subspaces of a vector space, V (F), then which of the following relation is not correct?

AS +T = L () S T ∪ BL (S ∪ T) = L (S) + L (T) CS ⊂ L (T) ⇔ L (S) ⊂ L (T) DL [L (T)] = L [T]

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EnglishRPSC PGT 2022

Q49.It t is a linear transformation defined from a vector space V(F) to V'(F), where V (F) is finite dimensional, then which of the following is true?

Arank (t) + dim (v) = nullity (t) Brank (t) + nullity (t) = dim (v) Cnullity (t) + dim (v) = rank (t) Dnullity (t) – dim (v) = rank (t)

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EnglishRPSC PGT 2022

Q50.If P is an invertible matrix, then incorrect statement is

AIf P is a diagonal matrix, then P–1 is also diagonal matrix. BIf P is a symmetric matrix, then P–1 will also be symmetric. CIf P is scalar matrix, then P–1 will also be scalar. DIf |P| = 6, then |P–1 | = 6

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EnglishRPSC PGT 2022

Q51.If P be a 3×3 matrix whose determinant value is 10, then the determinant value of the matrix –3P is -

A270 B–270 C207 D–207

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EnglishRPSC PGT 2022

Q52.t: R2 → R3, t (a,b) = (a + b, a – b, b) ∀ (a, b) ∈R2 is a linear transformation, then ker(t) is equal to -

A{(1, 0)} B{(1,–1)} C{(0,0)} D{(0,0,0)}

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EnglishRPSC PGT 2022

Q53.If A = (aij)2×2 and aij = ≠ 2 2 i + j;i j i – j;i = j, then A–1 is equal to -

A0 5/5 0 B1 0 5 1 0 5 C0 –5/–5 0 D1 0 5 1 0 5

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EnglishRPSC PGT 2022

Q54.Value of the determinant – x x x y y y z z z log x log y log z log x log y log z log x log y log z is-

A3 B1 C–1 D0

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EnglishRPSC PGT 2022

Q55.One of the eigen value of non singular matrix A3 is 7, and its determinant value is also 7, then the eigen value of Adj A is-

A49 B7 C1 DZero

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EnglishRPSC PGT 2022

Q56.If A = 1 2 2 1 2 1 –2 3 x 2 y is an orthogonal matrix, then (x +y) is equal to -

A9 B–9 C3 D–3

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EnglishDSSSB PGT 2021

Q57.If A is an idempotent matrix and A+B = I, then B is:

AA involuntary matrix BAn idempotent matrix CA null matrix DA nilpotent matrix

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EnglishDSSSB PGT 2021

Q58.If A and B are idempotent matrices of same order, then AB is idempotent matrix if and only if:

AAB = 0 BAB + BA = 0 CBA = 0 DAB = BA

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EnglishDSSSB PGT 2021

Q59.If M = –5 –8 0 3 5 0 1 2 –1, then M is -

AInvoluntary matrix BPeriodic matrix CNilpotent matrix DOrthogonal matrix

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EnglishDSSSB PGT 2021

Q60.If A and B are orthogonal matrices and det(A) + det(B) = 0 then (A+B) is a

ASingular BIdempotent CNon-singular DOrthogonal

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