Math Chapter Wise

EnglishKVS PGT 2023

Q21.A matrix A = α β γ −α is such that A2 = I, then:

A1 + α2 + βγ = 0 B1 – α2 + βγ = 0 C1 – α2 – βγ = 0 D1 + α2 – βγ = 0

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EnglishKVS PGT 2023

Q22.If matrix A = 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 2, then Rank of the matrix (A - I) is:

A4 B2 C3 D1

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EnglishKVS PGT 2023

Q23.If matrix A = 2 5 5 0 3 1 0 1 3 −, then Eigen value of the matrix A is:

A{2} B{1, 4} C{2, 4} D{1, 2}

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EnglishKVS PGT 2023

Q24.The characteristic polynomial of matrix A = 1 1 1 1 1 1 1 1 1 − − − − is:

A–λ3/+ 2λ2 Bλ3/–3λ2 Cλ3 – 3λ2 + 4λ Dλ3/+ 3λ2

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EnglishKVS PGT 2023

Q25.If A is a square matrix, then which among the following is/are true? (i) A + A' is a symmetric matrix. (ii) A - A' is a symmetric matrix. (iii) AA' is a skew symmetric matrix.

AOnly (i) is true. BOnly (ii) is true. COnly (iii) is true. D(i) and (ii) are true.

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EnglishNVS PGT 2022

Q26.If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 – 7A equals:

AA BI – A CI + A D3A

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EnglishNVS PGT 2022

Q27.Let A be a 3 × 3 complex Hermitian matrix which is unitary. Then the distinct eigen values of A are:

A± i B1 ± i C± 1 D() 1 1 i 2 ±

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EnglishNVS PGT 2022

Q28.Given 2x−y+2z=2 x − 2y + z = − 4 x + y +λz = 4 Then the value of λ such that the given system of equations has no solution is:

A3 B–3 C0 D1

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EnglishNVS PGT 2022

Q29.If the order of matrix A = 4 × 3, order of matrix B = 4 × 5 and order of matrix C = 7 × 3, then the order of (At × B)t × Ct is:

A4×5 B3×7 C4×3 D5×7

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EnglishNVS PGT 2022

Q30.If A and B are square matrices of order 3 such that det A = −1 and det B = 3, then is:

A–9 B–27 C–81 D81

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EnglishNVS PGT 2022

Q31.Given: Statement A: T: R3 → →R3 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, B is false. BB is true, A is false. CA and B both are true. DA and B both are false.

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EnglishNVS PGT 2022

Q32.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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EnglishNVS PGT 2022

Q33.If the vectors (0, 1, x), (x, 1, 0) and (1, x, 1) of vector space R3 (R) are linearly independent, then x will be:

A2/± B+1 C–1 D±2

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EnglishKVS PGT 2022

Q34.If the value of 2 x 2 x x x 6 x x 6 = ax4 + bx3 + cx2 + dx + e, then value of a + b + c + d is

A2 B24 C26 D0

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EnglishKVS PGT 2022

Q35.The system of linear equations x + y + z = 2 2x + y − z = 3 3x + 2y + kz = 4 will have unique solution if:

Ak ≠ 0 Bk = 0 C−1 < k < 1 D−2 < k < 2

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EnglishKVS PGT 2022

Q36.If A = 1 2 1 0 andB 3 5 0 2 = − are two matrices and X is a matrix such that A = BX, then matrix X is:

A5 4 1 3 2 11 − − − B2 4 1 3 5 2 − C−2 4/3 5 D1 4 1 3 10 2 −

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EnglishKVS PGT 2022

Q37.If A = a 0 0 0 a 0 0 0 a, the value of |Adj A| is:

Aa27 Ba9 Ca6 Da3

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EnglishKVS PGT 2022

Q38.The point (3, 4) undergoes the following two successive transformations. (i) Reflection along the line y=x (ii) Translation through a distance of 2 units along the negative x-axis The final position of the point is at:

A(3, 2) B(2, 3) C(6, 3) D7 7, 2 2

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EnglishKVS PGT 2022

Q39.Rank of 4×4 matrix 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 − − − is:

A1 B2 C3 D4

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EnglishKVS PGT 2022

Q40.The characteristic polynomial of matrix A = 1 2 2 2 1 2 2 2 1 is:

Aλ3 −3λ2 +9λ−5 Bλ3 +3λ2 −9λ+5 Cλ3 −3λ2 −9λ−5 Dλ3 +3λ2 −9λ+5

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