Math Chapter Wise

EnglishUKPSC GIC 2018

Q121.A pair of values of α and β for which the matrix A = 1 2 0 2 1 3 6 α β is invertible, is

Aα = 1 3. β = 6 Bα = 1, β = 4 Cα = 1, β = 5 Dα = 1 3, β = 4

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EnglishUKPSC GIC 2018

Q122.For matrices A = 1 4 -2 1 7 -6 0 -k k, B = k -2k -10 -k k 4 -k k 3, k ≠ 0 Which of the following is true?

AA–1 = –kB BA–1 = kB CA = kB–1 DA = –kB–1

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EnglishUKPSC GIC 2018

Q123.The value of the determinant 1 1 1 1 α β γ δ β + γ + δ + α +β δ α β γ is

Aα + β + γ + δ B1+ α + β + γ + δ C0 Dαβγδ

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EnglishUKPSC GIC 2018

Q124.If A = 3 1 7 5, the value of x and y, such that A2 = yA – xI, are respectively

A6, 8 B8, 6 C6, 6 D8, 8

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EnglishUKPSC GIC 2018

Q125.A is a square matrix such that A2 = I, then (A– I)3 +(A + I)3 – 7A:

AA BI–A CI+A D3A

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EnglishUKPSC GIC 2018

Q126.The diagonal elements of a skew-symmetric matrix are

A1 B–1 C0 Di

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EnglishUKPSC GIC 2018

Q127.In a matrix A = ij 3×3 a, if 11 12 13 a = 2,a = 5,a = –2 and A11 = 5, A12 = 4, A13 = 4, then determinant A is

A–22 B22 C18 D–18

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q128.Which of the given statements is true?

AEvery square matrix is diagonalizable. BThe product of diagonalizable matrices is also diagonalizable. CThe sum of diagonalizable matrices is also diagonalizable. DIf A is a diagonalizable matrix, then AT is diagonalizable.

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q129.Consider the subset: S= {[3,1,–1], [2,2,–1], [–5,–2,2], [1,3,1]} of 3. If A is the matrix having columns as vectors of set S, then: S= {[3,1,–1], [2,2,–1], [–5,–2,2], [1,3,1]} of 3.

Athe set S is linearly independent and the matrix A has rank 2. Bthe set S is linearly dependent and the matrix A has rank 2. Cthe set S is linearly dependent and the matrix A has rank 3. Dthe set S is linearly independent and the matrix A has rank 3.

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q130.Let A be nonsingular diagonalizable matrix of order 3 with eigenvalues λ1, λ2, λ3. Then A-1 diagonalizable if.

A1 2 3 1, 2, 0 λ = λ = λ = B1 2 3 2, 0, 0 λ = λ = λ = C1 2 3 0, 0, 0 λ = λ = λ = D1 2 3 2, 1, 3 λ = λ = λ =

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EnglishLT 2018

Q131.The value of the determinant 43 1 6 35 7 4 17 3 2 is

A0 B56 C756 D964

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EnglishLT 2018

Q132.The characteristic roots of the matrix 5 4 A 1 2 = are

A1, 6 B–1, 6 C–1, –6 D1, –6

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EnglishLT 2018

Q133.For square matrices A and B, which of the following is true?

A(AB)'=A'B' B(A+B)' = A'+B' C(AB)–1 =A–1 B–1 D(A+B)–1 =A–1 +B–1

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EnglishLT 2018

Q134.The characteristic roots of a Hermitian matrix are

Areal Bpurely imaginary Ccomplex Dnone of the above

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EnglishLT 2018

Q135.Every square matrix can be expressed as

Aa Hermitian matrix Ba skew-symmetric matrix Csum of symmetric and skew-symmetric matrices DNone of the above

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EnglishLT 2018

Q136.Every diagonal element of a skew-symmetric matrix is

Azero Bunity Cnon-zero Dpurely imaginary

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EnglishLT 2018

Q137.The eigen values of the matrix a h g A 0 b 0 0 c c = are

Aa, h, g Ba, g, c Ca, h, c Da, b, c

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EnglishLT 2018

Q138.A square matrix P satisfies P2 = I – P. If Pn = 5I – 8P, then n is equal to

A4 B5 C6 D7

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EnglishLT 2018

Q139.If A is a 3× × ×3 non-singular matirx, then det (adj A) is equal to

A2 det A B3 det A C(det A)2 D(det A)3

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EnglishLT 2018

Q140.If ((()) 2 1 x x f x x x 1 x 1 x = then the value of (((()))) 3 f 3 is

A–6 B6 C4 D–4

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