Math Chapter Wise

EnglishUP PCS (Pre) 2002

Q341.The trace A, where 2 -1 3 A = 3 4 5 is: 4 5 6

A16 B12 C2 3 DNone of the above

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EnglishUP PCS (Pre) 2002

Q342.If 2 1 0 0 A = 0 1 0, then A is: a b -1

AUnit matrix BA CZero matrix D–A

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EnglishUP PCS (Pre) 2002

Q343.Let 3× × ×3 real matrix A be of rank 2 and 1 1 0 B = 0 1 0 Then the rank of A.B: 1 0 1

Acan not be obtained definitely unless A is given Bis equal to1 Cis equal to 2 Dis equal to 3

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EnglishUP PCS (Pre) 2002

Q344.For two similar matrices A and B the incorrect statement is

AAT = BT Btr(A)=tr(B) Cρ(A) =ρ(B) DA B =

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EnglishUP PCS (Pre) 2002

Q345.The value of the determinant a a - c a - b b a + c b - a is: c c - a a + b

Aabc B2abc C4abc D0

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EnglishUP PCS (Pre) 2002

Q346.If A is a square matrix of order n and A = ∆, then the value of -5A is equal to:

A–5∆ B5∆ C–(5)n/∆ D() 2 n 5 − ∆

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EnglishUP PCS (Pre) 2002

Q347.The value of the determinant x + y z 1 y + z x 1 z + x y 1 is

A(x+y)(y+z)(z+x) Bxyz C1 D0

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EnglishUP PCS (Pre) 2002

Q348.If the determinant of an n-square matrix A is 3 and determinant of Adjoint of A is 243, then n is equal to

A4 B7 C5 D6

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EnglishUP PCS (Pre) 2002

Q349.The value of the determinant log6 log8 log10 log9 log12 log15 log12 log16 log20 is

A0 Blog 12 Clog 36 Dnone of the above

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EnglishUP PCS (Pre) 2003

Q350.If cos sin A sin cos which one of the following is not true

AA A A A BA A A Cn/(A ) A D1 A A − α =

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EnglishUP PCS (Pre) 2003

Q351.The inverse matrix of the matrix A exists if A is a square matrix and

AA = 0 BA ≠ 0 Cadj A ≠ 0 Ddet A ≠ 0

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EnglishUP PCS (Pre) 2003

Q352.Let a square matrix A be such that A, A2, A3 are non-zero matrix but A4 is zero matrix. Then (I – A)–1 is

A2 3/A A A B2 I A A + + C2 3 I A A + + D2 3 I A A A + + +

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EnglishUP PCS (Pre) 2003

Q353.The rank of the matrix 1 2 4 2 4 7 3 6 10 is:

A1 B2 C3 Dnone of the above

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EnglishUP PCS (Pre) 2003

Q354.If 1 2 3 A 1 3 4 1 4 3 then AdjA is equal to:

A– 4 B4 C– 2 D2

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EnglishUP PCS (Pre) 2003

Q355.The system of equations 3x y x 1, 2x y z 2, x 2y z 1 − + λ = + + = + − λ = − − + λ = + + = + − λ = − − + λ = + + = + − λ = − − + λ = + + = + − λ = − Has unique solution if

Aanyvalue B7/2 C7/2 D7/2

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EnglishUP PCS (Pre) 2003

Q356.If A and B are square matrices of the same order, which of the following is true

A2 2 2/(A B) A 2A.B B B2 2 (A B).(A B) A B + − = − C2 2/(A B).(A B) A B D(A B).(A B) (A B).(A B) + − + − + 2 2 2A 2B = −

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EnglishUP PCS (Pre) 2004

Q357.If 1 3 2 2 5 4 2 1 − λ is a singular matrix, then value of λ is–

A8 B4 C–4 D–8

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EnglishUP PCS (Pre) 2004

Q358.If A= 2 1 1 2 − and, A2 –4A–αI then value of α is

A1/3 B-3 C1/3 D3

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EnglishUP PCS (Pre) 2004

Q359.If 2 3 5 2 then 19A–1 is -

A1 A 2 B2A C3A DA

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EnglishUP PCS (Pre) 2004 & 2007

Q360.If A and B are square matrices of order 3 such that det A = -1 and det B = 3, then det (3AB) is equal to –

A–9 B–81 C–27 D–243

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