Math Chapter Wise

EnglishUP PCS (Pre) 2004

Q361.If A and B are two square matrices such that AB = A and BA = B, then

Aboth A and B are idempotent Bonly A is idempotent Conly B is idempotent Dneither A nor B is idempotent

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EnglishUP PCS (Pre) 2004

Q362.If 1 2 A 3 4, 2 3 B 4 5 and 4A–3B+C=0 then C=

A2 1/0 1 B2 1/0 1 C2 1/0 1 DNone of above

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EnglishUP PCS (Pre) 2004

Q363.Equations x y z 6, x 2y 3z 10 x 2y z Have infinite number of solutions, if

A3, 10 B3, is any real number C3, 10 Dnone of the above

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EnglishUP PCS (Pre) 2004

Q364.For what value of λ, the equations x y z 1, x y z, 3 x y z Do not have a solution

A-2 B–1 C0 D1

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EnglishUP PCS (Pre) 2004

Q365.The system of equations: 2x y z a, x 2y z b, x y 2z c + − = + − = + − = + − = is consistent if–

Aa b c 0 Ba b c 0 Ca b c 0 Da b c 0

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EnglishUP PCS (Pre) 2005

Q366.The rule A2 –B2 =(A+B)(A–B) always holds for two matrices A and B if

AA, B are square matrices BAB = BA CA, B are square matrices and AB=BA DA, B are of the same rank

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EnglishUP PCS (Pre) 2005

Q367.For 3× × ×3 matrix A the incorrect statement isc -

A2 adjA A = B() adj adjA = A A CA.adjA = A I Dadj(2A) = 4(adjA)

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EnglishUP PCS (Pre) 2005

Q368.If A is a real skew-symmetric matrix of order 3× × ×3, then the matrix A is -

Aorthogonal BHermitian Csingular Dnon-singular

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EnglishUP PCS (Pre) 2006

Q369.One of the roots of the equation 2 x 3 3 3 4 x 5 0 3 5 4 x − − = − is

A2 B–2 C–1 D1

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EnglishUP PCS (Pre) 2006

Q370.If (((()))) (((()))) ∆ k 1 k 1 k 1 k m m m 2 2 3 4 5 2 1 3 1 5 1 − − − − − − − − − − − − = − − − − − − − − − − − − then the value of ∆ m k k 1 = ∑ ∑ is equal to:

A1 B0 C–1 DNone of the above

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EnglishUP PCS (Pre) 2006

Q371.If A and B are 5× × ×5 matrices such that rank

A2 B3 C5 D5

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EnglishUP PCS (Pre) 2006

Q372.If A is a square matrix of order n and λ is a scalar, then adj (λ A) is equal to:

Aλn–1/adj A Bλn/Adj A CλAdj A D|λ|n–1/AdjA

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EnglishUP PCS (Pre) 2006

Q373.The rank of the matrix 1 2 3 2 3 4 3 4 5 is

A3 B3 or 1 C1 D2

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EnglishUP PCS (Pre) 2006

Q374.For a real skew symmetric matrix A of odd order, the determinant |A| is

Aequal to one Bequal to zero Cequal to –1 Dequal to 2

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EnglishUP PCS (Pre) 2007

Q375.If A = i 0 0 -1, B = 0 -i 1 0 and, 0 -i C = i 0 then A3 + B3 + C3 – AB – BC – CA is

AA + B + C B0 CI2 D–A –B –C

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EnglishUP PCS (Pre) 2007

Q376.The system of linear equations λx + y + z = 1 x + λy + z = λ x + y + λz = λ2 does not a solution if λ is equal to –

A–2 B–1 C0 D1

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EnglishUP PCS (Pre) 2007

Q377.The following two statements are given for a square matrix A such that A5 = 0 (I) I + A is invertible (II) I – A is invertible Of these statements

A(I) is correct but not (II) B(II) is correct but not (I) Cboth (I) and (II) are correct Dnone of (I) and (II) is correct

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EnglishUP PCS (Pre) 2007

Q378.The value of the determinant– -1 x -x y 1 -y z -z -1

Ax B1 Cxz D1 + yz + yx + zx

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EnglishUP PCS (Pre) 2007

Q379.The rank of the matrix– 3 1 2 6 2 4 is 3 1 2

A0 B1 C2 D3

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EnglishUP PCS (Pre) 2007

Q380.If 6 8 5 A 4 2 3 9 7 1 is the sum of a symmetric matrix B and a skew-symmetric matrix C, then B is–

A6 6 7 4 2 3 9 7 1 B0 2 2 2 0 2 2 2 0 C6 6 7 6 2 5 7 5 1 D0 2 2 2 0 2 2 2 0

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