Math Chapter Wise

EnglishPGT 2013

Q201.Matrix 0 3 5 2 3 0 9 5 2 9 0 − − − i is a –

ASymmetric matrix BSkew symmetric matrix CHermitian matrix DSkew Hermitian matrix

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EnglishPGT 2013

Q202.If A is a 3 × 3 matrix of order 3 and B is a 3 × 3 matrix of order 3, then the order of AB is

A5 B3 C1 D2

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EnglishPGT 2013, 2005

Q203.If 2 3 5 2 A = −, then 19A–1 is

A1 2 A B2A C3A DA

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EnglishPGT 2013

Q204.If ω is a complex root of unity then the value of the determinant 2 2 2 1 1 1 1 1 1 1 i i i ω + + − − − − − − − − − − − − − − + − − − − + − − − − + − − − − + − − will be–

Aω Bi C–1 D0

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EnglishPGT 2013

Q205.The system of equation 3 1 x y z λ − + = − + = − + = − + = 2 2 x y z + + = + + = + + = + + = 2 1 x y z λ + − = − + − = − + − = − + − = − has unique solution if

Aλ · 7 2 B7 2 λ − = C7 2 − ≠ λ D7 2 ≠ λ

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EnglishPGT 2010

Q206.If the lines ax + 2y + 1 = 0, bx+3y+1=0 and cx+4y+1=0 are concurrent, then a, b, c are in

AArithmetic Progression BGeometric progression CHarmonic Progression DNone of the above

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EnglishPGT 2010

Q207.If A is any matrix of order m×n such that AB and BA are both defined, then B is an–

Am×n matrix Bn×m matrix Cn×n matrix Dm×m matrix

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EnglishPGT 2010

Q208.If 4 x 2 A 2x 3 x 1 + = − + is symmetric matrix then x =

A3 B5 C2 D4

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EnglishPGT 2010

Q209.Which of the following is incorrect?

AA2 –B2 = (A+B)(A–B) B(AT)T = A C(AB)n = An Bn where A, B commutue D(A–I) (I+A) = 0⇔A2 =I

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EnglishPGT 2010

Q210.If a, b, c are in Arithmetic progression then the value of 1 2 2 3 3 4 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + x x x a x x x b x x x c is

A3 B–3 C0 DNone of these

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EnglishPGT 2010

Q211.For what value of x (x, 0, 7), (1, 2, 1) and (2,–1, 3) are linearly dependent?

Ax=3 Bx = 4 Cx =5 Dx = 6

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EnglishPGT 2010

Q212.If 2 0 A 0 3 − = − and 1 0 I 0 1 = then which of the following is zero matrix?

AA2/+5A+6I BA2/–5A+6I CA2/–5A–6I DA2/+5A–6I

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EnglishPGT 2010

Q213.For what value of k the equations 2x – 3y + 2z = a, 5x + 4y – 2z = –3 and x–13y + kz = 9 will not have a unique solution?

A8 B3 C2 D6

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EnglishPGT 2010

Q214.If 1 1 A 0 1 = then the value of A+A2 +A3 +…+An–1 is equal to

A1 2 0 1 n − B() 1 1 2 1 0 n − C() 1 1 2 0 1 n − D() 1 1 2 1 0 n −

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EnglishPGT 2010

Q215.If the matrix 3 1 A 1 2 = − then by Cayley – Hamilton theorem, the value of A2 –5A+7I is

A1 0/0 1 B0 0 C1 1 D0 1/1 0

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EnglishPGT 2009

Q216.If A = 3 2 4 1 2 1 0 1 1 − − and A–1 = 1 k adj

A7 B–7 C1/7 D11

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EnglishPGT 2009

Q217.The equation –2x + y + z = a x – 2y + z = b x + y – 2z = c have no solution unless

Aa + b + c = 1 Ba + b + c = –1 Ca + b + c = 0 DNone of these

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EnglishPGT 2009

Q218.The solution of the equations 3x + 5y – 7z = 13 4x + y – 12z = 6 2x + 9y – 3z = 20 by Cramer's rule is

Ax = 0, y = 1, z = 2 Bx = 1, y = 2, z = 0 Cx = 2, y = 3, z = 1 Dx = 3, y = 4, z = 2

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EnglishPGT 2005

Q219.If α, β are the roots of the equation 2x2 +3x+5 = 0, then the value of the determinants 0 β α β α is

A−3/5 B−15/4 C3/5 D14/5

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EnglishPGT 2005

Q220.If 0 1 1 0 = A then A100 is equal to

A1 0/0 1 B0 1/1 0 C1 1/0 0 D0 0/1 0

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