If α, β, γ are the cube root

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 Multiple Choice QuestionsMultiple Choice Questions

381.

The system of equations

x + y + z = 0

2x + 3y + z = 0

and x + 2y = 0

has

  • a unique solution; x = 0, y = 0, z = 0

  • infinite solutions

  • no solution

  • finite number of non-zero solutions


382.

If D = diag (d1, d2, ..., dn), where di  0, for i = 1, 2, ... , n then D-1 is equal to

  • DT

  • D

  • adj(D)

  • diagd1-1, d2-1, ..., dn-1


383.

If x, y, z are different from zero and  = ab - yc - za - xbc - za - xb - yc = 0, then the value of the expression ax + by + cz is

  • 0

  • - 1

  • 1

  • 2


384.

If x = - 5 is a root of 2x + 14822x2762x = 0, then the other roots are :

  • 3, 3.5

  • 1, 3.5

  • 1, 7

  • 2, 7


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385.

The simultaneous equations Kx + 2y - z = 1, (K - I)y - 2z = 2 and (K + 2)z = 3 have only one solution when :

  • K = - 2

  • K = - 1

  • K = 0

  • K = 1


386.

If the matrix Mr is given by Mr = rr - 1r - 1r, r = 1, 2, 3, ..., then the value of det(M1) + det(M2) + ... + det(M2008) is

  • 2007

  • 2008

  • (2008)2

  • (2007)2


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387.

If α, β, γ are the cube roots of unity, then the value of the determinant eαe2αe3α - 1eβe2βe3β - 1eγe2γe3γ - 1 is equal to

  • - 2

  • - 1

  • 0

  • 1


C.

0

Given α, β, γ are the cube roots of unity, then assume α = 1, β = w and γ = w2.

 eαe2αe3α - 1eβe2βe3β - 1eγe2γe3γ - 1= eαe2αe3αeβe2βe3βeγe2γe3γ + eαe2α- 1eβe2β- 1eγe2γ- 1= eαeβeγ1eαe2α1eβe2β1eγe2γ - 1eαe2α1eβe2β1eγe2γ= 1eαe2α1eβe2β1eγe2γeαeβeγ - 1 = 0 eαeβeγ = e1 + w + w2 = e0 = 1


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388.

If the three linear equations

x + 4ay + az = 0

x + 3by + bz = 0

x + 2cy + cz = 0

have a non-trivial solution, where aa  0, b  0, c  0, then ab + bc is equal to

  • 2ac

  • - ac

  • ac

  • - 2ac


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389.

If A = 1235, then the value of the determinant A2009 - 5A2008 is

  • - 6

  • - 5

  • - 4

  • 4


390.

The value of the determinant 15!16!17!16!17!18!17!18!19! is equal to

  • 15! + 16!

  • 2(15!)(16!)(17!)

  • 15! + 16! + 17!

  • 16! + 17!


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