What is the value of the determinant11111 + xyz1111&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

11.

If A = α22α and detA3 = 125, Then α = ?

  • ± 1

  • ± 2

  • ± 3

  • ± 5


12.

The equations

x + 2y + 3z = 12

x + y + 3z  = 25

x + 5y + 9z = 4

  • have the unique solution

  • Have infinitely many solutions

  • are inconsistent

  • None of the above


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13.

What is the value of the determinant

11111 + xyz1111 +xyz 

  • 1 + x + y + z

  • 2xyz

  • x2y2z2

  • 2x2y2z2


C.

x2y2z2

11111 + xyz1111 +xyz= 11 + xyz2 - 12 - 111 + xyz - 12 + 112 - 11 + xyz= 1 + x2y2z2 +2xyz - 1 - 1 + xyz - 1 +1 - 1 - xyz= x2y2z2 + 2xyz - xyz - xyz= x2y2z2 + 2xyz - 2xyz= x2y2z2


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14.

If xy00xyy0x = 0, then which one of the following is correct ?

  • xy is one of the cube roots of unity

  • x is one of the cube roots of unity

  • y is one of the cube roots of unity

  • xy is one of the cube roots - 1


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15.

Consider the set A of all matrices of order 3 x 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1. Let C be the subset of A consisting of all matrices whose determinant is - 1. Then which one of the following is correct ?

  • C is empty

  • B as as many elements as C

  • A = B  C

  • B has thrice as many elements as C


16.

If a denotes the absolute value of an integer, then which of the following are correct ?

1. ab = ab2. a + b  a + b3. a - b  a - b

Select the correct answer using the code given below :

  • 1 and 2 only

  • 2 and 3 only

  • 1 and 3 only

  • 1, 2 and 3


17.

The value of the determinant cos2θ2sin2θ2sin2θ2cos2θ2

for all values of θ, is

  • 1

  • cosθ

  • sinθ

  • cos2θ


18.

The system of equations kx + y + z = 1, x + ky + z = kand x + y + kz = k has no solution if k equal

  • 0

  • 1

  •  - 1

  •  - 2


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19.

If z - 4z = 2, he maximum value of Izl is equal to :

  • 1 + 3

  • 1 + 5

  • 1 - 5

  • 5 - 1


20.

The value of the determinant 1 - αα - α2α21 - ββ - β2β21 - γγ - γ2γ2 = ?

  • α - ββ - γα - γ

  • α - ββ - γγ - α

  • α - ββ - γα + β + γ

  • 0


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