The determinant abaα + bbcbα +&nb

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let f(x) = 51x, x < 0λx, x  0 and λ  R, then at x = 0

  • f is discontinuous

  • f is continuous only, if λ = 0

  • f is continuous only, whatever λ maybe

  • None of the above


2.

Which one of the following is not true?

  • Matrix addition is commutative

  • Matrix addition is associative

  • Matrix multiplication is commutative

  • Matrix multiplication is associative


3.

If matrix 01- 2- 103λ- 30 is singular, then λ equal to

  • - 2

  • - 1

  • 1

  • 2


4.

If A = 2x0xx and A-1- 10- 12, then x equals

  • 2

  • - 12

  • S

  • 12


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5.

The determinant ab + bbc + c + b + c0 = 0, if a, b, c are in

  • AP

  • GP

  • HP

  • None of these


B.

GP

Given, ab + bbc + c + b + c0 = 0Applying R3  R3 - αR1 - R2 ab + bbc + c00- 2 +2 + c = 0 a- c2 +2 + c - 0 - b- b2 +2 + c - 0 = 0 - ac2 +2 + c + b22 +2 + c = 0             b2 - ac2 +2 + c = 0Either b2 - ac = 0 or 2 +2 + c = 0 Either a, b, c are in GP or 2 +2 + c = 0


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6.

If tan-1x - 1 + tan-1x + tan-1x + 1 = tan-13x, then x is

  • ± 12

  • 0, 12

  • 0, - 12

  • 0, ± 12


7.

The minimum value of x2 + 11 + x2 is at

  • x = 0

  • x = 1

  • x = 4

  • x = 3


8.

Let f(x) = 12 - tanπx2, - 1 < x < 1 and g(x) = 3 + 4x - 4x2, then dom(f + g) is given by

  • 12, 1

  • [12, - 1)

  • [ - 12, 1)

  • - 12, - 1


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9.

If a  b  c, the value of x which satisfies the equation 0x - ax - bx + a0x - cx + bx + c0 = 0, is

  • x = 0

  • x = a

  • x = b

  • 1


10.

For how many values of x in the closed interval [- 4, - 1], is the matrix 3- 1 + x23- 1x + 2x + 3- 12 singular ?

  • 2

  • 0

  • 3

  • 1


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