For how many values of x in the closed interval [- 4, - 1], is th

Subject

Mathematics

Class

JEE Class 12

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 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


Advertisement
5.

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

  • AP

  • GP

  • HP

  • None of these


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


Advertisement
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


Advertisement

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


D.

1

The given matrix is singular, if3- 1 + x23- 1x + 2x + 3- 12 = 0Applying R2  R2 - R1, R3  R3 - R1              3- 1 + x20- xxx- x0 = 0Applying C1  C1 + C2 + C3   x + 4- 1 + x20- xx0- x0 = 0

Hence, x = - 4 is the only solution which lies in the given internal.


Advertisement
Advertisement