The value of 1- tanθ4tanθ411tanθ4-&nb

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.

The solution of equation 

sin-11 - x2 - 2sin-1x2 = π2 is

  • x = 0

  • x = 12

  • x = 0 and 12

  • None of these


2.

Let f(x) = - 2sinx,     - π  x  - π2asinx + b,    - π2  x  π2cosx,                  π2  x  π. If f(x) is continuous on - π, π, then

  • a = 1, b = 1

  • a = - 1, b = - 1

  • a = - 1, b = 1

  • a = 1, b = - 1


3.

If f(x) = x1 + exp1x ,     x  00                     ,     x = 0, then f(x) at x = 0 is

  • continuous

  • not continuous

  • differentiable

  • not differentiable


4.

The maximum value of f(x) = 2sinx + cos2x, 0  x  π2 occurs at x is equal to

  • 0

  • π6

  • π2

  • None of these


Advertisement
5.

If f(x) = x - 2 and g(x) = f(f(x)), then dgxdx for x > 10 is

  • 1 or - 1

  • 1

  • - 1

  • None of these


6.

If y = sin-11 + x + 1 - x2, then the value of dydx at x = 0 is

  • 1/2

  • - 1/2

  • 0

  • None of these


7.

The distance (in metre) travelled by a vehicle in time t (in seconds) is given by the equation s = 3t3 + 2t2 + t + 1. The difference in the acceleration between t = 2 and t = 4 is

  • 36 m/s2

  • 38 m/s2

  • 45 m/s2

  • 46 m/s2


Advertisement

8.

The value of 1- tanθ4tanθ411tanθ4- tanθ41-1 is

  • cosθ2sinθ2- sinθ2cosθ2

  • cosθ2- sinθ2sinθ2cosθ2

  • sinθ2cosθ2cosθ2sinθ2

  • sinθ2- cosθ2cosθ2sinθ2


B.

cosθ2- sinθ2sinθ2cosθ2

1- tanθ4tanθ411tanθ4- tanθ41-1   = 1- tanθ4tanθ4111 + tan2θ41- tanθ4tanθ41   = 1sec2θ41- tanθ4tanθ411- tanθ4tanθ41   = cos2θ41 - tan2θ4- 2tanθ42tanθ41 - tan2θ4

   = cos2θ4cos2θ4 - sin2θ4cos2θ4- 2sinθ4cosθ42sinθ4cosθ4cos2θ4 - sin2θ4cos2θ4   = cosθ2- sinθ2sinθ2cosθ2


Advertisement
Advertisement
9.

The value of λ and µ for whichi the simultaneous equation x + y + z = 6, x + 2y + 3z = 10 and x + 2y + λz = µ have a unique solution are

  • λ  3

  • μ = 3 only

  • λ = 3 and μ = 3

  • λ  3 and μ can take any value.


10.

If X is any matrix of order n x p (n and p are integers) and I is an identity matrix of order nxn, then the matrix M = I -  X(X'X)-1X' is

(i) idempotent matrix (ii) MX = 0

Choose the correct answer

  • (i) is correct

  • (ii) is correct

  • (i) is incorrect

  • (ii) is incorrect


Advertisement