The range of the function sinsin-1x + cos-1x, 

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.

If y = 2x . 32x - 1, then d2ydx2 is equal to :

  • log2log3

  • log18

  • log182y2

  • log18y


2.

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing, is

  • a constant

  • proportional to the radius

  • inversely proportional to the radius

  • inversely proportional to the surface area


3.

The length of the subtangent to the curve x2 + xy + y2 = 7 at (1, - 3) is :

  • 3

  • 5

  • 35

  • 15


4.

If y = x + x2 + x3 + ... to  where x < 1, then for y < 1dxdy is equal to :

  • y + y2 + y3 + ... to 

  • 1 - y + y2 - y3 + ... to 

  • 1 - 2y + 3y- ... to 

  • 1 + 2y + 3y2 + ... to 


Advertisement
5.

Twenty two metres are available to fence a flower bed in the form of a circular sector. If the flower bed should have the greatest possible surface area, the radius of the circle must be :

  • 4 m

  • 3 m

  • 6 m

  • 5 m


6.

If y = sinx + sinx + sinx + ... , then dydx is equal to :

  • cosx2y - 1

  • - cosx2y - 1

  • sinx1 - 2y

  • - sinx1 - 2y


7.

Given f(0) = 0 and f(x) = 11 - e- 1x for x  0. Then only one of the following statements on f (x) is true. That is f(x), is :

  • continuous at x = 0

  • not continuous at x = 0

  • both continuous and differentiable at x = 0

  • not defined at x = 0


8.

The value of x for which the polynomial 2x3 - 9x2 + 12x + 4 is a decreasing function of x, is :

  • - 1 < x < 1

  • 0 < x < 2

  • x > 3

  • 1 < x < 2


Advertisement
Advertisement

9.

The range of the function sinsin-1x + cos-1x, x  1 :

  • [- 1, 1]

  • [1, - 1]

  • {0}

  • {1}


D.

{1}

sinsin-1x + cos-1x, x  1 = sinπ2 = 1 Range of sinsin-1x + cos-1x = 1


Advertisement
10.

Let f : R  R : f(x) = x2 and g : R  R : g(x) = x + 5, then gof is :

  • (x + 5)

  • (x + 52)

  • (x2 + 52)

  • (x2 + 5)


Advertisement