Continuity and Differentiability Class 12 MCQs Questions with Answers

1. f (x) = max {x, x3},then the number of points where f (x) is not differentiable, are

2. The function f (x) = [x] is

3. Find dy/dx if x= a cos θ, y = b sin θ

4. Let function f (x) =

5. If f (x) = 2x and g (x) = x²/2 + 1, then’which of the following can be a discontinuous function

6. The set of points where the function f given by f (x) =| 2x – 1| sin x is differentiable is

7. If x2 + y2 = 1, then

8. If y = (1 + x)(1 + x2)(1 + x4)…..(1 + x2n), then the value of dy/dx at x = 0 is

9. The derivative of y = (1 – x)(2 – x) ….. (n – x) at x = 1 is equal to

10. Find dy/dx if x = cos3θ, y = sin3 θ

11. If f(x) =

is continuous at x = π/2, then

12. The number of discontinuous functions y(x) on [-2, 2] satisfying x2 + y2 = 4 is

13. If y = (tan x)sin x, then dy/dx is equal to

14.  If f : R → R be a differentiable function, such that f (x + 2y) = f (x) + f (2y) + 4xy for all x, y ∈ R then

15. If sin y + e-xcos y = e, then dy/dx at (1, π) is equal to

16. The function f(x) = e|x| is

17. For the function f(x) = x + 1/x, x ∈ [1, 3] the value of c for mean value theorem is

18. The value of c in Rolle’s Theorem for the function f(x) = ex sin x, x ∈ [0, π] is

19. If f (x + y) = 2f (x) f (y) for all x, y ∈ R where f ‘ (0) = 3 and f (4) = 2, then f ‘ (4) is equal to

20. If Rolle’s theorem holds for the function f(x) = x3 + bx2 + ax + 5 on [1, 3] with c = (2 + 1/3√), find the value of a and b.