CBSE Class 12 Maths Continuity and Differentiability Quiz 1

1. If f (x) = 2x and g (x) = \(\frac{x^2}{2}\) + 1, then’which of the following can be a discontinuous function

A f(x) + g(x) B f(x) – g(x) C f(x).g(x) D \(\frac{g(x)}{f(x)}\)

2. The function f(x) = \(\frac{4-x^2}{4x-x^3}\) is

A discontinuous at only one point at x = 0 B discontinuous at exactly two points C discontinuous at exactly three points D None of these

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

A R B R = {\(\frac{1}{2}\)} C (0, ∞) D None of these

4. The function f(x) = cot x is discontinuous on the set

A {x = nπ, n ∈ Z} B {x = 2nπ, n ∈ Z} C {x = (2n + 1) \(\frac{π}{2}\) n ∈ Z} D {x – \(\frac{nπ}{2}\) n ∈ Z}

5. The function f(x) = e is

A continuous everywhere but not differentiable at x = 0 B continuous and differentiable everywhere C not continuous at x = 0 D None of these

6. If f(x) = x² sin\(\frac{1}{x}\), where x ≠ 0, then the value of the function f(x) at x = 0, so that the function is continuous at x = 0 is

A 0 B -1 C 1 D None of these

7. If f(x) = is continuous at x = \(\frac{π}{2}\), then

A m = 1, n = 0 B m = \(\frac{nπ}{2}\) + 1 C n = \(\frac{mπ}{2}\) D m = n = \(\frac{π}{2}\)

8. If y = log(\(\frac{1-x^2}{1+x^2}\)), then \(\frac{dy}{dx}\) is equal to

A \(\frac{4x^3}{1-x^4}\) B \(\frac{-4x}{1-x^4}\) C \(\frac{1}{4-x^4}\) D \(\frac{-4x^3}{1-x^4}\)

9. Let f(x) = |sin x| Then

A f is everywhere differentiable B f is everywhere continuous but not differentiable at x = nπ, n ∈ Z C f is everywhere continuous but no differentiable at x = (2n + 1) \(\frac{π}{2}\) n ∈ Z D None of these

10. If y = \(\sqrt{sin x+y}\) then \(\frac{dy}{dx}\) is equal to

A \(\frac{cosx}{2y-1}\) B \(\frac{cosx}{1-2y}\) C \(\frac{sinx}{1-xy}\) D \(\frac{sinx}{2y-1}\)