Class 12 Mathematics Chapter 5 Continuity And Differentiability Quiz 4 (15 MCQs)

Quiz Instructions

Select an option to see the correct answer instantly.

1. Differentiation of $a^x$

Correct Answer: C) $a^x\log a$.

2. Explain the concept of differentiability.

Correct Answer: D) Differentiability refers to the existence of the derivative of a function at every point within a given interval.

3. A polynomial function is continuous to all real numbers.

Correct Answer: A) TRUE.

4. Derivative of cos(sinx)

Correct Answer: B) -cosx.sin(sinx).

5. Determine the domain:$g\left(x\right)=\sqrt{15+5x}$

Correct Answer: A) $x\ge-3$.

6. Identify the point(s) of discontinuity. $f\left(x\right)=\frac{4}{x-6}$

Correct Answer: B) X = 6.

7. The function f(x) = $\frac{\left(4-x^2\right)}{4x-x^3}$

Correct Answer: C) Discontinuous at exactly three points.

8. Which of the following statements is true regarding the function f(x) = |x|?

Correct Answer: D) It is continuous everywhere.

9. One of the conditions a function must satisfy to be continuous at x=c is "f(c) must exist"

Correct Answer: A) TRUE.

10. Which of the following statements is true regarding limits of functions?

Correct Answer: A) Limits can exist at points of discontinuity.

11. A continuous function can have some points where limit does not exist.

Correct Answer: B) False.

12. The function f (x) = [x], where [x] denotes the greatest integer function, is continuous at:

Correct Answer: D) 1.5.

13. For what x value, if any, is the function below neither continuous nor differentiable? $f\left(x\right)=\frac{2-x}{\left|2-x\right|}$

Correct Answer: A) 2.

14. How can you determine if a function is differentiable at a point?

Correct Answer: B) Calculate the derivative of the function and check if it exists at the given point.

15. Statement 1:The function f(x) = $\left|x\right|$ $\left|x+1\right|$

Correct Answer: D) Statement 1 is true, and Statement 2 is true, Statement 2 is the not correct explanation for Statement 1.