Teachoo MCQ Test

Assertion Reasoning Quiz

Chapter 5 Class 12 Continuity and Differentiability | 5 questions

Timed test. Answer every question before time runs out. Correct answers and solutions appear after submission.
Time remaining 360
Question 1 of 5
Question 1 of 5
Assertion (A): A finction must be continuous at a point if it is differentiable at that point.
Reason (R): If the limit of a function exists at a point, it must be differentiable at that point.
Select one option. Answers are shown after the test.
Question 2 of 5
Assertion (A): The function \(f(x)=\cos |x|\) is differentiable at \(x=0\).
Reason (R): The cosine function is an even function, so \(\cos (-x)=\cos (x)\).
Select one option. Answers are shown after the test.
Question 3 of 5
Assertion (A): The function \(f(x)=[x]\) has a jump discontinuity at every integer.
Reason (R): The left-hand limit and the right-hand limit at any integer are not equal.
Select one option. Answers are shown after the test.
Question 4 of 5
Assertion (A): The function \(f(x)=\log (x)\) is continuous for all \(x>0\).
Reason (R): The graph of \(\log (x)\) can be drawn without lifting the pen for all \(x\) in its domain.
Select one option. Answers are shown after the test.
Question 5 of 5
Assertion (A): The function \(f(x)=x^3\) is differentiable everywhere.
Reason (R): The graph of \(y=x^3\) is smooth and has no sharp corners or breaks.
Select one option. Answers are shown after the test.