Teachoo MCQ Test

Assertion Reasoning Quiz

Preparing for CBSE

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
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Question 1 of 5
Assertion (A): The function \(f(x)=\sin \left(x^2\right)\) is a continuous function.
Reason (R): The composition of two continuous functions is a continuous function.
Select one option. Answers are shown after the test.
Question 2 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 3 of 5
Assertion (A): If a car moves with constant velocity, its acceleration is zero.
Reason (R): Acceleration is the second derivative of the position function, and the derivative of a constant (velocity) is zero.
Select one option. Answers are shown after the test.
Question 4 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 5 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.