JEE Exam  >  JEE Tests  >  Mathematics (Maths) Class 12  >  Test: Continuity and Differentiability- Assertion & Reason Type Questions - JEE MCQ

Test: Continuity and Differentiability- Assertion & Reason Type Questions - JEE MCQ


Test Description

8 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Continuity and Differentiability- Assertion & Reason Type Questions

Test: Continuity and Differentiability- Assertion & Reason Type Questions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Continuity and Differentiability- Assertion & Reason Type Questions questions and answers have been prepared according to the JEE exam syllabus.The Test: Continuity and Differentiability- Assertion & Reason Type Questions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Continuity and Differentiability- Assertion & Reason Type Questions below.
Solutions of Test: Continuity and Differentiability- Assertion & Reason Type Questions questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Test: Continuity and Differentiability- Assertion & Reason Type Questions solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Continuity and Differentiability- Assertion & Reason Type Questions | 8 questions in 16 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 1

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion: If y = sin-1 then

Reason:

Detailed Solution for Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 1
put 3x = sin θ or θ = sin-1 3x

= 2θ

= 2 sin-1 3x

A is true. R is false.

Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 2

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : |sin x| is continuous for all x ∈ R.

Reason : sin x and |x| are continuous in R.

Detailed Solution for Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 2
sin x and |x| are continuous in R. hence R is true.

Consider the functions f(x) = sin x and g(x) = |x| both of which are continuous in R.

gof(x) = g(f(x)) = g(sin x) = |sin x |.

Since f(x) and g(x) are continuous in R, gof(x) is also continuous in R.

Hence A is true.

R is the correct explanation of A.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 3

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : A continuous function is always differentiable.

Reason : A differentiable function is always continuous.

Detailed Solution for Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 3
The function f(x) is differentiable at x = a, if it is continuous at x = a and LHD = RHD at x = a.

A differentiable function is always continuous. Hence R is true.

A continuous function need not be always differentiable.

For example, |x| is continuous at x = 0, but not differentiable at x = 0.

Hence A is false.

Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 4

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : f(x) = tan2 x is continuous at x = π/2

Reason : g(x) = x2 is continuous at x = π/2.

Detailed Solution for Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 4
g(x) = x2 is a polynomial function. It is continuous for all x ∈ R.

Hence R is true.

f(x) = tan2 x is not defined when x = π/2.

Therefore f(π/2) does not exist and hence f(x) is not continuous at x = π/2.

A is false.

Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 5

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : f(x) = [x] is not differentiable at x = 2.

Reason : f(x) = [x] is not continuous at x = 2.

Detailed Solution for Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 5
f(x) = [x] is not continuous when x is an integer.

So f(x) is not continuous at x = 2. Hence R is true.

A differentiable function is always continuous.

Since f(x) = [x] is not continuous at x = 2, it is also not differentiable at x = 2.

Hence A is true.

R is the correct explanation of A.

Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 6

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Consider the function which is continuous at x = 0.

Assertion (A): The value of k is – 3.

Detailed Solution for Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 6

This is the definition for modulus function and hence true.

Hence R is true.

Since f is continuous at x = 0,

Here f(0) = 3,

∴ -k = 3 or k = -3

Hence A is true.

R is the correct explanation of A.

Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 7

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): |sin x| is continuous at x = 0.

Reason (R): |sin x| is differentiable at x = 0.

Detailed Solution for Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 7
Since sin x and |x| are continuous functions in R, |sin x| is continuous at x = 0.

Hence A is true.

At x = 0, LHD ≠ RHD.

So f(x) is not differentiable at x = 0.

Hence R is false.

Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 8

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Consider the function

which is continuous at x = 2.

Assertion (A): The value of k is 0.

Reason (R): f(x) is continuous at x = a, if

Detailed Solution for Test: Continuity and Differentiability- Assertion & Reason Type Questions - Question 8
f(x) is continuous at x = a,

∴ R is true.

∴ k = 7

Hence A is false.

204 videos|288 docs|139 tests
Information about Test: Continuity and Differentiability- Assertion & Reason Type Questions Page
In this test you can find the Exam questions for Test: Continuity and Differentiability- Assertion & Reason Type Questions solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Continuity and Differentiability- Assertion & Reason Type Questions, EduRev gives you an ample number of Online tests for practice

Top Courses for JEE

204 videos|288 docs|139 tests
Download as PDF

Top Courses for JEE