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

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

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

Test: Continuity and Differentiability- Assertion & Reason Type Questions for Commerce 2024 is part of Commerce preparation. The Test: Continuity and Differentiability- Assertion & Reason Type Questions questions and answers have been prepared according to the Commerce exam syllabus.The Test: Continuity and Differentiability- Assertion & Reason Type Questions MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Continuity and Differentiability- Assertion & Reason Type Questions below.
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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.

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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.

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