Test: Integrals- Assertion & Reason Type Questions - JEE MCQ

# Test: Integrals- Assertion & Reason Type Questions - JEE MCQ

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## 8 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Integrals- Assertion & Reason Type Questions

Test: Integrals- Assertion & Reason Type Questions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Integrals- Assertion & Reason Type Questions questions and answers have been prepared according to the JEE exam syllabus.The Test: Integrals- 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: Integrals- Assertion & Reason Type Questions below.
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Test: Integrals- Assertion & Reason Type Questions - Question 1

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

Detailed Solution for Test: Integrals- Assertion & Reason Type Questions - Question 1

This is a standard integral and hence R is true.

Hence A is true and R is the correct explanation for A.

Test: Integrals- Assertion & Reason Type Questions - Question 2

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

Detailed Solution for Test: Integrals- Assertion & Reason Type Questions - Question 2
Let y = xx

⇒ log y = x log x

Differentiating w.r.t. X

Hence R is true.

Since

Using the concept of anti-derivative, A is true.

R is the correct explanation for A.

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Test: Integrals- Assertion & Reason Type Questions - Question 3

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

Detailed Solution for Test: Integrals- Assertion & Reason Type Questions - Question 3
Let

∴ I = π/4

Hence R is true.

From (ii), A is also true.

R is the correct explanation for A.

Test: Integrals- Assertion & Reason Type Questions - Question 4

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

Detailed Solution for Test: Integrals- Assertion & Reason Type Questions - Question 4

This is a standard integral and hence true. So R is true.

Hence A is true and R is the correct explanation for A.

Test: Integrals- Assertion & Reason Type Questions - Question 5

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

Assertion (A): ∫ex[sin x - cos x] dx = ex sin x + C

Reason (R): ∫ex [f(x) +f′(x)]dx =ex f(x) + c

Detailed Solution for Test: Integrals- Assertion & Reason Type Questions - Question 5

∫ex [f(x) + f′(x)]dx = ∫exf(x)dx + ∫exf′(x)dx

= f(x)ex - ∫f′(x)exdx + ∫f′(x)exdx

= ex f(x) + c

Hence R is true.

∫ex(sin x - cos x)dx = ex (-cos) + c

= -ex cos x + c

Hence A is false.

Test: Integrals- Assertion & Reason Type Questions - Question 6

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

Detailed Solution for Test: Integrals- Assertion & Reason Type Questions - Question 6
Since

∴ A is true

which can not be integrated.

∴ R is false.

Test: Integrals- Assertion & Reason Type Questions - Question 7

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

Reason (R): f(x) = x3 + 5 is an odd function.

Detailed Solution for Test: Integrals- Assertion & Reason Type Questions - Question 7
Let f(x) = x3 + 5

f(-x) = (-x)3 + 5

= -x3 + 5

f(x) is neither even nor odd. Hence R is false.

Hence A is true.

Test: Integrals- Assertion & Reason Type Questions - Question 8

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

Detailed Solution for Test: Integrals- Assertion & Reason Type Questions - Question 8

This is a property of the definite integrals and hence R is true.

Hence A is false.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests
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## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests