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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): Principal value of cos–1(1) is π
Reason (R): Value of cos 0° is 1
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'D'. Can you explain this answer?
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Directions : In the following questions, A statement of Assertion (A)...
In case of Assertion
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cos-1(1) = y
Cos y= 1
Cos y = cos 00 [∴ cos 00 = 1]
∴ y = 0
⇒ Principal value of cos–1 (1) is 0
Hence Assertion is in correct.
Reason is correct.
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Directions : In the following questions, A statement of Assertion (A)...
Assertion and Reasoning Questions in JEE
Assertion and Reasoning questions are a part of the JEE (Joint Entrance Examination) question paper. In these types of questions, two statements are given - an Assertion (A) and a Reasoning (R).
The candidate needs to assess the validity of both statements and determine if they are true or false. Additionally, the candidate needs to determine if the Reasoning statement is the correct explanation for the Assertion statement.
Explanation of the Given Question
Assertion (A): Principal value of cos–1(1) is π
Reason (R): Value of cos 0° is 1
The Assertion statement is true. The principal value of cos–1(1) is π because by definition, cos–1(x) is the inverse function of cos(x), which is defined on the interval [0,π]. The value of cos 0° is 1, so cos–1(1) = 0° + 2kπ, where k is an integer. The principal value of cos–1(1) is π, which is the smallest non-negative value of cos–1(1) that lies in the interval [0,π].
The Reasoning statement is also true. The value of cos 0° is 1, which means that cos–1(1) = 0° + 2kπ, where k is an integer. However, the Reasoning statement does not provide a correct explanation for the Assertion statement. The principal value of cos–1(1) is π because it is defined as the smallest non-negative value of cos–1(1) that lies in the interval [0,π], not because of the value of cos 0°.
Therefore, the correct answer is option D - A is false and R is true.
Assertion and Reasoning questions are a part of the JEE (Joint Entrance Examination) question paper. In these types of questions, two statements are given - an Assertion (A) and a Reasoning (R).
The candidate needs to assess the validity of both statements and determine if they are true or false. Additionally, the candidate needs to determine if the Reasoning statement is the correct explanation for the Assertion statement.
Explanation of the Given Question
Assertion (A): Principal value of cos–1(1) is π
Reason (R): Value of cos 0° is 1
The Assertion statement is true. The principal value of cos–1(1) is π because by definition, cos–1(x) is the inverse function of cos(x), which is defined on the interval [0,π]. The value of cos 0° is 1, so cos–1(1) = 0° + 2kπ, where k is an integer. The principal value of cos–1(1) is π, which is the smallest non-negative value of cos–1(1) that lies in the interval [0,π].
The Reasoning statement is also true. The value of cos 0° is 1, which means that cos–1(1) = 0° + 2kπ, where k is an integer. However, the Reasoning statement does not provide a correct explanation for the Assertion statement. The principal value of cos–1(1) is π because it is defined as the smallest non-negative value of cos–1(1) that lies in the interval [0,π], not because of the value of cos 0°.
Therefore, the correct answer is option D - A is false and R is true.
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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): Principal value of cos–1(1) is πReason (R): Value of cos 0° is 1a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?
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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): Principal value of cos–1(1) is πReason (R): Value of cos 0° is 1a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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): Principal value of cos–1(1) is πReason (R): Value of cos 0° is 1a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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): Principal value of cos–1(1) is πReason (R): Value of cos 0° is 1a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
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): Principal value of cos–1(1) is πReason (R): Value of cos 0° is 1a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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): Principal value of cos–1(1) is πReason (R): Value of cos 0° is 1a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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): Principal value of cos–1(1) is πReason (R): Value of cos 0° is 1a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Solutions for 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): Principal value of cos–1(1) is πReason (R): Value of cos 0° is 1a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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ample number of questions to practice 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): Principal value of cos–1(1) is πReason (R): Value of cos 0° is 1a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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