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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): |sin x| is continuous at x = 0.
Reason (R): |sin x| is differentiable at x = 0.
- 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 'C'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) ...
Since sin x and |x| are continuous functions in R, |sin x| is continuous at x = 0.
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Hence A is true.
At x = 0, LHD ≠ RHD.
So f(x) is not differentiable at x = 0.
Hence R is false.
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Directions: In the following questions, A statement of Assertion (A) ...
Answer:
Assertion (A): |sin x| is continuous at x = 0.
Reason (R): |sin x| is differentiable at x = 0.
To determine the correct choice, we need to evaluate the statements of both Assertion (A) and Reason (R).
Assertion (A): |sin x| is continuous at x = 0.
The absolute value function |x| is continuous for all real values of x. This means that as x approaches any value, the function does not have any abrupt jumps or breaks. In the case of |sin x|, the function is simply the absolute value of the sine function. The sine function itself is continuous for all real values of x, including x = 0. Therefore, |sin x| is also continuous at x = 0.
Reason (R): |sin x| is differentiable at x = 0.
To determine if |sin x| is differentiable at x = 0, we need to check if the derivative of |sin x| exists at x = 0. The derivative of |x| is not defined at x = 0 because the function has a sharp corner at that point. However, the derivative of sin x is defined and continuous for all real values of x. Therefore, the derivative of |sin x| exists at x = 0.
Conclusion:
From the evaluations of both Assertion (A) and Reason (R), we can see that both statements are individually true. However, the Reason (R) is not the correct explanation of Assertion (A).
The correct answer is option 'C': A is true but R is false.
Assertion (A): |sin x| is continuous at x = 0.
Reason (R): |sin x| is differentiable at x = 0.
To determine the correct choice, we need to evaluate the statements of both Assertion (A) and Reason (R).
Assertion (A): |sin x| is continuous at x = 0.
The absolute value function |x| is continuous for all real values of x. This means that as x approaches any value, the function does not have any abrupt jumps or breaks. In the case of |sin x|, the function is simply the absolute value of the sine function. The sine function itself is continuous for all real values of x, including x = 0. Therefore, |sin x| is also continuous at x = 0.
Reason (R): |sin x| is differentiable at x = 0.
To determine if |sin x| is differentiable at x = 0, we need to check if the derivative of |sin x| exists at x = 0. The derivative of |x| is not defined at x = 0 because the function has a sharp corner at that point. However, the derivative of sin x is defined and continuous for all real values of x. Therefore, the derivative of |sin x| exists at x = 0.
Conclusion:
From the evaluations of both Assertion (A) and Reason (R), we can see that both statements are individually true. However, the Reason (R) is not the correct explanation of Assertion (A).
The correct answer is option 'C': A is true but R is false.
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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): |sin x| is continuous at x = 0.Reason (R): |sin x| is differentiable at x = 0.a)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 'C'. 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): |sin x| is continuous at x = 0.Reason (R): |sin x| is differentiable at x = 0.a)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 'C'. Can you explain this answer? for JEE 2024 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): |sin x| is continuous at x = 0.Reason (R): |sin x| is differentiable at x = 0.a)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 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 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): |sin x| is continuous at x = 0.Reason (R): |sin x| is differentiable at x = 0.a)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 'C'. 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): |sin x| is continuous at x = 0.Reason (R): |sin x| is differentiable at x = 0.a)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 'C'. Can you explain this answer? for JEE 2024 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): |sin x| is continuous at x = 0.Reason (R): |sin x| is differentiable at x = 0.a)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 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 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): |sin x| is continuous at x = 0.Reason (R): |sin x| is differentiable at x = 0.a)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 'C'. 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): |sin x| is continuous at x = 0.Reason (R): |sin x| is differentiable at x = 0.a)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 'C'. 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): |sin x| is continuous at x = 0.Reason (R): |sin x| is differentiable at x = 0.a)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 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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