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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:
Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.
Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πr
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'B'. Can you explain this answer?
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Direction: In the Following Questions, A Statement of Assertion (A) I...
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
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Area swept by minute hand in 5 minutes
(Angle in 5 minutes by minute hand is 30o)
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Direction: In the Following Questions, A Statement of Assertion (A) I...
Assertion: The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm².
Reason: The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πr.
Explanation:
To understand why the correct answer is option 'B', let's break down the assertion and reason separately:
Assertion: The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm².
The assertion states that the length of the minute hand of a clock is 7cm. This means that the radius of the circular motion of the minute hand is 7cm.
The area swept by the minute hand in 5 minutes can be calculated by finding the area of the sector formed by the minute hand's motion. The formula for the area of a sector is given by:
A = (θ/360) x πr²
where A is the area, θ is the angle (in degrees), and r is the radius.
In this case, the minute hand sweeps an angle of 360 degrees in 60 minutes (1 hour). Therefore, in 5 minutes, it sweeps an angle of:
θ = (360/60) x 5 = 30 degrees
Substituting the values into the formula, we get:
A = (30/360) x π(7)² = (1/12) x 49π = 49π/12
Simplifying this expression, we get:
A = 4.083π
Now, to compare this with the given answer, we need to rationalize the denominator:
A = 4.083π x (6/6) = (24.498π)/6 ≈ 4.083π
Therefore, the area swept by the minute hand in 5 minutes is approximately 4.083π cm².
Now, let's move on to the reason given in the question.
Reason: The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πr.
The reason states the formula for the length of an arc of a sector, which is correct. However, it is not directly related to the calculation of the area swept by the minute hand. The formula for the area of a sector was used in the explanation of the assertion.
Conclusion: Both the assertion and the reason are true, but the reason does not provide the correct explanation for the assertion. Therefore, the correct answer is option 'B'.
Reason: The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πr.
Explanation:
To understand why the correct answer is option 'B', let's break down the assertion and reason separately:
Assertion: The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm².
The assertion states that the length of the minute hand of a clock is 7cm. This means that the radius of the circular motion of the minute hand is 7cm.
The area swept by the minute hand in 5 minutes can be calculated by finding the area of the sector formed by the minute hand's motion. The formula for the area of a sector is given by:
A = (θ/360) x πr²
where A is the area, θ is the angle (in degrees), and r is the radius.
In this case, the minute hand sweeps an angle of 360 degrees in 60 minutes (1 hour). Therefore, in 5 minutes, it sweeps an angle of:
θ = (360/60) x 5 = 30 degrees
Substituting the values into the formula, we get:
A = (30/360) x π(7)² = (1/12) x 49π = 49π/12
Simplifying this expression, we get:
A = 4.083π
Now, to compare this with the given answer, we need to rationalize the denominator:
A = 4.083π x (6/6) = (24.498π)/6 ≈ 4.083π
Therefore, the area swept by the minute hand in 5 minutes is approximately 4.083π cm².
Now, let's move on to the reason given in the question.
Reason: The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πr.
The reason states the formula for the length of an arc of a sector, which is correct. However, it is not directly related to the calculation of the area swept by the minute hand. The formula for the area of a sector was used in the explanation of the assertion.
Conclusion: Both the assertion and the reason are true, but the reason does not provide the correct explanation for the assertion. Therefore, the correct answer is option 'B'.
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πra)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer?
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πra)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πra)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πra)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer?.
Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πra)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πra)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πra)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:Assertion : The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 125/6cm2.Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πra)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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