Class 10 Exam > Class 10 Questions > Directions: In the following questions, A st...
Start Learning for Free
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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.
Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.
- 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 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Directions: In the following questions, A statement of Assertion (A) ...
In the case of assertion
View all questions of this test
Let r1 = 24 cm and r2 = 7 cm
Area of first circle = πr12 = π(24)2 = 576π cm2
Area of second circle = πr22 =π(7)2 = 49π cm2
According to question,
Area of circle = Area of first circle + Area of second circle
πR2 = 576π +49π
[where, R be radius of circle]
R2 = 625 =25 cm
Diameter of a circle = 2R = 2 × 25 = 50 cm.
∴ Assertion is correct.
In case of reason:
Let the radius of the circle be r.
Circumference of circle = 2πr
Area of circle = πr2
Given that, the circumference of the circle and the area of the circle are equal. This implies, 2πr = pπ2
r = 2
Therefore, the radius of the circle is 2 units.
∴ Reason is correct.
Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
Assertion (A): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.
Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.
Correct Answer: Option B - Both A and R are true but R is NOT the correct explanation of A
Explanation:
Let's analyze the assertion and reason separately to understand why the correct answer is option B.
Assertion (A): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.
To find the diameter of the circle, we need to find its area first. The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
The area of the first circle with a radius of 24 cm is A1 = π(24)^2 = 576π cm^2.
The area of the second circle with a radius of 7 cm is A2 = π(7)^2 = 49π cm^2.
The sum of the areas of these two circles is A1 + A2 = 576π + 49π = 625π cm^2.
Now, let's find the diameter of the circle whose area is equal to the sum of the areas of these two circles. The formula for the area of a circle is A = πr^2, where r is the radius of the circle. Rearranging the formula, we get r = √(A/π).
The radius of the circle with an area of 625π cm^2 is r = √(625π/π) = √625 = 25 cm.
Therefore, the diameter of this circle is 2r = 2(25) = 50 cm.
Hence, assertion (A) is true.
Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.
The reason given is not relevant to the assertion. The relationship between the perimeter and the area of a circle is not being discussed in the assertion. Therefore, reason (R) is not the correct explanation of assertion (A).
Hence, the correct answer is option B - Both A and R are true but R is NOT the correct explanation of A.
Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.
Correct Answer: Option B - Both A and R are true but R is NOT the correct explanation of A
Explanation:
Let's analyze the assertion and reason separately to understand why the correct answer is option B.
Assertion (A): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.
To find the diameter of the circle, we need to find its area first. The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
The area of the first circle with a radius of 24 cm is A1 = π(24)^2 = 576π cm^2.
The area of the second circle with a radius of 7 cm is A2 = π(7)^2 = 49π cm^2.
The sum of the areas of these two circles is A1 + A2 = 576π + 49π = 625π cm^2.
Now, let's find the diameter of the circle whose area is equal to the sum of the areas of these two circles. The formula for the area of a circle is A = πr^2, where r is the radius of the circle. Rearranging the formula, we get r = √(A/π).
The radius of the circle with an area of 625π cm^2 is r = √(625π/π) = √625 = 25 cm.
Therefore, the diameter of this circle is 2r = 2(25) = 50 cm.
Hence, assertion (A) is true.
Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.
The reason given is not relevant to the assertion. The relationship between the perimeter and the area of a circle is not being discussed in the assertion. Therefore, reason (R) is not the correct explanation of assertion (A).
Hence, the correct answer is option B - Both A and R are true but R is NOT the correct explanation of A.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 'B'. Can you explain this answer?
Question Description
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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 '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 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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 '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 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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 'B'. 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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 '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 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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 '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 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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 'B'. 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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 'B'. Can you explain this answer?, a detailed solution 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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 'B'. Can you explain this answer? has been provided alongside types of 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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 'B'. Can you explain this answer? theory, EduRev gives you an
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): The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.Reason (R): If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units.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 'B'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup