Question 20 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards
Last updated at August 6, 2026 by Teachoo
Question 20
Statement A (Assertion):
If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same.
Statement R (Reason)
:
The length of the arc subtending angle θ at the centre of a circle of radius r =πrθ/180
(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 and 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.
Question 20 Statement A (Assertion): If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same. Statement R (Reason): The length of the arc subtending angle Īø at the centre of a circle of radius r =ššš/180 (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 and 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.Checking Assertion
If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same.
Now,
Perimeter of sector = Length of arc + 2 Ć Radius
= š/360 Ć (2šš)+2r
= šš½š/ššš +šš«
Now,
New Radius = R = r/2
New Angle = Īø = 2Īø
New Perimeter of sector = ššš /180 +2š
= š2š(š/2)/180 +2(r/2)
= š š½š/ššš +š
But this not the same as original perimeter
So, Assertion is false
Checking Reason
The length of the arc subtending angle Īø at the centre of a circle of radius r =ššš/180
Formula of length of an arc is
Length of Arc = š½/ššš Ć (šš š)
= ššš/180
Which same as mentioned in reasoning
Thus, Reason is true.
So,
Assertion is false
Reasoning is true
So, the correct answer is (d)
Made by
Davneet Singh
Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.
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