Question 20 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Sept. 26, 2024 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.

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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.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 × Radius
= 𝜃/360 × (2𝜋𝑟)+2r
= 𝜋𝜽𝒓/𝟏𝟖𝟎 +𝟐𝐫
Now,
New Radius = R = r/2
New Angle = θ = 2θ
New Perimeter of sector = 𝜋𝜃𝑅/180 +2𝑅
= 𝜋2𝜃(𝑟/2)/180 +2(r/2)
= 𝝅𝜽𝒓/𝟏𝟖𝟎 +𝒓
But this not the same as original perimeter
So, Assertion is false
Checking Reason
The length of the arc subtending angle θ at the centre of a circle of radius r =𝜋𝑟𝜃/180
Formula of length of an arc is
Length of Arc = 𝜽/𝟑𝟔𝟎 × (𝟐𝝅𝒓)
= 𝜋𝑟𝜃/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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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