Assertion Reasoning Quiz

Assertion (A):
\( \pi \) is an irrational number and cannot be written exactly as a ratio of two integers.
Reason (R):
The value of \( \pi \) is exactly equal to \( \frac{22}{7} \).

Assertion: In the same circle, an arc subtending \(120^\circ\) at the centre is twice as long as an arc subtending \(60^\circ\).
Reason: The length of an arc of radius \(r\) and central angle \(\theta\) is \[l=2\pi r\times\frac{\theta}{360^\circ}.\]

Assertion (A):
The perimeter of a quarter circle (quadrant) of radius \( r \) is exactly \( \frac{\pi r}{2} \).
Reason (R):
The boundary of a sector of a circle includes both the length of the circular arc and the two straight bounding radii.

Assertion: If every side of a triangle is multiplied by \(3\), its area becomes \(9\) times the original area.
Reason: The perimeter of the enlarged triangle becomes \(3\) times the original perimeter.

Assertion: A sector with central angle \(\theta\) occupies the fraction \[\frac{\theta}{360^\circ}\] of the circle’s area, and its arc has the same fraction of the circle’s circumference.
Reason: A sector is a region bounded only by an arc of a circle.