RRB ALP CBT I 11 Feb 2026 Shift 1 Paper

Concept:The perimeter of a sector is the sum of its arc length and two radii, while the circumference of the whole circle is the perimeter of the full $360^\circ$ arc.Explanation:Let the radius of the circle be $r$.The circumference of the circle is $C = 2\pi r$.The arc length of a sector with central angle $\theta = 30^\circ$ is given by$$\text{Arc length} = \frac{\theta}{360^\circ} \times 2\pi r = \frac{30}{360} \times 2\pi r = \frac{1}{12} \times 2\pi r = \frac{\pi r}{6}.$$The perimeter of the sector is$$P = \text{Arc length} + 2r = \frac{\pi r}{6} + 2r = r\left(\frac{\pi}{6} + 2\right) = r\left(\frac{\pi + 12}{6}\right).$$Therefore, the required ratio is$$C : P = 2\pi r : r\left(\frac{\pi + 12}{6}\right).$$Cancelling $r$ from both terms,$$C : P = 2\pi : \frac{\pi + 12}{6}.$$Multiplying both sides by $6$ gives$$C : P = 12\pi : (\pi + 12).$$Substitute $\pi = 3.14$:$$12\pi = 12 \times 3.14 = 37.68, \quad \pi + 12 = 3.14 + 12 = 15.14.$$Thus,$$C : P = 37.68 : 15.14.$$Multiplying by $100$ to remove decimals,$$C : P = 3768 : 1514.$$Dividing both terms by $2$,$$C : P = 1884 : 757.$$Hence, the ratio of the circumference of the circle to the perimeter of the sector is $1884 : 757$.Answer:$1884 : 757$ Therefore, Option D is the correct answer.