SSC CGL 2024 Tier-I · 12 September 2024, Shift 3 · Quantitative Aptitude · Question 25 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

If the sectorial angle with radius 9.6 units is 75°, what is the length of the arc?

(a)2π
(b)4π
(c)π
(d)3π

Answer

Why

Correct — B. An arc is the angle's share of the whole circumference: arc = (θ⁄360) × 2πr.

θ⁄360 = 75⁄360 = 5⁄24
2πr = 2 × π × 9.6 = 19.2π
Arc = (5⁄24) × 19.2π
19.2 ÷ 24 = 0.8, and 0.8 × 5 = 4

So the arc is 4π units → option (b).

Why the others are wrong

(a)
2π — 2π is exactly what (75⁄360) × πr gives. The circumference is 2πr, not πr, and dropping that factor of 2 halves every arc you compute.
(c)
π — For the arc to come to π the angle would have to be 18.75°, a quarter of the 75° given. Five twenty-fourths of 19.2π cannot fall that low.
(d)
3π — 3π answers for an angle of 56.25°, not 75°. Multiplying 19.2 by 5⁄24 gives exactly 4, and no rounding step turns a 4 into a 3.

Concept

An arc is a fraction of its circle, and the fraction is θ⁄360. Multiply that by the circumference 2πr and the length follows.

With r = 9.6 the circumference is 19.2π, and 75° is 5⁄24 of a full turn, so the arc is 4π. The numbers are chosen so that 19.2 × 5⁄24 lands on a whole number.

In radians the same statement is shorter: arc = rθ, with 75° = 5π⁄12 radians, giving 9.6 × 5π⁄12 = 4π.

The radius is given in units rather than centimetres and π is left in the answer, so no decimal approximation is wanted here.

Key facts

Arc length = (θ⁄360) × 2πr in degrees, or rθ with θ measured in radians.
75⁄360 reduces to 5⁄24, so a 75° arc is five twenty-fourths of the circumference.
A radius of 9.6 gives a circumference of 19.2π.
(5⁄24) × 19.2π = 4π.

Study next

Area of a sector, and the segment left once the chord is removedConverting degrees to radians so that arc = rθ can be used directlyPerimeter of a sector, where the two radii are added to the arc

Common traps

Using πr in place of 2πr for the circumference, which returns 2π.
Computing the sector area instead, which here is also 19.2π and looks deceptively like the circumference.
Adding the two radii, which answers for the perimeter of the sector rather than the arc.

The angle and radius are picked so the arc is a clean multiple of π, which lets you check the fraction rather than a decimal. The same sector geometry is asked numerically at 12 Sep 2024, 16:00, Quant Q.20, where π is fixed at 3.14 and the two radii must be added in.

Related PYQs

No directly related past PYQ was found.