SSC CGL 2025 Tier-I · 14 September 2025, Shift 3 · Quantitative Aptitude · Question 18 of 95

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

Convert 2.5 radians to degrees.

(a)130°
(b)143.24°
(c)180°
(d)200.56°

Answer

Why

Correct — B.
Rule: degrees = radians × 180⁄π, because π radians = 180°.

Multiply by 180: 2.5 × 180 = 450
Divide by π: 450 ÷ 3.14159 = 143.239…
Round to two decimals: 143.24° → option (b)

Why the others are wrong

(a)
130° — 130° is only 130 × π⁄180 ≈ 2.27 radians. It falls short of 2.5 rad by about 0.23 rad, roughly 13°.
(c)
180° — 180° is π radians, about 3.14 rad. 2.5 rad is less than π, so its degree value must be under 180°.
(d)
200.56° — 200.56° is about 3.5 radians (200.56 × π⁄180 ≈ 3.50). That is a full radian more than the 2.5 given, about 57.3° too many.

Concept

A radian is the angle at the centre of a circle when the arc equals the radius. A full turn holds 2π radians, so π rad = 180° and 1 rad = 180⁄π ≈ 57.3°.

To go from radians to degrees, multiply by 180⁄π. To go back, multiply by π⁄180. A quick estimate, 2.5 × 57.3 ≈ 143°, already sits next to 143.24° and far from 130°, 180° and 200.56°.

The printed 143.24 needs π ≈ 3.1416. With π = 22⁄7 the same working gives 3150⁄22 ≈ 143.18°, still nearest to 143.24°.

Key facts

π radians = 180°, so 1 radian = 180⁄π ≈ 57.3°.
Radians to degrees: multiply by 180⁄π. Degrees to radians: multiply by π⁄180.
2.5 radians = 450⁄π degrees ≈ 143.24°.
A radian is the central angle whose arc length equals the radius.

Study next

Degrees to radians: multiply by π⁄180, so 225° = 5π⁄4Arc length s = rθ with θ in radiansSector area ½r²θ with θ in radians

Common traps

Multiplying by π⁄180 instead of 180⁄π, which turns 2.5 into about 0.044 rather than 143.24.
Using π = 22⁄7, getting 143.18, and then doubting the printed 143.24: pick the nearest value.

The stem gives a decimal radian value with no π in it, so the division by π has to be done by hand. Radian-to-degree conversion is also asked 12 Sep 2025, 12:30, Quant Q.17 (5π⁄4 radians = 225°), and Quant Q.19 of this sitting gives its sector angle in radians.

Related PYQs

No directly related past PYQ was found.

Topic: Trigonometric ratio, Degree and Radian Measures, Standard Identities, Complementary angles, Heights and Distances — all 131 SSC CGL questions on it, every solved shift.