SSC CGL 2025 Tier-I · 12 September 2025, Shift 2 · Quantitative Aptitude · Question 17 of 100

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.

What is 5π⁄4 radians in degrees?

(a)225°
(b)180°
(c)240°
(d)360°

Answer

Why

Correct — A. π radians = 180°, so radians turn into degrees on multiplying by 180°⁄π.

Multiply: 5π⁄4 × 180°⁄π
Cancel π: 5 × 180° ÷ 4
= 900° ÷ 4 = 225° → option (a)

Why the others are wrong

(b)
180° — 180° is π radians. 5π⁄4 is π plus π⁄4, so it lies 45° beyond 180°.
(c)
240° — 240° is 4π⁄3 radians (240 × π⁄180), which is 15° more than 5π⁄4.
(d)
360° — 360° is 2π radians, a full turn. 5π⁄4 is only 1.25π, so it is less than 360°.

Concept

Radians and degrees measure the same angle in different units. A full turn is 2π radians = 360°, so π radians = 180°.

Degrees = radians × 180⁄π, and radians = degrees × π⁄180.

For multiples of π⁄4, each π⁄4 is 45°: 5π⁄4 is five of them, 5 × 45° = 225°, which lies between 180° and 270°.

Key facts

π radians = 180°, so 1 radian = 180°⁄π ≈ 57.3°.
π⁄6 = 30°, π⁄4 = 45°, π⁄3 = 60° and π⁄2 = 90°.
5π⁄4 = 225°, an angle between 180° and 270°.

Study next

Arc length s = rθ with θ in radiansSector area when the angle is given in radiansTrigonometric values of angles between 180° and 270°

Common traps

Multiplying by π⁄180 instead of 180⁄π: that is the degrees-to-radians factor, and here it gives 5π²⁄720, not an angle in degrees.
Taking 5π⁄4 as 5⁄4 of a full turn (360°) instead of 5⁄4 of π (180°), which gives 450°.

The same conversion decides sector comparisons: on 17 Sep 2025, 16:00, Quant Q.17 the first sector has a central angle of 180° and the second one of π⁄2 radians (90°), both of radius 12 cm, so first : second = 2 : 1.

On 18 Sep 2025, 12:30, Quant Q.17 the two angles are 120° and 2π⁄3 radians, which are the same angle, so the ratio is 1 : 1.

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.