SSC CGL 2025 Tier-I · 20 September 2025, Shift 1 · 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.

Where this paper and its answers come from

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.

IfcotA = 7⁄24, then what is cosecA?

(a)25⁄24
(b)24⁄25
(c)25⁄7
(d)25⁄25

Answer

Why

Correct — A.
cot A = adjacent ⁄ opposite = 7⁄24
Take adjacent = 7, opposite = 24
Hypotenuse = √(7² + 24²) = √(49 + 576) = √625 = 25

cosec A = hypotenuse ⁄ opposite = 25⁄24 → option (a)

Identity check: cosec²A = 1 + cot²A = 1 + 49⁄576 = 625⁄576, so cosec A = 25⁄24

Why the others are wrong

(b)
24⁄25 — 24⁄25 is opposite ⁄ hypotenuse, which is sin A — the reciprocal of cosec A. It is also below 1, and cosec A is never between −1 and 1.
(c)
25⁄7 — 25⁄7 is hypotenuse ⁄ adjacent, which is sec A. Cosec puts the side opposite A, 24, in the denominator.
(d)
25⁄25 — 25⁄25 equals 1, and cosec A = 1 only when A = 90°, where cot A = 0 — not 7⁄24.

Concept

The six ratios come in reciprocal pairs: sin and cosec, cos and sec, tan and cot. Given one ratio, draw a right triangle with those two sides, find the third by Pythagoras, and read off any other ratio.

7, 24, 25 is a Pythagorean triple, so the hypotenuse comes out whole. The identity cosec²A = 1 + cot²A reaches the same answer without the triangle.

The stem does not say A is acute. cot A is also positive in the third quadrant, where cosec A would be −25⁄24. No choice is negative, so the acute-angle reading is the intended one. The sheet itself prints the last choice as 25⁄25.

Key facts

cot A = adjacent ⁄ opposite and cosec A = hypotenuse ⁄ opposite
cosec²A − cot²A = 1
7² + 24² = 25², since 49 + 576 = 625
sin A and cosec A are reciprocals, so cosec A is never between −1 and 1

Study next

Finding sin A, cos A and sec A from a single given ratioThe identities sec²A = 1 + tan²A and cosec²A = 1 + cot²ASigns of trigonometric ratios in the four quadrants

Common traps

Putting the adjacent side, 7, under the hypotenuse, which gives sec A = 25⁄7
Stopping at sin A = 24⁄25 and forgetting that cosec is its reciprocal

18 Sep 2025, 12:30, Quant Q.22 gives cot A = 2 and asks for sin A − cos A: the same triangle method (sides 2, 1, √5) gives the keyed −1⁄√5. 17 Sep 2025, 16:00, Quant Q.22 uses the identity instead: cot A = x + 1⁄x gives cosec²A = x² + 1⁄x² + 3.

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.