SSC CGL Quant – Trigonometry – Tier II Level · Marathon | Online Quiz

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SSC CGL Quant – Trigonometry – Tier II Level · Marathon – 13 questions, subject: Quantitative Aptitude. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

The maximum value of 8 sin θ + 15 cos θ is:

Correct Answer: B [17]

Explanation:

√(8² + 15²) = √289 = 17.

The minimum value of 16 tan² θ + 9 cot² θ is:

Correct Answer: A [24]

Explanation:

2√(16 × 9) = 2 × 12 = 24 (AM ≥ GM).

The minimum value of 3 sin² θ + 5 cos² θ is:

Correct Answer: C [3]

Explanation:

= 3 + 2 cos² θ, and cos² θ ≥ 0 → minimum 3 (at θ = 90°).

The value of tan 15° is:

Correct Answer: D [2 − √3]

Explanation:

tan(45° − 30°) = (1 − 1/√3)/(1 + 1/√3) = 2 − √3.

If tan θ + cot θ = 2 (θ acute), then tan¹⁰ θ + cot¹⁰ θ equals:

Correct Answer: D [2]

Explanation:

Only tan θ = 1 works → 1 + 1 = 2.

Using sin(A + B) = sin A cos B + cos A sin B, find sin 75°.

Correct Answer: C [(√6 + √2)/4]

Explanation:

sin 45° cos 30° + cos 45° sin 30° = (√3 + 1)/(2√2) = (√6 + √2)/4.

A man walks towards a tower at a steady speed. The angle of elevation of its top changes from 30° to 60° in 12 minutes. How much more time will he take to reach the tower?

Correct Answer: A [6 minutes]

Explanation:

30-60 Ladder: the remaining distance is half the gap walked → 12/2 = 6 min.

A kite is flying on a string 100 m long. The string makes 60° with the ground (assume it is straight). The height of the kite is:

Correct Answer: B [50√3 m]

Explanation:

h = 100 × sin 60° = 50√3 m.

From a point on the ground, the angle of elevation of the top of a 20 m building is 30° and of the top of a flagstaff on it is 45°. The length of the flagstaff is:

Correct Answer: D [20(√3 − 1) m]

Explanation:

Distance = 20√3; top of flag = 20√3 × tan 45° = 20√3 → flag = 20√3 − 20 m.

10.

If x = a sec θ and y = b tan θ, then x²/a² − y²/b² equals:

Correct Answer: C [1]

Explanation:

sec² θ − tan² θ = 1.

11.

If sec θ + tan θ = 2, then sin θ equals:

Correct Answer: B [3/5]

Explanation:

sin θ = (p² − 1)/(p² + 1) = 3/5.

12.

If cosec θ + cot θ = 5, then cos θ equals:

Correct Answer: A [12/13]

Explanation:

cos θ = (p² − 1)/(p² + 1) = 24/26 = 12/13.

13.

If cosec θ − sin θ = l and sec θ − cos θ = m, then l²m²(l² + m² + 3) equals:

Correct Answer: B [1]

Explanation:

l = cos² θ/sin θ, m = sin² θ/cos θ → l²m² = sin² θ cos² θ and l² + m² + 3 = 1/(sin² θ cos² θ) → product 1.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude

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