NDA · Mathematics · UPSC · 2025

Trigonometric Functions — NDA Mathematics PYQs

19 questions from this chapter, asked in 1 NDA exams between 2025.

19questions

1NDA exams

2025years covered

Questions asked per year

202519 Qs

Practice questions first 10 of 19 — free

Q1MCQ2025

Answer Logic

Consider the following for the three (03) items that follow :
Let $p = sin 35°$ , $q = sin 25°$ and $r = sin (- 95°)$ .

What is $(p + q + r)$ equal to?

(A)

- 1

(B)

0

(C)

2 sin 5°

(D)

2 cos 5°

Q2MCQ2025

Answer Logic

Consider the following for the three (03) items that follow :
Let $p = sin 35°$ , $q = sin 25°$ and $r = sin (- 95°)$ .

What is $(pq + q r + r p)$ equal to?

(A)

- \frac{3}{4}

(B)

0

(C)

\frac{1}{4}

(D)

\frac{3}{4}

Q3MCQ2025

Answer Logic

Consider the following for the three (03) items that follow :
Let $p = sin 35°$ , $q = sin 25°$ and $r = sin (- 95°)$ .

What is $(p^{2} + q^{2} + r^{2})$ equal to?

(A)

\frac{1}{2}

(B)

1

(C)

\frac{3}{2}

(D)

2

Q4MCQ2025

Answer Logic

Consider the following for the two (02) items that follow :
Let $p = ∣ sin α - sin (α - 90°) ∣$ .

What is the minimum value of $p$ ?

(A)

0

(B)

\frac{1}{2}

(C)

\frac{1}{2}

(D)

1

Q5MCQ2025

Answer Logic

Consider the following for the two (02) items that follow :
Let $p = ∣ sin α - sin (α - 90°) ∣$ .

What is the maximum value of $p$ ?

(A)

1

(B)

2

(C)

3

(D)

2

Q6MCQ2025

Answer Logic

Consider the following for the three (03) items that follow :
Let $p = tan 2 α - tan α$ and $q = cot α - cot 2 α$ .

What is $\frac{p}{q}$ equal to?

(A)

- tan α \cdot tan 2 α

(B)

- cot α \cdot cot 2 α

(C)

tan α \cdot tan 2 α

(D)

cot α \cdot cot 2 α

Q7MCQ2025

Answer Logic

Consider the following for the three (03) items that follow :
Let $p = tan 2 α - tan α$ and $q = cot α - cot 2 α$ .

What is $(p + q)$ equal to?

(A)

sec 4 α

(B)

cosec 4 α

(C)

2 sec 4 α

(D)

2 cosec 4 α

Q8MCQ2025

Answer Logic

Consider the following for the three (03) items that follow :
Let $p = tan 2 α - tan α$ and $q = cot α - cot 2 α$ .

What is $tan^{2} α$ equal to?

(A)

\frac{pq}{p + q}

(B)

\frac{p + 2 q}{p}

(C)

\frac{p}{p + 2 q}

(D)

\frac{p}{2 p + q}

Q9MCQ2025

Answer Logic

Consider the following for the two (02) items that follow :
Let $2 sin α + cos α = 2$ , where $0 < α < 90°$ .

What is $tan α$ equal to?

(A)

\frac{1}{2}

(B)

1

(C)

\frac{3}{4}

(D)

2

Q10MCQ2025

Answer Logic

Consider the following for the two (02) items that follow :
Let $2 sin α + cos α = 2$ , where $0 < α < 90°$ .

What is $2 sin 2 α + cos 2 α$ equal to?

(A)

\frac{11}{10}

(B)

\frac{11}{5}

(C)

\frac{12}{5}

(D)

\frac{13}{5}

Why practise Trigonometric Functions PYQs?

Trigonometric Functions has appeared in the 1 NDA Mathematics exam we track between 2025. UPSC examiners consistently reuse concepts and question patterns from this topic — practising its previous year questions is the most reliable way to know exactly what to expect in your exam.

Trigonometric Functions — NDA Mathematics PYQs

Questions asked per year

Practice questions first 10 of 19 — free

Why practise Trigonometric Functions PYQs?

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