NDA 2025 previous year paper · official paper and PYQ-pattern practice

NDA 2025 PYQ-pattern questions

Showing 10 of the 20 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · Trigonometry

   If sin θ + cos θ = √2, then the value of sin θ · cos θ is:

   • A. 1/2
   • B. 1
   • C. √2
   • D. 1/4
   Answer and solution

   Answer: A

   Squaring both sides: (sin θ + cos θ)² = 2, thus sin²θ + cos²θ + 2 sin θ cos θ = 2. Since sin²θ + cos²θ = 1, we get 1 + 2 sin θ cos θ = 2, giving sin θ cos θ = 1/2.

2. Q2 · Algebra

   If the sum of the first n natural numbers is 210, then n equals:

   • A. 18
   • B. 20
   • C. 19
   • D. 21
   Answer and solution

   Answer: B

   Sum of first n natural numbers = n(n+1)/2 = 210. Thus n(n+1) = 420. Solving: n² + n - 420 = 0 gives n = 20.

3. Q3 · Probability

   A bag contains 5 red balls, 4 blue balls, and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are of different colours?

   • A. 41/66
   • B. 47/66
   • C. 25/66
   • D. 19/66
   Answer and solution

   Answer: B

   Total balls = 12. Total ways to draw 2 balls = C(12,2) = 66. Same colour pairs: C(5,2) + C(4,2) + C(3,2) = 10+6+3 = 19. Different colour pairs = 66-19 = 47. Probability = 47/66.

4. Q4 · Sentence Improvement

   Choose the best alternative to improve the underlined part: The commanding officer emphasized that discipline is the backbone to a successful military career.

   • A. backbone to
   • B. backbone of
   • C. backbone for
   • D. backbone in
   Answer and solution

   Answer: B

   The correct idiomatic expression is 'backbone of', not 'backbone to'. Option B provides the grammatically correct improvement.

5. Q5 · Synonyms

   Choose the word that is most similar in meaning to the word 'ZEALOUS'.

   • A. Indifferent
   • B. Enthusiastic
   • C. Lazy
   • D. Reluctant
   Answer and solution

   Answer: B

   ZEALOUS means showing great energy or enthusiasm in pursuit of a cause or objective, which is closest in meaning to 'Enthusiastic'.

6. Q6 · Sentence Arrangement / Para Jumbles

   Arrange the following sentences in proper sequence to form a meaningful paragraph: 1. However, discipline alone cannot guarantee success. 2. Discipline is the foundation of all great achievements. 3. One must also possess creativity and adaptability. 4. These qualities together lead to holistic development.

   • A. 2, 1, 3, 4
   • B. 1, 2, 3, 4
   • C. 2, 3, 1, 4
   • D. 3, 2, 1, 4
   Answer and solution

   Answer: A

   The correct sequence is 2-1-3-4: Starting with discipline as foundation, then stating its limitation, adding other qualities needed, and concluding with the combined effect.

7. Q7 · Chemistry (~15%)

   Which one of the following is NOT a noble gas?

   • A. Helium
   • B. Neon
   • C. Nitrogen
   • D. Argon
   Answer and solution

   Answer: C

   Nitrogen is not a noble gas; it belongs to group 15 of the periodic table, whereas noble gases (He, Ne, Ar, Kr, Xe, Rn) are in group 18.

8. Q8 · History, Freedom Movement (~20%)

   Which session of the Indian National Congress in 1929 declared 'Purna Swaraj' (complete independence) as its goal?

   • A. Calcutta Session
   • B. Lahore Session
   • C. Karachi Session
   • D. Lucknow Session
   Answer and solution

   Answer: B

   The Lahore Session of the Indian National Congress in 1929, under the presidency of Jawaharlal Nehru, adopted the resolution for Purna Swaraj.

9. Q9 · Analytical Geometry of Two and Three Dimensions

   Find the equation of the circle passing through the origin and having its center at (3, 4).

   • A. x² + y² – 6x – 8y = 0
   • B. x² + y² + 6x + 8y = 0
   • C. x² + y² – 3x – 4y = 0
   • D. x² + y² + 3x + 4y = 0
   Answer and solution

   Answer: A

   Radius = √(3² + 4²) = 5. Circle equation: (x – 3)² + (y – 4)² = 25 expands to x² + y² – 6x – 8y = 0.

10. Q10 · Probability

    Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the two dice is 9?

    • A. 1/9
    • B. 1/6
    • C. 1/12
    • D. 5/36
    Answer and solution

    Answer: A

    Favorable outcomes for sum = 9: (3,6), (4,5), (5,4), (6,3) = 4 outcomes. Total outcomes = 36. Probability = 4/36 = 1/9.