NDA 2023 previous year paper practice · PYQ-pattern set

NDA 2023 PYQ-pattern questions

Showing 10 of the 18 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 · Matrices and Determinants

   If matrix A = [[2, 3], [1, 4]], then the value of det(A) is:

   • A. 5
   • B. 8
   • C. 11
   • D. 6
   Answer and solution

   Answer: A

   For a 2×2 matrix [[a, b], [c, d]], determinant = ad - bc = (2)(4) - (3)(1) = 8 - 3 = 5.

2. Q2 · Vector Algebra

   If vector a = 2i + 3j and vector b = i + 4j, then a · b (dot product) is:

   • A. 14
   • B. 10
   • C. 12
   • D. 8
   Answer and solution

   Answer: A

   Dot product a · b = (2)(1) + (3)(4) = 2 + 12 = 14.

3. Q3 · Probability

   A fair die is rolled twice. What is the probability that the sum of the two numbers obtained is 9?

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

   Answer: A

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

4. Q4 · Spotting Errors

   Identify the part of the sentence that contains an error: (A) The cadets were / (B) asked to assembled / (C) in the parade ground / (D) at six o'clock sharp.

   • A. The cadets were
   • B. asked to assembled
   • C. in the parade ground
   • D. at six o'clock sharp
   Answer and solution

   Answer: B

   The error is in part B. After 'to', the base form 'assemble' should be used, not 'assembled'. The correct phrase is 'asked to assemble'.

5. Q5 · Idioms and Phrases

   Choose the correct meaning of the idiom: 'To burn the midnight oil'.

   • A. To waste resources
   • B. To work late into the night
   • C. To celebrate excessively
   • D. To be angry at someone
   Answer and solution

   Answer: B

   The idiom 'To burn the midnight oil' means to work late into the night, typically studying or completing tasks.

6. Q6 · Physics (~25%)

   A body of mass 5 kg is moving with a velocity of 10 m/s. What is its kinetic energy?

   • A. 150 J
   • B. 250 J
   • C. 500 J
   • D. 50 J
   Answer and solution

   Answer: B

   Kinetic energy = ½mv². Substituting: KE = ½ × 5 × (10)² = ½ × 5 × 100 = 250 J.

7. Q7 · Chemistry (~15%)

   The process of rusting of iron in the presence of moisture and oxygen is an example of which type of reaction?

   • A. Decomposition reaction
   • B. Displacement reaction
   • C. Oxidation reaction
   • D. Neutralization reaction
   Answer and solution

   Answer: C

   Rusting of iron is an oxidation reaction where iron reacts with oxygen and moisture to form iron oxide (rust).

8. Q8 · Geography (~20%)

   Which one of the following pairs of river and its source is correctly matched?

   • A. Ganga – Gangotri Glacier
   • B. Brahmaputra – Milam Glacier
   • C. Godavari – Amarkantak
   • D. Narmada – Mahabaleshwar
   Answer and solution

   Answer: A

   The Ganga originates from the Gangotri Glacier in Uttarakhand. Brahmaputra originates from Angsi Glacier in Tibet, Godavari from Trimbakeshwar, and Narmada from Amarkantak.

9. Q9 · Integral Calculus and Differential Equations

   The value of ∫(3x² + 4x) dx is:

   • A. x³ + 2x² + C
   • B. x³ + 4x² + C
   • C. 3x³ + 2x² + C
   • D. x³/3 + 2x² + C
   Answer and solution

   Answer: A

   ∫(3x² + 4x) dx = 3(x³/3) + 4(x²/2) + C = x³ + 2x² + C.

10. Q10 · Analytical Geometry of Two and Three Dimensions

    The distance between the points A(2, 3) and B(5, 7) is:

    • A. 5
    • B. 4
    • C. 3
    • D. 6
    Answer and solution

    Answer: A

    Distance = √[(5–2)² + (7–3)²] = √(9 + 16) = √25 = 5.