NDA 2024 previous year paper practice · PYQ-pattern set

NDA 2024 PYQ-pattern questions

Showing 10 of the 19 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 · Algebra

   If x² - 7x + 12 = 0, then the product of the roots is:

   • A. 7
   • B. 12
   • C. -12
   • D. -7
   Answer and solution

   Answer: B

   For a quadratic equation ax² + bx + c = 0, the product of roots equals c/a. Here c/a = 12/1 = 12.

2. Q2 · Integral Calculus and Differential Equations

   The value of ∫(0 to π/2) sin x dx is:

   • A. 0
   • B. 1
   • C. π/2
   • D. 2
   Answer and solution

   Answer: B

   ∫ sin x dx = -cos x. Evaluating from 0 to π/2: [-cos(π/2)] - [-cos(0)] = 0 - (-1) = 1.

3. Q3 · Grammar and Usage

   Choose the correctly punctuated sentence:

   • A. The officer said, 'I will inspect the camp tomorrow'.
   • B. The officer said, "I will inspect the camp tomorrow."
   • C. The officer said I will inspect the camp tomorrow.
   • D. The officer said; I will inspect the camp tomorrow.
   Answer and solution

   Answer: B

   Direct speech requires quotation marks and a period inside them. Option B uses proper punctuation with double quotes and a period before the closing quote.

4. Q4 · Cohesion in Extended Text

   Arrange the following sentences in a logical sequence to form a coherent paragraph: (P) This rigorous training builds both physical endurance and mental toughness. (Q) Cadets at the National Defence Academy undergo extensive military training. (R) Eventually, they emerge as confident officers ready to serve the nation. (S) They learn leadership skills, discipline, and strategic thinking.

   • A. QPSR
   • B. QSPR
   • C. PQRS
   • D. SQPR
   Answer and solution

   Answer: B

   The logical flow is: Q introduces cadets' training, S describes what they learn, P explains the outcome of training, and R concludes with the final result. Hence QSPR is correct.

5. Q5 · Antonyms

   Select the word that is most opposite in meaning to 'TRANQUIL'.

   • A. Peaceful
   • B. Calm
   • C. Turbulent
   • D. Serene
   Answer and solution

   Answer: C

   TRANQUIL means free from disturbance or calm. The opposite is 'Turbulent', which means characterized by conflict or disorder.

6. Q6 · Cloze Test

   Fill in the blank with the most appropriate word: 'The soldier displayed remarkable _____ during the operation, refusing to retreat despite heavy fire.'

   • A. cowardice
   • B. valor
   • C. hesitation
   • D. confusion
   Answer and solution

   Answer: B

   'Valor' means great courage in the face of danger, especially in battle, which fits the context of a soldier refusing to retreat under fire.

7. Q7 · General Science (~10%)

   Which of the following organs is primarily responsible for filtering waste from the blood in the human body?

   • A. Liver
   • B. Kidneys
   • C. Heart
   • D. Lungs
   Answer and solution

   Answer: B

   The kidneys filter blood and remove waste products and excess water, which are then excreted as urine.

8. Q8 · Geography (~20%)

   The Tropic of Cancer does NOT pass through which one of the following Indian states?

   • A. Gujarat
   • B. Rajasthan
   • C. Madhya Pradesh
   • D. Uttarakhand
   Answer and solution

   Answer: D

   The Tropic of Cancer passes through Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura, and Mizoram, but not through Uttarakhand.

9. Q9 · Differential Calculus

   If y = x³ – 3x² + 5x – 7, then the value of dy/dx at x = 2 is:

   • A. 5
   • B. 9
   • C. 7
   • D. 11
   Answer and solution

   Answer: A

   Differentiate: dy/dx = 3x² - 6x + 5. At x=2: 3(4) - 6(2) + 5 = 12 - 12 + 5 = 5.

10. Q10 · Differential Calculus

    If y = x³ – 3x² + 9x – 7, then the value of dy/dx at x = 2 is:

    • A. 5
    • B. 9
    • C. 7
    • D. 11
    Answer and solution

    Answer: B

    dy/dx = 3x² – 6x + 9. At x = 2: 3(4) – 12 + 9 = 12 – 12 + 9 = 9.