NDA 2021 previous year paper practice · PYQ-pattern set

NDA 2021 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 · Differential Calculus

   If f(x) = x³ - 6x² + 9x + 1, then the critical points of f(x) are at x equal to:

   • A. 1, 2
   • B. 1, 3
   • C. 2, 3
   • D. 0, 3
   Answer and solution

   Answer: B

   Critical points occur when f'(x) = 0. f'(x) = 3x² - 12x + 9 = 0 ⇒ x² - 4x + 3 = 0 ⇒ (x-1)(x-3) = 0, so x = 1 or 3.

2. Q2 · Comprehension

   Read the passage: 'The naval exercises conducted in the Indian Ocean were aimed at enhancing strategic coordination among allied forces. The drills focused on anti-submarine warfare and maritime security.' What was the PRIMARY objective of the exercises?

   • A. To test new weapon systems
   • B. To improve strategic coordination among allied forces
   • C. To patrol international waters
   • D. To conduct research on marine life
   Answer and solution

   Answer: B

   The passage explicitly states that the exercises were 'aimed at enhancing strategic coordination among allied forces,' making option B the correct answer.

3. Q3 · Fill in the Blanks

   Choose the pair of words that best completes the sentence: The cadet's _______ to follow orders without question is a _______ of good military training.

   • A. reluctance – sign
   • B. ability – hallmark
   • C. failure – result
   • D. hesitation – proof
   Answer and solution

   Answer: B

   The sentence requires positive words. 'Ability' (capacity to do something) and 'hallmark' (distinguishing feature) fit the context of commendable military training. Option B is correct.

4. Q4 · Spelling Check

   Identify the correctly spelled word.

   • A. Recieve
   • B. Receeve
   • C. Receive
   • D. Recive
   Answer and solution

   Answer: C

   The correct spelling is 'Receive'. It follows the rule 'i before e, except after c'.

5. Q5 · Physics (~25%)

   Which of the following is a vector quantity?

   • A. Speed
   • B. Distance
   • C. Velocity
   • D. Mass
   Answer and solution

   Answer: C

   Velocity is a vector quantity as it has both magnitude and direction. Speed, distance, and mass are scalar quantities having only magnitude.

6. Q6 · General Science (~10%)

   According to Newton's Third Law of Motion, for every action there is an equal and opposite reaction. Which one of the following best illustrates this principle?

   • A. A car accelerating on a highway
   • B. A swimmer pushing water backward and moving forward
   • C. A ball rolling down a slope
   • D. A stone falling under gravity
   Answer and solution

   Answer: B

   When a swimmer pushes water backward (action), the water pushes the swimmer forward (reaction), demonstrating Newton's third law.

7. Q7 · Current Events (~10%)

   The International Day of United Nations Peacekeepers is observed annually on which date?

   • A. May 15
   • B. May 29
   • C. June 5
   • D. June 21
   Answer and solution

   Answer: B

   The International Day of United Nations Peacekeepers is observed on May 29 each year to honor UN peacekeepers who have served and lost their lives.

8. Q8 · Statistics

   The mean of the numbers 4, 6, 8, 10, and 12 is:

   • A. 7
   • B. 8
   • C. 9
   • D. 10
   Answer and solution

   Answer: B

   Mean = (4 + 6 + 8 + 10 + 12) / 5 = 40 / 5 = 8.

9. Q9 · Grammar and Usage

   Fill in the blank with the most appropriate option: 'The officer, along with his subordinates, _____ attending the ceremony.'

   • A. is
   • B. are
   • C. were
   • D. have been
   Answer and solution

   Answer: A

   The subject 'The officer' is singular, and 'along with his subordinates' is a phrase that does not change the number. Hence 'is' is correct.

10. Q10 · Fill in the Blanks

    Fill in the blank with the most appropriate word: The captain's __________ leadership inspired the team to achieve victory against all odds.

    • A. weak
    • B. exemplary
    • C. ordinary
    • D. negligent
    Answer and solution

    Answer: B

    'Exemplary' means serving as a desirable model, which fits the context of leadership that inspires a team to victory.