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Defence Exams MCQ & Objective Questions

Defence Exams play a crucial role in shaping the future of aspiring candidates in India. These exams not only assess knowledge but also test the ability to apply concepts in real-world scenarios. Practicing MCQs and objective questions is essential for effective exam preparation, as it helps students identify important questions and enhances their understanding of key topics.

What You Will Practise Here

Fundamentals of Defence Studies
Key Historical Events and Their Impact
Important Defence Policies and Strategies
Current Affairs Related to National Security
Basic Concepts of Military Operations
Understanding Defence Technologies
Analysing Defence Budget and Expenditure

Exam Relevance

The topics covered in Defence Exams are highly relevant across various educational boards, including CBSE and State Boards, as well as competitive exams like NEET and JEE. Students can expect questions that focus on historical events, current affairs, and fundamental concepts related to defence. Common question patterns include multiple-choice questions that assess both theoretical knowledge and practical application.

Common Mistakes Students Make

Overlooking current affairs, which are often integrated into exam questions.
Confusing similar historical events or dates, leading to incorrect answers.
Neglecting the importance of definitions and key terms in objective questions.
Relying solely on rote memorization instead of understanding concepts.

FAQs

Question: What types of questions can I expect in Defence Exams?
Answer: You can expect a mix of MCQs covering historical events, current affairs, and fundamental concepts related to defence.

Question: How can I improve my performance in Defence Exams?
Answer: Regular practice of MCQs and understanding key concepts will significantly enhance your performance.

Start your journey towards success by solving practice MCQs today! Testing your understanding will not only boost your confidence but also prepare you for the important Defence Exams ahead.

NDA

Q. Calculate the median of the following set: 1, 2, 3, 4, 5, 6, 7, 8. (2020)

A. 4
B. 4.5
C. 5
D. 6

Solution

Arranging the numbers: 1, 2, 3, 4, 5, 6, 7, 8. The median is the average of the 4th and 5th numbers: (4 + 5) / 2 = 4.5.

Correct Answer: B — 4.5

Q. Calculate the median of the following set: 22, 19, 25, 30, 28, 24.

A. 24
B. 25
C. 26
D. 27

Solution

Arrange the numbers: 19, 22, 24, 25, 28, 30. The median is the average of the 3rd and 4th values: (24 + 25) / 2 = 24.5.

Correct Answer: A — 24

Q. Calculate the variance for the following data: 2, 4, 4, 4, 5, 5, 7, 9. (2019)

A. 4
B. 5
C. 6
D. 7

Solution

Mean = 5. Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 4.

Correct Answer: B — 5

Q. Calculate the variance for the following data: 3, 7, 7, 19. (2022)

A. 20
B. 25
C. 30
D. 35

Solution

Mean = (3 + 7 + 7 + 19) / 4 = 9. Variance = [(3-9)² + (7-9)² + (7-9)² + (19-9)²] / 4 = 25.

Correct Answer: B — 25

Q. Calculate the variance for the following data: 5, 7, 9, 11. (2022)

A. 2.5
B. 3.5
C. 4.0
D. 5.0

Solution

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 3.5.

Correct Answer: B — 3.5

Q. Calculate the variance of the following numbers: 1, 2, 3, 4, 5. (2022)

A. 2
B. 1.5
C. 1
D. 0.5

Solution

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

Correct Answer: B — 1.5

Q. Consider the data set: 4, 4, 4, 5, 6, 6, 7, 8. What is the mode?

A. 4
B. 5
C. 6
D. 7

Solution

The mode is 4, as it appears 3 times, more than any other number.

Correct Answer: A — 4

Q. Consider the data set: 5, 6, 7, 8, 8, 9, 9, 10. What is the mode?

A. 5
B. 6
C. 8
D. 9

Solution

The mode is 8 and 9, but since we need to select one, we can choose 8 as it appears first.

Correct Answer: C — 8

Q. Consider the following data set: 10, 20, 20, 30, 40, 30, 30. What is the mode?

A. 10
B. 20
C. 30
D. 40

Solution

The mode is 30, as it appears three times, which is more than any other number.

Correct Answer: C — 30

Q. Consider the following data set: 5, 6, 6, 7, 8, 8, 8, 9. What is the mode?

A. 5
B. 6
C. 7
D. 8

Solution

The number 8 appears 3 times, which is more than any other number, making it the mode.

Correct Answer: D — 8

Q. Consider the following numbers: 1, 2, 2, 3, 4, 4, 4, 5. What is the mode?

A. 1
B. 2
C. 3
D. 4

Solution

The mode is 4, which appears most frequently (three times).

Correct Answer: D — 4

Q. Determine the angle between the lines y = 2x + 1 and y = -1/2x + 3. (2021)

A. 90 degrees
B. 45 degrees
C. 60 degrees
D. 30 degrees

Solution

The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|) = tan⁻¹(5/3), which is approximately 90 degrees.

Correct Answer: A — 90 degrees

Q. Determine the coefficient of x^5 in the expansion of (3x - 4)^7.

A. 252
B. 336
C. 672
D. 840

Solution

The coefficient of x^5 in (3x - 4)^7 is C(7, 5) * (3)^5 * (-4)^2 = 21 * 243 * 16 = 68016.

Correct Answer: A — 252

Q. Determine the continuity of the function f(x) = { x^2, x < 1; 2, x = 1; x + 1, x > 1 } at x = 1.

A. Continuous
B. Not continuous
C. Depends on the limit
D. Only left continuous

Solution

The left limit as x approaches 1 is 1, the right limit is 2, and f(1) = 2. Since the left and right limits do not match, f(x) is not continuous at x = 1.

Correct Answer: B — Not continuous

Q. Determine the continuity of the function f(x) = { x^2, x < 1; 2x - 1, x ≥ 1 } at x = 1.

A. Continuous
B. Discontinuous
C. Only left continuous
D. Only right continuous

Solution

At x = 1, f(1) = 2(1) - 1 = 1 and lim x→1- f(x) = 1, lim x→1+ f(x) = 1. Thus, f(x) is continuous at x = 1.

Correct Answer: A — Continuous

Q. Determine the continuity of the function f(x) = |x| at x = 0. (2020)

A. Continuous
B. Not continuous
C. Depends on the limit
D. Only left continuous

Solution

The function f(x) = |x| is continuous at x = 0 since both the left-hand limit and right-hand limit equal f(0) = 0.

Correct Answer: A — Continuous

Q. Determine the critical points of the function f(x) = x^2 - 4x + 4. (2022)

A. 0
B. 1
C. 2
D. 3

Solution

f'(x) = 2x - 4; Setting f'(x) = 0 gives x = 2 as the critical point.

Correct Answer: C — 2

Q. Determine the derivative of f(x) = x^3 - 4x + 7. (2023)

A. 3x^2 - 4
B. 3x^2 + 4
C. x^2 - 4
D. 3x^2 - 7

Solution

Using the power rule, f'(x) = 3x^2 - 4.

Correct Answer: A — 3x^2 - 4

Q. Determine the derivative of f(x) = x^5 - 3x^3 + 2x. (2023)

A. 5x^4 - 9x^2 + 2
B. 5x^4 - 9x + 2
C. 5x^4 - 3x^2 + 2
D. 5x^4 - 3x^3

Solution

Using the power rule, f'(x) = 5x^4 - 9x^2 + 2.

Correct Answer: A — 5x^4 - 9x^2 + 2

Q. Determine the distance between the points (-1, -1) and (2, 2).

A. 3
B. 4
C. 5
D. 6

Solution

Using the distance formula: d = √[(2 - (-1))² + (2 - (-1))²] = √[(2 + 1)² + (2 + 1)²] = √[9 + 9] = √18 = 3√2 ≈ 4.24.

Correct Answer: C — 5

Q. Determine the distance between the points (0, 0) and (0, 8).

A. 8
B. 6
C. 4
D. 2

Solution

Using the distance formula: d = √[(0 - 0)² + (8 - 0)²] = √[0 + 64] = √64 = 8.

Correct Answer: A — 8

Q. Determine the distance between the points (1, 2) and (4, 6). (2022)

A. 5
B. 4
C. 3
D. 6

Solution

Using the distance formula: d = √[(4 - 1)² + (6 - 2)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

Q. Determine the distance between the points (2, 3) and (2, -1).

A. 4
B. 5
C. 3
D. 2

Solution

Using the distance formula: d = √[(2 - 2)² + (-1 - 3)²] = √[0 + 16] = √16 = 4.

Correct Answer: A — 4

Q. Determine the distance from the point (1, 2) to the line 2x + 3y - 6 = 0. (2023)

A. 1
B. 2
C. 3
D. 4

Solution

Using the formula for distance from a point to a line, the distance is |2(1) + 3(2) - 6| / sqrt(2^2 + 3^2) = 1.

Correct Answer: B — 2

Q. Determine the local maxima and minima of f(x) = x^2 - 4x + 3.

A. Maxima at x=2
B. Minima at x=2
C. Maxima at x=1
D. Minima at x=1

Solution

f'(x) = 2x - 4. Setting f'(x) = 0 gives x = 2. f''(x) = 2 > 0 indicates a local minimum at x = 2.

Correct Answer: B — Minima at x=2

Q. Determine the local maxima and minima of f(x) = x^4 - 8x^2 + 16. (2023)

A. Maxima at x = 0
B. Minima at x = 2
C. Maxima at x = 2
D. Minima at x = 0

Solution

f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x = 0, ±2. f''(x) = 12x^2 - 16. Minima at x = 0.

Correct Answer: D — Minima at x = 0

Q. Determine the local maxima of f(x) = -x^2 + 4x. (2022)

A. (2, 4)
B. (0, 0)
C. (4, 0)
D. (1, 1)

Solution

f'(x) = -2x + 4. Setting f'(x) = 0 gives x = 2. f(2) = -2^2 + 4(2) = 4.

Correct Answer: A — (2, 4)

Q. Determine the local maxima or minima of f(x) = -x^2 + 4x. (2019)

A. Maxima at x=2
B. Minima at x=2
C. Maxima at x=4
D. Minima at x=4

Solution

f'(x) = -2x + 4. Setting f'(x) = 0 gives x = 2. Since f''(x) = -2 < 0, it is a maxima.

Correct Answer: A — Maxima at x=2

Q. Determine the maximum value of f(x) = -2x^2 + 4x + 1. (2023)

A. 1
B. 2
C. 3
D. 4

Solution

The vertex is at x = -4/(2*(-2)) = 1. The maximum value is f(1) = -2(1)^2 + 4(1) + 1 = 3.

Correct Answer: C — 3

Q. Determine the maximum value of f(x) = -x^2 + 4x. (2020)

A. 4
B. 8
C. 16
D. 0

Solution

f'(x) = -2x + 4. Setting f'(x) = 0 gives x = 2. f(2) = -2^2 + 4(2) = 8.

Correct Answer: A — 4

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