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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. If a wire carries a current of 4 A and has a resistance of 2 ohms, what is the power dissipated in the wire?

A. 8 W
B. 16 W
C. 4 W
D. 2 W

Solution

Power (P) is given by P = I^2 * R. Thus, P = (4 A)^2 * 2 Ω = 16 W.

Correct Answer: B — 16 W

Q. If a woman with blood type A (genotype AO) has a child with a man with blood type B (genotype BO), what are the possible blood types of their child?

A. A, B, AB, O
B. A, B, AB
C. A, O
D. B, O

Solution

The possible blood types from AO x BO are A, B, AB, and O.

Correct Answer: A — A, B, AB, O

Q. If B = [[1, 0, 2], [0, 1, 3], [0, 0, 1]], what is the rank of matrix B?

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

Solution

The rank of matrix B is the number of non-zero rows in its row echelon form, which is 3.

Correct Answer: C — 3

Q. If B = [[2, 3], [5, 7]], what is the value of det(B)? (2020)

A. -1
B. 1
C. 7
D. 1

Solution

The determinant of B is calculated as (2*7) - (3*5) = 14 - 15 = -1.

Correct Answer: A — -1

Q. If C = [[1, 0, 0], [0, 1, 0], [0, 0, 0]], what is the determinant of C? (2022)

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

Solution

The determinant of C is 0 because it has a row of zeros.

Correct Answer: B — 0

Q. If C = [[1, 0, 2], [-1, 3, 1], [2, 1, 0]], find det(C).

A. -9
B. 9
C. 0
D. 6

Solution

Using the determinant formula for 3x3 matrices, det(C) = 1(3*0 - 1*1) - 0 + 2(-1*1 - 3*2) = 0 - 0 - 12 = -12.

Correct Answer: A — -9

Q. If C = [[1, 0, 2], [0, 1, 3], [0, 0, 1]], what is det(C)? (2019)

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

Solution

The determinant of an upper triangular matrix is the product of its diagonal elements. Here, det(C) = 1 * 1 * 1 = 1.

Correct Answer: B — 1

Q. If C = [[1, 2], [3, 5]], find C^2.

A. [[7, 14], [21, 35]]
B. [[11, 28], [15, 35]]
C. [[11, 16], [18, 35]]
D. [[11, 16], [15, 25]]

Solution

C^2 = C * C = [[1*1 + 2*3, 1*2 + 2*5], [3*1 + 5*3, 3*2 + 5*5]] = [[11, 16], [18, 35]].

Correct Answer: C — [[11, 16], [18, 35]]

Q. If cos A = 5/13, what is the value of tan A?

A. 12/5
B. 5/12
C. 13/5
D. 5/13

Solution

Using the identity tan A = sin A / cos A, we find sin A = √(1 - cos²A) = √(1 - (5/13)²) = 12/13. Thus, tan A = (12/13) / (5/13) = 12/5.

Correct Answer: A — 12/5

Q. If cos B = 0.6, what is the value of sin B?

A. 0.8
B. 0.6
C. 0.4
D. 0.2

Solution

Using the Pythagorean identity, sin B = √(1 - cos²B) = √(1 - 0.6²) = √(1 - 0.36) = √(0.64) = 0.8.

Correct Answer: A — 0.8

Q. If cos B = 1/2, what is the value of angle B in degrees?

A. 30°
B. 60°
C. 90°
D. 120°

Solution

Cosine of 60° is 1/2, hence angle B = 60°.

Correct Answer: B — 60°

Q. If cos B = 5/13, what is the value of sin B?

A. 12/13
B. 5/13
C. 13/5
D. 3/5

Solution

Using the Pythagorean identity, sin B = √(1 - cos²B) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13.

Correct Answer: A — 12/13

Q. If cos C = 0.5, what is the value of angle C in degrees?

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

Solution

The angle C for which cos C = 0.5 is 60°.

Correct Answer: B — 60

Q. If cot A = 1, what is the value of A? (2022)

A. 45°
B. 90°
C. 60°
D. 30°

Solution

Cotangent is 1 when the angle A is 45°, as cot A = cos A/sin A = 1 when both are equal.

Correct Answer: A — 45°

Q. If cot A = 3/4, what is the value of sin A?

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

Solution

cot A = cos A/sin A = 3/4 implies sin A = 4/5 using the identity sin²A + cos²A = 1.

Correct Answer: A — 3/5

Q. If cot D = 3/4, what is the value of sin D?

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

Solution

cot D = 3/4 implies tan D = 4/3. Therefore, sin D = 4/5 (using the identity sin²D + cos²D = 1).

Correct Answer: A — 3/5

Q. If cot θ = 1, what is the value of θ?

A. 0°
B. 45°
C. 90°
D. 180°

Solution

cot θ = 1 implies tan θ = 1, which occurs at θ = 45°.

Correct Answer: B — 45°

Q. If D = [[2, 1], [1, 2]], what is the trace of D?

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

Solution

The trace of a matrix is the sum of its diagonal elements. Trace(D) = 2 + 2 = 4.

Correct Answer: C — 3

Q. If D = [[4, 2], [1, 3]], find the inverse of D. (2022)

A. [[3, -2], [-1, 4]]
B. [[3, 2], [-1, 4]]
C. [[3, -2], [1, 4]]
D. [[4, -2], [-1, 3]]

Solution

The inverse of D is given by (1/det(D)) * adj(D). Here, det(D) = (4*3) - (2*1) = 10, and adj(D) = [[3, -2], [-1, 4]]. Thus, D^(-1) = (1/10) * [[3, -2], [-1, 4]].

Correct Answer: A — [[3, -2], [-1, 4]]

Q. If D = [[4, 2], [1, 3]], what is the inverse of D?

A. [[3, -2], [-1, 4]]
B. [[3, 2], [-1, 4]]
C. [[4, -2], [-1, 3]]
D. [[3, -4], [1, 2]]

Solution

The inverse of D is given by (1/det(D)) * adj(D). Here, det(D) = (4*3) - (2*1) = 10. The adjugate is [[3, -2], [-1, 4]]. Thus, D^(-1) = (1/10) * [[3, -2], [-1, 4]].

Correct Answer: A — [[3, -2], [-1, 4]]

Q. If E = [[1, 2], [2, 4]], what can be said about the matrix E? (2023)

A. Invertible
B. Singular
C. Non-square
D. Diagonal

Solution

Matrix E is singular because its determinant is 0 (1*4 - 2*2 = 0).

Correct Answer: B — Singular

Q. If F = [[1, 0], [0, 1]], what is F^(-1)?

A. [[1, 0], [0, 1]]
B. [[0, 1], [1, 0]]
C. [[1, 1], [1, 1]]
D. [[0, 0], [0, 0]]

Solution

The inverse of the identity matrix F is itself, so F^(-1) = F.

Correct Answer: A — [[1, 0], [0, 1]]

Q. If F = [[1, 2], [2, 4]], what is the determinant of F? (2021)

A. 0
B. 1
C. 2
D. 4

Solution

The determinant of F is calculated as (1*4) - (2*2) = 4 - 4 = 0.

Correct Answer: A — 0

Q. If F = [[1, 2], [2, 4]], what is the rank of F?

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

Solution

The second row is a multiple of the first row, so there is only one linearly independent row. Therefore, the rank of F is 1.

Correct Answer: A — 1

Q. If F = [[1, 2], [3, 5]], what is the trace of F? (2020)

A. 3
B. 5
C. 6
D. 8

Solution

The trace of F is the sum of the diagonal elements: 1 + 5 = 6.

Correct Answer: D — 8

Q. If f(x) = 3x + 2, what is the value of f(1) and is it continuous?

A. 5, Continuous
B. 5, Not Continuous
C. 3, Continuous
D. 3, Not Continuous

Solution

f(1) = 3(1) + 2 = 5. Since f(x) is a linear function, it is continuous everywhere.

Correct Answer: A — 5, Continuous

Q. If f(x) = 3x + 2, what is the value of f(2) and is it continuous?

A. 8, Continuous
B. 8, Discontinuous
C. 7, Continuous
D. 7, Discontinuous

Solution

f(2) = 3(2) + 2 = 8. Since f(x) is a polynomial, it is continuous everywhere.

Correct Answer: A — 8, Continuous

Q. If f(x) = 3x^2 + 2x, what is f'(2)? (2023)

A. 10
B. 14
C. 12
D. 8

Solution

First, find f'(x) = 6x + 2. Then, f'(2) = 6(2) + 2 = 12 + 2 = 14.

Correct Answer: A — 10

Q. If f(x) = 4x^3 - 2x^2 + x, what is f''(x)?

A. 24x - 4
B. 12x - 2
C. 12x - 4
D. 24x - 2

Solution

First, find f'(x) = 12x^2 - 4x + 1, then differentiate again to get f''(x) = 24x - 4.

Correct Answer: A — 24x - 4

Q. If f(x) = 5x^2 + 3x - 1, what is f''(x)? (2020)

A. 10
B. 5
C. 0
D. 3

Solution

The first derivative f'(x) = 10x + 3, and the second derivative f''(x) = 10.

Correct Answer: A — 10

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