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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 vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector A + B? (2019)

A. 3i + 5j
B. 5i + j
C. 3i + j
D. 5i + 5j

Solution

A + B = (4 - 1)i + (3 + 2)j = 3i + 5j.

Correct Answer: A — 3i + 5j

Q. If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector R = A + B? (2019)

A. 3i + 5j
B. 5i + j
C. 3i + j
D. 5i + 5j

Solution

R = A + B = (4 - 1)i + (3 + 2)j = 3i + 5j.

Correct Answer: A — 3i + 5j

Q. If vector A = 4i + 3j and vector B = 3i + 4j, what is the angle between A and B?

A. 45 degrees
B. 60 degrees
C. 90 degrees
D. 135 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (12 + 12) / (5 * 5) = 24/25, θ = cos^(-1)(24/25) ≈ 60 degrees.

Correct Answer: B — 60 degrees

Q. If vector A = 4i + 3j and vector B = 4i - 3j, what is the angle between A and B? (2019)

A. 0 degrees
B. 90 degrees
C. 180 degrees
D. 45 degrees

Solution

A · B = 16 - 9 = 7. |A| = 5, |B| = 5. cos(θ) = 7/(5*5) = 0.28, θ = 180 degrees.

Correct Answer: C — 180 degrees

Q. If vector A = 5i + 12j and vector B = -5i + 12j, what is the angle between them?

A. 0 degrees
B. 90 degrees
C. 180 degrees
D. 45 degrees

Solution

A · B = (5)(-5) + (12)(12) = -25 + 144 = 119. Since A and B are in opposite directions, the angle is 180 degrees.

Correct Answer: C — 180 degrees

Q. If vector A = 5i + 12j and vector B = -5i + 12j, what is the resultant vector A + B? (2021)

A. 0i + 24j
B. 10i + 0j
C. 0i + 12j
D. 5i + 12j

Solution

A + B = (5 - 5)i + (12 + 12)j = 0i + 24j.

Correct Answer: A — 0i + 24j

Q. If vector A = 5i + 12j and vector B = 12i - 5j, what is the angle between A and B?

A. 30 degrees
B. 60 degrees
C. 90 degrees
D. 120 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (5*12 + 12*(-5)) / (√(169) * √(169)) = 0, θ = 90 degrees.

Correct Answer: C — 90 degrees

Q. If vector A = 5i + 12j and vector B = 12i - 5j, what is the value of A × B?

A. -85
B. 85
C. 0
D. 60

Solution

A × B = |i  j  k| |5  12  0| |12 -5  0| = (0 - 0)i - (0 - 0)j + (5*-5 - 12*12)k = -85k.

Correct Answer: A — -85

Q. If vector A = 5i + 12j and vector B = 5i - 12j, what is the angle between A and B?

A. 0 degrees
B. 90 degrees
C. 180 degrees
D. 45 degrees

Solution

A · B = 5*5 + 12*(-12) = 25 - 144 = -119. Since A · B < 0, angle is 180 degrees.

Correct Answer: C — 180 degrees

Q. If vector A = 5i + 5j and vector B = 5i - 5j, what is the angle between A and B?

A. 0 degrees
B. 45 degrees
C. 90 degrees
D. 180 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (25 - 25) / (√(50) * √(50)) = 0, θ = 90 degrees.

Correct Answer: C — 90 degrees

Q. If vector A = 5i + 5j and vector B = 5i - 5j, what is the angle between them?

A. 0 degrees
B. 45 degrees
C. 90 degrees
D. 135 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (25 - 25) / (5√2 * 5√2) = 0, θ = 90 degrees.

Correct Answer: C — 90 degrees

Q. If vector A = 6i + 8j, what is the unit vector in the direction of A? (2023)

A. 3/5 i + 4/5 j
B. 6/10 i + 8/10 j
C. 1/5 i + 2/5 j
D. 2/5 i + 3/5 j

Solution

Magnitude |A| = √(6^2 + 8^2) = 10. Unit vector = (1/10)(6i + 8j) = (3/5)i + (4/5)j.

Correct Answer: A — 3/5 i + 4/5 j

Q. If vector G = 4i - 3j + 2k, what is the y-component of G?

A. 4
B. -3
C. 2
D. 0

Solution

The y-component of G is -3.

Correct Answer: B — -3

Q. If vector J = 5i + 12j, what is the angle between J and the positive x-axis?

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

Solution

tan(θ) = 12/5; θ = tan^(-1)(12/5) which is approximately 67.38 degrees, closest to 60 degrees.

Correct Answer: C — 60 degrees

Q. If vector K = 2i + 2j and vector L = -i + 3j, what is the resultant vector K + L?

A. i + 5j
B. i + j
C. 3i + 5j
D. 3i + j

Solution

K + L = (2i + 2j) + (-i + 3j) = (2 - 1)i + (2 + 3)j = 1i + 5j = i + 5j.

Correct Answer: A — i + 5j

Q. If vectors A = 3i + 4j and B = 2i - j, what is the dot product A · B?

A. -1
B. 2
C. 10
D. 11

Solution

A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.

Correct Answer: C — 10

Q. If vectors A and B are perpendicular, then A · B equals:

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

Solution

If A and B are perpendicular, then by definition A · B = |A||B|cos(90°) = 0.

Correct Answer: A — 0

Q. If x + y = 10 and xy = 21, what is the value of x^2 + y^2? (2021)

A. 49
B. 59
C. 61
D. 41

Solution

We know that x^2 + y^2 = (x + y)^2 - 2xy. Substituting the values, we get (10)^2 - 2(21) = 100 - 42 = 58.

Correct Answer: A — 49

Q. If x + y = 10 and xy = 21, what is the value of x² + y²?

A. 49
B. 59
C. 61
D. 41

Solution

x² + y² = (x + y)² - 2xy = 10² - 2*21 = 100 - 42 = 58.

Correct Answer: A — 49

Q. If x = -3, what is the value of |x| + x?

A. 0
B. -3
C. -6
D. -9

Solution

|-3| = 3, so |x| + x = 3 - 3 = 0.

Correct Answer: B — -3

Q. If x = -5, what is the value of |x|?

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

Solution

The absolute value |x| of -5 is 5.

Correct Answer: C — 5

Q. If x = 1/2, what is the value of 1/x? (2022)

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

Solution

1/x = 1/(1/2) = 2.

Correct Answer: A — 2

Q. If x = 3 and y = 4, what is the value of x² + y²?

A. 25
B. 20
C. 15
D. 12

Solution

x² + y² = 3² + 4² = 9 + 16 = 25.

Correct Answer: A — 25

Q. If x = 3, what is the value of 2x^2 + 3x - 5?

A. 10
B. 12
C. 14
D. 16

Solution

Substituting x = 3 into the expression: 2(3^2) + 3(3) - 5 = 2(9) + 9 - 5 = 18 + 9 - 5 = 22.

Correct Answer: B — 12

Q. If x = 4 and y = 5, what is the value of x² - y²?

A. -9
B. 9
C. 20
D. 1

Solution

x² - y² = 4² - 5² = 16 - 25 = -9.

Correct Answer: B — 9

Q. If x = 4, what is the value of 2x - 3? (2022)

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

Solution

2x - 3 = 2(4) - 3 = 8 - 3 = 5.

Correct Answer: C — 7

Q. If x = 4, what is the value of 3x - 2? (2019)

A. 10
B. 12
C. 14
D. 16

Solution

3x - 2 = 3(4) - 2 = 12 - 2 = 10.

Correct Answer: B — 12

Q. If x = 5, what is the value of (x - 1)²?

A. 16
B. 20
C. 25
D. 36

Solution

(x - 1)² = (5 - 1)² = 4² = 16.

Correct Answer: A — 16

Q. If x^2 - 5x + 6 = 0, what are the values of x? (2019)

A. 2, 3
B. 1, 6
C. 3, 2
D. 0, 6

Solution

Factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.

Correct Answer: A — 2, 3

Q. If z = -1 + i, what is the square of the modulus of z?

A. 2
B. 1
C. 3
D. 5

Solution

The modulus of z = -1 + i is |z| = √((-1)² + 1²) = √(1 + 1) = √2. The square of the modulus is |z|² = 2.

Correct Answer: D — 5

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