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Defence Exams

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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. For vectors A = 2i + j and B = 3i + 4j, what is the scalar product A · B?

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

Solution

A · B = (2)(3) + (1)(4) = 6 + 4 = 10.

Correct Answer: A — 14

Q. For vectors A = 4i + 3j and B = 3i - 4j, find A · B.

A. -6
B. 0
C. 6
D. 12

Solution

A · B = (4)(3) + (3)(-4) = 12 - 12 = 0.

Correct Answer: A — -6

Q. For vectors A = 6i + 8j and B = 2i + 3j, find A · B.

A. 42
B. 48
C. 36
D. 30

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: A — 42

Q. For which value of c is the function f(x) = { x^2, x < 1; c, x = 1; 2x, x > 1 } continuous at x = 1? (2022)

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

Solution

To make f(x) continuous at x = 1, we need c = 1^2 = 1. Thus, c must be 1.

Correct Answer: B — 2

Q. For which value of k does the equation x^2 + kx + 16 = 0 have equal roots? (2019)

A. -8
B. -4
C. 4
D. 8

Solution

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0. Solving gives k = -8.

Correct Answer: B — -4

Q. For which value of k is the function f(x) = kx + 2 continuous at x = 3? (2023)

A. k = 0
B. k = 1
C. k = -1
D. k = 2

Solution

The function f(x) = kx + 2 is a linear function and is continuous for all k at x = 3.

Correct Answer: B — k = 1

Q. For which value of k is the function f(x) = { kx + 1, x < 2; 3, x >= 2 } continuous at x = 2?

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

Solution

To be continuous at x = 2, k(2) + 1 must equal 3. Thus, 2k + 1 = 3, leading to k = 1.

Correct Answer: B — 2

Q. For which value of k is the function f(x) = { kx + 1, x < 2; 3, x = 2; 2x - 1, x > 2 } continuous at x = 2?

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

Solution

To ensure continuity at x = 2, k(2) + 1 must equal 3. Thus, k = 1.

Correct Answer: B — 2

Q. For which value of k is the function f(x) = { kx + 1, x < 2; 3, x ≥ 2 } continuous at x = 2? (2019)

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

Solution

To be continuous at x = 2, k(2) + 1 must equal 3. Thus, 2k + 1 = 3, giving k = 1.

Correct Answer: B — 2

Q. From a deck of 52 cards, how many ways can you choose 5 cards?

A. 2598960
B. 1001
C. 3125
D. 1024

Solution

The number of ways to choose 5 cards from 52 is 52C5 = 2598960.

Correct Answer: A — 2598960

Q. From a group of 8 people, how many ways can a team of 3 be selected? (2022)

A. 56
B. 24
C. 36
D. 48

Solution

The number of ways to choose 3 people from 8 is given by 8C3 = 56.

Correct Answer: A — 56

Q. From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill? (2022)

A. 173.21 m
B. 100 m
C. 200 m
D. 150 m

Solution

Distance = height / tan(30) = 100 / (1/√3) = 100√3 ≈ 173.21 m.

Correct Answer: A — 173.21 m

Q. From the top of a 100 m high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building? (2020)

A. 50 m
B. 100 m
C. 150 m
D. 200 m

Solution

Distance = height / tan(angle) = 100 / tan(45) = 100 / 1 = 100 m.

Correct Answer: B — 100 m

Q. From the top of a 50 m high tower, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the tower? (2022)

A. 50 m
B. 100 m
C. 75 m
D. 25 m

Solution

Using tan(30) = 1/√3, distance = height * √3 = 50 * √3 ≈ 86.60 m, which rounds to 100 m.

Correct Answer: B — 100 m

Q. From the top of a tower, the angle of depression to a point on the ground is 45 degrees. If the height of the tower is 100 meters, how far is the point from the base of the tower? (2020)

A. 100 m
B. 50 m
C. 70 m
D. 80 m

Solution

Using tan(45) = 1, Distance = Height = 100 m.

Correct Answer: A — 100 m

Q. Given A = 1i + 1j and B = 1i + 1j, what is A · B?

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

Solution

A · B = (1)(1) + (1)(1) = 1 + 1 = 2.

Correct Answer: A — 2

Q. Given A = 2i + 2j and B = 3i + 3j, what is the scalar product A · B?

A. 12
B. 18
C. 10
D. 14

Solution

A · B = (2)(3) + (2)(3) = 6 + 6 = 12.

Correct Answer: A — 12

Q. Given the data set 8, 8, 9, 10, 10, 10, 11, 12, what is the mode?

A. 8
B. 9
C. 10
D. 11

Solution

The mode is 10, as it appears 3 times, which is more than any other number.

Correct Answer: C — 10

Q. Given the data set: 1, 1, 2, 3, 4, 4, 4, 5, 5, what is the mode?

A. 1
B. 2
C. 4
D. 5

Solution

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

Correct Answer: C — 4

Q. Given vectors A = 2i + 2j and B = 3i + 4j, what is the value of A · B?

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

Solution

A · B = (2)(3) + (2)(4) = 6 + 8 = 14.

Correct Answer: A — 14

Q. Given vectors A = 4i + 2j and B = -i + 3j, calculate A · B.

A. 6
B. 10
C. 8
D. 12

Solution

A · B = (4)(-1) + (2)(3) = -4 + 6 = 2.

Correct Answer: C — 8

Q. Given vectors A = 4i + 3j and B = 1i + 2j, calculate A · B.

A. 10
B. 11
C. 12
D. 13

Solution

A · B = (4)(1) + (3)(2) = 4 + 6 = 10.

Correct Answer: A — 10

Q. Given vectors A = i + 2j + 3k and B = 2i + 3j + 4k, calculate A · B.

A. 20
B. 22
C. 24
D. 26

Solution

A · B = (1)(2) + (2)(3) + (3)(4) = 2 + 6 + 12 = 20.

Correct Answer: C — 24

Q. Given vectors A = i + 2j + 3k and B = 4i + 5j + 6k, calculate A · B.

A. 32
B. 30
C. 28
D. 34

Solution

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.

Correct Answer: B — 30

Q. Given vectors A = i + 2j + 3k and B = 4i + 5j + 6k, find A · B. (2019)

A. 32
B. 34
C. 36
D. 38

Solution

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32

Correct Answer: B — 34

Q. Given vectors A = i + 2j and B = 3i + 4j, calculate A · B. (2022)

A. 11
B. 10
C. 12
D. 13

Solution

A · B = (1)(3) + (2)(4) = 3 + 8 = 11.

Correct Answer: A — 11

Q. How many degrees of longitude correspond to a time difference of 1 hour? (2022)

A. 15°
B. 30°
C. 45°
D. 60°

Solution

1 hour corresponds to 15° of longitude since the Earth rotates 360° in 24 hours.

Correct Answer: A — 15°

Q. How many degrees of longitude correspond to a time difference of 2 hours?

A. 30°
B. 15°
C. 45°
D. 60°

Solution

A time difference of 1 hour corresponds to 15° of longitude, so 2 hours = 2 * 15° = 30°.

Correct Answer: B — 15°

Q. How many degrees of longitude correspond to a time difference of 4 hours? (2022)

A. 60 degrees
B. 45 degrees
C. 30 degrees
D. 15 degrees

Solution

A time difference of 4 hours corresponds to 4 * 15 = 60 degrees of longitude.

Correct Answer: A — 60 degrees

Q. How many different ways can 4 students be selected from a class of 10?

A. 210
B. 120
C. 240
D. 300

Solution

The number of ways to choose 4 students from 10 is 10C4 = 210.

Correct Answer: A — 210

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