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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. The equation of a parabola with vertex at (0, 0) and focus at (0, 3) is?

A. x^2 = 12y
B. y^2 = 12x
C. x^2 = 6y
D. y^2 = 6x

Solution

The distance from the vertex to the focus is 3, so the equation is x^2 = 12y.

Correct Answer: A — x^2 = 12y

Q. The equation x^2 - 2x + 1 = 0 has how many distinct roots?

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

Solution

The discriminant is 0, indicating that there is exactly one distinct root.

Correct Answer: B — 1

Q. The equation x^2 - 2x + k = 0 has roots that are both positive. What is the range of k?

A. k < 0
B. k > 0
C. k > 1
D. k < 1

Solution

For both roots to be positive, k must be greater than 1 (from Vieta's formulas).

Correct Answer: C — k > 1

Q. The equation x^2 - 4x + k = 0 has equal roots when k is equal to:

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

Solution

For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0 leads to k = 4.

Correct Answer: A — 4

Q. The equation x^2 - 4x + k = 0 has no real roots if k is:

A. < 4
B. ≥ 4
C. ≤ 4
D. > 4

Solution

The discriminant must be less than zero: (-4)^2 - 4*1*k < 0 leads to k > 4.

Correct Answer: A — < 4

Q. The equation x^2 - 6x + 9 = 0 has how many distinct roots?

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

Solution

The equation can be factored as (x - 3)(x - 3) = 0, indicating it has one distinct root (a double root).

Correct Answer: B — 1

Q. The equation x^2 - 7x + 10 = 0 has roots that are:

A. 1 and 10
B. 2 and 5
C. 3 and 4
D. 5 and 2

Solution

Factoring the equation gives (x - 2)(x - 5) = 0, so the roots are 2 and 5.

Correct Answer: C — 3 and 4

Q. The equation x^3 - 3x^2 + 3x - 1 = 0 has a root at x = 1. What is the multiplicity of this root? (2023)

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

Solution

The polynomial can be expressed as (x - 1)^3, indicating that the root x = 1 has a multiplicity of 3.

Correct Answer: C — 3

Q. The equation x^3 - 3x^2 + 3x - 1 = 0 has how many distinct real roots? (2022)

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

Solution

The given polynomial can be factored as (x - 1)^3 = 0, which has one distinct real root, x = 1.

Correct Answer: A — 1

Q. The following data represents the number of books read by students in a month: 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the mode?

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

Solution

The mode is 3, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 3

Q. The following data represents the number of books read by students in a month: 4, 5, 6, 5, 4, 5, 7, 8, 5. What is the mode?

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

Solution

The mode is 5, as it appears 4 times, more than any other number.

Correct Answer: B — 5

Q. The following data set has the numbers: 2, 3, 4, 4, 5, 5, 5, 6, 7. What is the mode of this data set? (2020)

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

Solution

The number 5 appears most frequently (3 times), so the mode is 5.

Correct Answer: B — 5

Q. The following data set represents the ages of participants in a survey: 22, 25, 22, 30, 25, 22, 28. What is the mode?

A. 22
B. 25
C. 28
D. 30

Solution

The mode is 22, as it appears most frequently (three times) in the data set.

Correct Answer: A — 22

Q. The following data set shows the number of pets owned by families: 2, 3, 2, 4, 3, 2, 5. What is the mode?

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

Solution

The mode is 2, as it appears 3 times, which is more than any other number.

Correct Answer: A — 2

Q. The following data shows the number of goals scored by a team in 7 matches: 1, 2, 2, 3, 2, 4, 5. What is the mode?

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

Solution

The mode is 2, as it appears 3 times, more than any other number.

Correct Answer: B — 2

Q. The following data shows the number of pets owned by families: 0, 1, 1, 2, 2, 2, 3, 4. What is the mode?

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

Solution

The mode is 2, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 2

Q. The following data shows the number of pets owned by families: 1, 1, 2, 2, 3, 3, 3, 4. What is the mode?

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

Solution

The mode is 3, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 3

Q. The following numbers are given: 8, 3, 5, 12, 7. What is the median?

A. 5
B. 7
C. 8
D. 12

Solution

Arrange the numbers: 3, 5, 7, 8, 12. The median is the middle value, which is 7.

Correct Answer: C — 8

Q. The following numbers represent the number of books read by students: 1, 2, 2, 3, 4, 4, 4, 5. What is the mode?

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

Solution

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

Correct Answer: C — 4

Q. The following numbers represent the number of books read by students: 5, 3, 5, 2, 5, 4, 3. What is the mode?

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

Solution

The mode is 5, as it appears 4 times, which is more than any other number.

Correct Answer: D — 5

Q. The following numbers represent the number of games won by a team in a season: 5, 6, 6, 7, 8, 8, 8, 9. What is the mode?

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

Solution

The mode is 8, as it appears most frequently (3 times) in the data set.

Correct Answer: D — 8

Q. The following numbers represent the number of goals scored by a team in 10 matches: 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the mode?

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

Solution

The mode is 3, as it appears most frequently (3 times) in the data set.

Correct Answer: B — 3

Q. The following numbers represent the number of hours studied by students: 1, 2, 2, 3, 3, 4, 4, 4, 5. What is the mode?

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

Solution

The mode is 4, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 4

Q. The following numbers represent the number of hours studied by students: 5, 6, 5, 7, 8, 5, 6. What is the mode?

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

Solution

The mode is 5, as it appears 3 times, more than any other number.

Correct Answer: A — 5

Q. The following numbers represent the number of hours studied by students: 5, 6, 6, 7, 8, 8, 8, 9, 10. What is the mode?

A. 6
B. 7
C. 8
D. 9

Solution

The mode is 8, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 8

Q. The following numbers represent the number of languages spoken by individuals: 1, 2, 2, 3, 3, 3, 4, 5. What is the mode?

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

Solution

The mode is 3, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 3

Q. The following numbers represent the number of pets owned by a group of people: 0, 1, 1, 2, 2, 2, 3. What is the mode?

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

Solution

The number 2 appears 3 times, which is more than any other number, making it the mode.

Correct Answer: C — 2

Q. The following numbers represent the number of pets owned by families: 0, 1, 1, 2, 2, 2, 3, 4. What is the mode?

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

Solution

The mode is 2, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 2

Q. The following numbers represent the scores of a game: 20, 30, 20, 40, 30, 30, 50. What is the mode?

A. 20
B. 30
C. 40
D. 50

Solution

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

Correct Answer: B — 30

Q. The following numbers represent the scores of a test: 45, 55, 65, 75, 85, 95. What is the median score? (2019)

A. 65
B. 70
C. 75
D. 80

Solution

Arrange the scores: 45, 55, 65, 75, 85, 95. The median is the average of the 3rd and 4th scores: (65 + 75) / 2 = 70.

Correct Answer: C — 75

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