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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 the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the nature of its roots? (2019)

A. Real and distinct
B. Real and equal
C. Complex
D. None of the above

Solution

The discriminant is 2^2 - 4*1*1 = 0, indicating that the roots are real and equal.

Correct Answer: B — Real and equal

Q. If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the nature of the roots? (2022)

A. Real and distinct
B. Real and equal
C. Complex
D. None of the above

Solution

The discriminant is 0, indicating that the roots are real and equal.

Correct Answer: B — Real and equal

Q. If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the value of x? (2023)

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

Solution

The equation can be factored as (x + 1)^2 = 0, giving the root x = -1.

Correct Answer: A — -1

Q. If the quadratic equation x^2 + 2x + k = 0 has one root equal to -1, what is the value of k? (2022)

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

Solution

Substituting x = -1 into the equation gives (-1)^2 + 2(-1) + k = 0, leading to 1 - 2 + k = 0, thus k = 1.

Correct Answer: B — 1

Q. If the quadratic equation x^2 + 2x + k = 0 has roots 1 and -3, what is the value of k? (2022)

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

Solution

The product of the roots is 1 * (-3) = -3, hence k = -3.

Correct Answer: A — -3

Q. If the quadratic equation x^2 + 2x + k = 0 has roots that are both negative, what is the condition on k? (2023)

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

Solution

For both roots to be negative, k must be greater than 0.

Correct Answer: A — k > 0

Q. If the quadratic equation x^2 + 2x + k = 0 has roots that are both negative, what is the condition for k? (2023)

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

Solution

For both roots to be negative, k must be greater than 0.

Correct Answer: C — k > 0

Q. If the quadratic equation x^2 + 2x + k = 0 has roots that are both positive, what is the condition on k? (2019)

A. k < 0
B. k > 0
C. k < 4
D. k > 4

Solution

For both roots to be positive, k must be less than 4 (from the condition of the sum and product of roots).

Correct Answer: C — k < 4

Q. If the quadratic equation x^2 + 4x + 4 = 0 is solved, what is the nature of its roots? (2019)

A. Two distinct real roots
B. One real root
C. Two complex roots
D. No roots

Solution

The discriminant is 0, indicating one real root (a repeated root).

Correct Answer: B — One real root

Q. If the quadratic equation x^2 + 5x + 6 = 0 is solved, what is the product of the roots? (2022)

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

Solution

The product of the roots is given by c/a = 6/1 = 6.

Correct Answer: A — 6

Q. If the quadratic equation x^2 + 5x + k = 0 has one root as 2, what is the value of k? (2019)

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

Solution

Substituting x = 2 into the equation gives 2^2 + 5(2) + k = 0, leading to 4 + 10 + k = 0, thus k = -14.

Correct Answer: A — 6

Q. If the quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of its roots? (2019)

A. Two distinct real roots
B. One real root
C. Two complex roots
D. No roots

Solution

The discriminant is 0, indicating one real root (a repeated root).

Correct Answer: B — One real root

Q. If the quadratic equation x^2 + 6x + k = 0 has roots that are both positive, what is the minimum value of k? (2021)

A. 0
B. 1
C. 4
D. 9

Solution

For both roots to be positive, k must be greater than 9 (since the sum of roots is -b/a and must be positive).

Correct Answer: C — 4

Q. If the quadratic equation x^2 + 7x + k = 0 has roots that are both positive, what is the minimum value of k? (2021)

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

Solution

For both roots to be positive, k must be greater than 12 (from Vieta's formulas). The minimum integer k is 13.

Correct Answer: C — 8

Q. If the quadratic equation x^2 + kx + 16 = 0 has roots that are both real and distinct, what is the condition for k? (2022)

A. k > 8
B. k < -8
C. k > -8
D. k < 8

Solution

The discriminant must be positive: k^2 - 4*1*16 > 0, which simplifies to k^2 > 64, hence k < -8 or k > 8.

Correct Answer: B — k < -8

Q. If the quadratic equation x^2 + px + q = 0 has roots 3 and -2, what is the value of p? (2020)

A. -1
B. 1
C. 5
D. -5

Solution

Using the sum of roots formula, p = -(3 + (-2)) = -1. Therefore, p = 1.

Correct Answer: C — 5

Q. If the quadratic equation x^2 + px + q = 0 has roots 3 and -2, what is the value of p + q? (2023)

A. 1
B. 5
C. 7
D. 3

Solution

Using Vieta's formulas, p = -(3 + (-2)) = -1 and q = 3 * (-2) = -6. Therefore, p + q = -1 - 6 = -7.

Correct Answer: B — 5

Q. If the quadratic equation x^2 + px + q = 0 has roots 3 and 4, what is the value of p + q? (2023)

A. 7
B. 12
C. 10
D. 11

Solution

Using Vieta's formulas, p = -(3 + 4) = -7 and q = 3 * 4 = 12. Therefore, p + q = -7 + 12 = 5.

Correct Answer: B — 12

Q. If the quadratic equation x^2 - 10x + 25 = 0 is solved, what is the value of x? (2022)

A. 5
B. 10
C. 0
D. 25

Solution

The equation can be factored as (x - 5)^2 = 0, giving the root x = 5.

Correct Answer: A — 5

Q. If the quadratic equation x^2 - 8x + 15 = 0 is solved, what are the roots? (2022)

A. 3 and 5
B. 2 and 6
C. 1 and 7
D. 4 and 4

Solution

Factoring gives (x - 3)(x - 5) = 0, hence the roots are 3 and 5.

Correct Answer: A — 3 and 5

Q. If the radius of a circle is 7 cm, what is its circumference? (2023)

A. 14π cm
B. 21π cm
C. 28π cm
D. 35π cm

Solution

Circumference = 2πr = 2π × 7 cm = 14π cm.

Correct Answer: B — 21π cm

Q. If the radius of a circle is 7 cm, what is its circumference? (Use π ≈ 3.14)

A. 43.96 cm
B. 21.98 cm
C. 31.4 cm
D. 14 cm

Solution

Circumference = 2πr = 2 × 3.14 × 7 cm = 43.96 cm.

Correct Answer: A — 43.96 cm

Q. If the radius of a circle is 7 units, what is its circumference?

A. 14π units
B. 21π units
C. 28π units
D. 7π units

Solution

Circumference = 2 * π * radius = 2 * π * 7 = 14π units.

Correct Answer: A — 14π units

Q. If the radius of a circle is doubled, what happens to its area? (2020)

A. It remains the same
B. It doubles
C. It triples
D. It quadruples

Solution

The area of a circle is given by A = πr². If the radius is doubled (r becomes 2r), the new area is A' = π(2r)² = 4πr², which is four times the original area.

Correct Answer: D — It quadruples

Q. If the radius of a sphere is 3 cm, what is its volume? (2022)

A. 36π cm³
B. 27π cm³
C. 9π cm³
D. 18π cm³

Solution

Volume = (4/3) * π * (radius)³ = (4/3) * π * (3)³ = (4/3) * π * 27 = 36π cm³

Correct Answer: B — 27π cm³

Q. If the Rajya Sabha has 12 members nominated by the President and the total number of members is 245, how many members are elected? (2019)

A. 233
B. 235
C. 240
D. 250

Solution

Total members in Rajya Sabha = 245. Nominated members = 12. Therefore, elected members = 245 - 12 = 233.

Correct Answer: A — 233

Q. If the Rajya Sabha has 12 members nominated by the President and the total number of members is 245, what percentage of the Rajya Sabha is nominated?

A. 4.89%
B. 5.00%
C. 6.12%
D. 7.14%

Solution

Percentage of nominated members = (12/245) * 100 = 4.89%.

Correct Answer: B — 5.00%

Q. If the Rajya Sabha has 12 members nominated by the President and the total number of members is 245, what percentage of the Rajya Sabha members are nominated?

A. 4.89%
B. 5.00%
C. 6.12%
D. 7.14%

Solution

Percentage of nominated members = (12 / 245) * 100 = 4.89%.

Correct Answer: B — 5.00%

Q. If the Rajya Sabha has 12 nominated members and the total number of members is 245, what percentage of the Rajya Sabha members are nominated?

A. 4.89%
B. 5.00%
C. 6.12%
D. 7.14%

Solution

Percentage of nominated members = (12 / 245) * 100 = 4.89%.

Correct Answer: B — 5.00%

Q. If the Rajya Sabha has 12 nominated members and the total number of members is 245, how many members are elected?

A. 233
B. 232
C. 230
D. 240

Solution

Total members = 245, Nominated members = 12. Therefore, Elected members = 245 - 12 = 233.

Correct Answer: A — 233

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