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

A. 27
B. 23
C. 22
D. 20

Solution

First, find f'(x) = 10x + 3. Then, f'(2) = 10(2) + 3 = 20 + 3 = 23.

Correct Answer: A — 27

Q. If f(x) = 5x^2 - 3x + 7, what is f''(x)? (2020)

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

Solution

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

Correct Answer: A — 10

Q. If f(x) = e^x + x^2, what is f'(0)? (2021)

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

Solution

f'(x) = e^x + 2x. Thus, f'(0) = e^0 + 2(0) = 1 + 0 = 1.

Correct Answer: A — 1

Q. If f(x) = e^x, what is f''(x)? (2020)

A. e^x
B. xe^x
C. 2e^x
D. 0

Solution

The second derivative f''(x) = d^2/dx^2(e^x) = e^x.

Correct Answer: A — e^x

Q. If f(x) = e^x, what is the value of f''(0)? (2021)

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

Solution

f'(x) = e^x and f''(x) = e^x. Therefore, f''(0) = e^0 = 1.

Correct Answer: A — 1

Q. If f(x) = ln(x), what is f'(1)? (2020)

A. 1
B. 0
C. undefined
D. ln(1)

Solution

f'(x) = 1/x. Therefore, f'(1) = 1/1 = 1.

Correct Answer: A — 1

Q. If f(x) = ln(x), what is f'(e)?

A. 1
B. 0
C. e
D. ln(e)

Solution

f'(x) = 1/x. Therefore, f'(e) = 1/e.

Correct Answer: A — 1

Q. If f(x) = ln(x^2 + 1), find f'(1). (2022)

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

Solution

f'(x) = (2x)/(x^2 + 1). At x = 1, f'(1) = (2*1)/(1^2 + 1) = 1.

Correct Answer: B — 1

Q. If f(x) = ln(x^2 + 1), what is f'(x)?

A. 2x/(x^2 + 1)
B. 1/(x^2 + 1)
C. 2/(x^2 + 1)
D. x/(x^2 + 1)

Solution

Using the chain rule, f'(x) = (1/(x^2 + 1)) * (2x) = 2x/(x^2 + 1).

Correct Answer: A — 2x/(x^2 + 1)

Q. If f(x) = sin(x) + cos(x), what is f'(x)?

A. cos(x) - sin(x)
B. -sin(x) + cos(x)
C. sin(x) + cos(x)
D. -cos(x) - sin(x)

Solution

Using the derivative rules, f'(x) = cos(x) - sin(x).

Correct Answer: B — -sin(x) + cos(x)

Q. If f(x) = sin(x) + cos(x), what is f'(π/4)?

A. 0
B. √2
C. 1
D. √2/2

Solution

f'(x) = cos(x) - sin(x). At x = π/4, f'(π/4) = cos(π/4) - sin(π/4) = √2/2 - √2/2 = 0.

Correct Answer: C — 1

Q. If f(x) = x^2 * e^x, find f'(x). (2019)

A. e^x(x^2 + 2x)
B. e^x(x^2 - 2x)
C. x^2 * e^x
D. 2x * e^x

Solution

Using the product rule, f'(x) = e^x(x^2 + 2x).

Correct Answer: A — e^x(x^2 + 2x)

Q. If f(x) = x^2 * e^x, what is f'(x)? (2019)

A. e^x(x^2 + 2x)
B. e^x(x^2 - 2x)
C. 2xe^x
D. x^2e^x

Solution

Using the product rule, f'(x) = e^x(x^2 + 2x).

Correct Answer: A — e^x(x^2 + 2x)

Q. If f(x) = x^2 * ln(x), what is f'(x)? (2022)

A. 2x * ln(x) + x
B. x * ln(x) + 2x
C. 2x * ln(x) - x
D. x * ln(x) - 2x

Solution

Using the product rule, f'(x) = 2x * ln(x) + x.

Correct Answer: A — 2x * ln(x) + x

Q. If f(x) = x^2 + 2x + 1, what is f''(x)? (2023)

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

Solution

First derivative f'(x) = 2x + 2. Second derivative f''(x) = 2.

Correct Answer: A — 2

Q. If f(x) = x^2 + 2x + 1, what is f(-1)? Is f(x) continuous at x = -1? (2019)

A. 0, Yes
B. 0, No
C. 1, Yes
D. 1, No

Solution

f(-1) = (-1)^2 + 2*(-1) + 1 = 0. The function is a polynomial and is continuous everywhere, including at x = -1.

Correct Answer: C — 1, Yes

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

A. 6, Continuous
B. 6, Discontinuous
C. 5, Continuous
D. 5, Discontinuous

Solution

f(1) = 1^2 + 3(1) + 2 = 6. Since f(x) is a polynomial function, it is continuous everywhere.

Correct Answer: A — 6, Continuous

Q. If f(x) = x^2 + 3x + 2, what is the limit as x approaches -1?

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

Solution

lim x→-1 f(x) = (-1)^2 + 3(-1) + 2 = 1 - 3 + 2 = 0.

Correct Answer: C — 2

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

A. 0, Continuous
B. 0, Discontinuous
C. 4, Continuous
D. 4, Discontinuous

Solution

f(-1) = (-1)^2 + 3(-1) + 2 = 0. Since f(x) is a polynomial, it is continuous everywhere.

Correct Answer: C — 4, Continuous

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

A. 2
B. 0
C. 3
D. 5

Solution

The first derivative f'(x) = 2x + 3, and the second derivative f''(x) = 2.

Correct Answer: A — 2

Q. If f(x) = x^2 - 4, what is the continuity of f(x) at x = 2?

A. Continuous
B. Not Continuous
C. Only left continuous
D. Only right continuous

Solution

f(x) = x^2 - 4 is a polynomial function, which is continuous everywhere, including at x = 2.

Correct Answer: A — Continuous

Q. If f(x) = x^2 for x < 1 and f(x) = 2x - 1 for x ≥ 1, is f(x) continuous at x = 1? (2019)

A. Yes
B. No
C. Only left continuous
D. Only right continuous

Solution

At x = 1, f(1) = 1^2 = 1 and the limit from the left is also 1, hence f(x) is continuous at x = 1.

Correct Answer: A — Yes

Q. If f(x) = x^2 for x < 1 and f(x) = 3 for x ≥ 1, is f(x) continuous at x = 1?

A. Yes
B. No
C. Only left continuous
D. Only right continuous

Solution

At x = 1, f(1) = 3 and limit from left is 1^2 = 1. Since they are not equal, f(x) is discontinuous at x = 1.

Correct Answer: B — No

Q. If f(x) = x^3 - 3x + 2, what is f(1)? Is f(x) continuous at x = 1? (2019)

A. 0, Yes
B. 0, No
C. 1, Yes
D. 1, No

Solution

f(1) = 1^3 - 3*1 + 2 = 0. The function is a polynomial and hence continuous everywhere, including at x = 1.

Correct Answer: C — 1, Yes

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

A. 0, Continuous
B. 0, Not Continuous
C. 1, Continuous
D. 1, Not Continuous

Solution

f(1) = 1^3 - 3(1) + 2 = 0. Since f(x) is a polynomial, it is continuous everywhere.

Correct Answer: A — 0, Continuous

Q. If f(x) = x^3 - 3x^2 + 4, what is f'(2)? (2020)

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

Solution

First, find f'(x) = 3x^2 - 6x. Then, f'(2) = 3(2^2) - 6(2) = 12 - 12 = 0.

Correct Answer: A — 0

Q. If f(x) = x^3 - 4x + 1, what is f''(x)? (2023)

A. 6x - 4
B. 6x + 4
C. 3x^2 - 4
D. 3x^2 + 4

Solution

First derivative f'(x) = 3x^2 - 4, then f''(x) = 6x.

Correct Answer: A — 6x - 4

Q. If f(x) = x^3 - 6x^2 + 9x, find the inflection point. (2023)

A. (1, 4)
B. (2, 0)
C. (3, 0)
D. (0, 0)

Solution

Find f''(x) = 6x - 12. Set f''(x) = 0 gives x = 2. The inflection point is (2, f(2)) = (2, 0).

Correct Answer: B — (2, 0)

Q. If f(x) = x^4 - 2x^3 + x, what is f'(1)? (2023)

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

Solution

First, find f'(x) = 4x^3 - 6x^2 + 1. Then, f'(1) = 4(1)^3 - 6(1)^2 + 1 = 4 - 6 + 1 = -1.

Correct Answer: A — 2

Q. If f(x) = x^4 - 4x^3 + 6x^2, what is f'(2)? (2019)

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

Solution

f'(x) = 4x^3 - 12x^2 + 12x; f'(2) = 4(2^3) - 12(2^2) + 12(2) = 32 - 48 + 24 = 8.

Correct Answer: B — 4

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