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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. Find the coefficient of x^3 in the expansion of (x + 1)^8.

A. 56
B. 70
C. 84
D. 120

Solution

The coefficient of x^3 in (x + 1)^8 is given by 8C3 = 56.

Correct Answer: C — 84

Q. Find the coefficient of x^4 in the expansion of (x + 1)^8.

A. 70
B. 80
C. 90
D. 100

Solution

The coefficient of x^4 is C(8, 4) = 70.

Correct Answer: A — 70

Q. Find the coefficient of x^5 in the expansion of (3x + 2)^6.

A. 486
B. 729
C. 729
D. 486

Solution

The coefficient of x^5 in (3x + 2)^6 is C(6, 5)(3)^5(2)^1 = 6 * 243 * 2 = 2916.

Correct Answer: A — 486

Q. Find the conjugate of the complex number z = 2 - 5i.

A. 2 + 5i
B. 2 - 5i
C. -2 + 5i
D. -2 - 5i

Solution

The conjugate of z = 2 - 5i is z* = 2 + 5i.

Correct Answer: A — 2 + 5i

Q. Find the critical points of the function f(x) = x^3 - 3x^2 + 4.

A. x = 0, 2
B. x = 1, 2
C. x = 1, 3
D. x = 0, 1

Solution

To find critical points, set f'(x) = 0. f'(x) = 3x^2 - 6x = 3x(x - 2). Critical points are x = 0 and x = 2.

Correct Answer: B — x = 1, 2

Q. Find the derivative of f(x) = 4x^3 - 2x + 1. (2022)

A. 12x^2 - 2
B. 12x^2 + 2
C. 4x^2 - 2
D. 4x^2 + 2

Solution

Using the power rule, f'(x) = 12x^2 - 2.

Correct Answer: A — 12x^2 - 2

Q. Find the derivative of f(x) = 5x^2 + 3x - 1. (2020)

A. 10x + 3
B. 5x + 3
C. 10x - 1
D. 5x^2 + 3

Solution

Using the power rule, f'(x) = 10x + 3.

Correct Answer: A — 10x + 3

Q. Find the derivative of f(x) = 5x^2 + 3x - 7. (2020)

A. 10x + 3
B. 5x + 3
C. 10x - 3
D. 5x - 3

Solution

Using the power rule, f'(x) = 10x + 3.

Correct Answer: A — 10x + 3

Q. Find the derivative of f(x) = 5x^3 - 4x + 7. (2019)

A. 15x^2 - 4
B. 15x^2 + 4
C. 5x^2 - 4
D. 5x^2 + 4

Solution

Using the power rule, f'(x) = 15x^2 - 4.

Correct Answer: A — 15x^2 - 4

Q. Find the derivative of f(x) = x^3 * ln(x). (2023)

A. 3x^2 * ln(x) + x^2
B. 3x^2 * ln(x) + x^3/x
C. 3x^2 * ln(x) + x^3
D. 3x^2 * ln(x) + 1

Solution

Using the product rule, f'(x) = (x^3)' * ln(x) + x^3 * (ln(x))' = 3x^2 * ln(x) + x^2.

Correct Answer: A — 3x^2 * ln(x) + x^2

Q. Find the derivative of f(x) = x^4 + 2x^3 - x + 1. (2023)

A. 4x^3 + 6x^2 - 1
B. 4x^3 + 2x^2 - 1
C. 3x^3 + 6x^2 - 1
D. 4x^3 + 2x - 1

Solution

Using the power rule, f'(x) = 4x^3 + 6x^2 - 1.

Correct Answer: A — 4x^3 + 6x^2 - 1

Q. Find the derivative of f(x) = x^4 - 4x^3 + 6x^2 - 2.

A. 4x^3 - 12x^2 + 12x
B. 4x^3 - 12x + 6
C. 12x^2 - 4x + 6
D. 4x^3 - 12x^2 + 2

Solution

Using the power rule, f'(x) = 4x^3 - 12x^2 + 12x.

Correct Answer: A — 4x^3 - 12x^2 + 12x

Q. Find the derivative of f(x) = x^4 - 4x^3 + 6x^2 - 24x + 5. (2023)

A. 4x^3 - 12x^2 + 12x - 24
B. 4x^3 - 12x^2 + 6x - 24
C. 4x^3 - 12x^2 + 12x
D. 4x^3 - 12x^2 + 6x

Solution

Using the power rule, f'(x) = 4x^3 - 12x^2 + 12x - 24.

Correct Answer: A — 4x^3 - 12x^2 + 12x - 24

Q. Find the derivative of f(x) = x^5 - 2x^3 + x. (2019)

A. 5x^4 - 6x^2 + 1
B. 5x^4 - 6x
C. 5x^4 + 2x^2 + 1
D. 5x^4 - 2x^2

Solution

Using the power rule, f'(x) = 5x^4 - 6x^2 + 1.

Correct Answer: A — 5x^4 - 6x^2 + 1

Q. Find the derivative of g(x) = sin(x) + cos(x). (2020)

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

Solution

Using the derivatives of sine and cosine, g'(x) = cos(x) - sin(x).

Correct Answer: A — cos(x) - sin(x)

Q. Find the determinant of the matrix \( D = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \). (2019)

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

Solution

Det(D) = (1*4) - (2*3) = 4 - 6 = -2.

Correct Answer: A — -2

Q. Find the distance between the points (-1, -1) and (2, 2).

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

Solution

Using the distance formula: d = √[(2 - (-1))² + (2 - (-1))²] = √[9 + 9] = √18 = 3√2.

Correct Answer: C — 5

Q. Find the distance between the points (-2, -3) and (4, 5).

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

Solution

Using the distance formula: d = √[(4 - (-2))² + (5 - (-3))²] = √[(4 + 2)² + (5 + 3)²] = √[36 + 64] = √100 = 10.

Correct Answer: B — 7

Q. Find the distance between the points (0, 0) and (x, y) where x = 6 and y = 8.

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

Solution

Using the distance formula: d = √[(6 - 0)² + (8 - 0)²] = √[36 + 64] = √100 = 10.

Correct Answer: A — 10

Q. Find the distance between the points (1, 1) and (4, 5). (2023)

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

Solution

Using the distance formula: d = √[(4 - 1)² + (5 - 1)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

Q. Find the distance between the points (3, 3) and (3, 7).

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

Solution

Using the distance formula: d = √[(3 - 3)² + (7 - 3)²] = √[0 + 16] = √16 = 4.

Correct Answer: A — 4

Q. Find the distance between the points (3, 7) and (3, 1).

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

Solution

Using the distance formula: d = √((3 - 3)² + (1 - 7)²) = √(0 + 36) = √36 = 6.

Correct Answer: A — 6

Q. Find the distance between the points (5, 5) and (5, 1).

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

Solution

Using the distance formula: d = √[(5 - 5)² + (1 - 5)²] = √[0 + 16] = √16 = 4.

Correct Answer: A — 4

Q. Find the eigenvalues of the matrix G = [[2, 1], [1, 2]]. (2020)

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

Solution

The characteristic polynomial is det(G - λI) = (2-λ)(2-λ) - 1 = λ^2 - 4λ + 3 = 0. The eigenvalues are λ = 1 and λ = 3.

Correct Answer: A — 1, 3

Q. Find the eigenvalues of the matrix G = [[5, 4], [2, 3]]. (2020)

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

Solution

The eigenvalues are found by solving the characteristic equation det(G - λI) = 0. This gives λ^2 - 8λ + 7 = 0, which factors to (λ - 1)(λ - 7) = 0, hence λ = 1, 7.

Correct Answer: A — 1, 7

Q. Find the equation of the line passing through the points (2, 3) and (4, 7). (2020)

A. y = 2x - 1
B. y = 2x + 1
C. y = 3x - 3
D. y = 2x + 3

Solution

The slope m = (7 - 3) / (4 - 2) = 2. Using point-slope form: y - 3 = 2(x - 2) gives y = 2x + 1.

Correct Answer: B — y = 2x + 1

Q. Find the general solution of the differential equation dy/dx = 3x^2.

A. y = x^3 + C
B. y = 3x^3 + C
C. y = x^2 + C
D. y = 3x^2 + C

Solution

Integrating both sides gives y = (3/3)x^3 + C = x^3 + C.

Correct Answer: A — y = x^3 + C

Q. Find the general solution of the differential equation dy/dx = 4y.

A. y = Ce^(4x)
B. y = 4Ce^x
C. y = Ce^(x/4)
D. y = 4Ce^(x)

Solution

This is a separable differential equation. Integrating gives y = Ce^(4x), where C is the constant.

Correct Answer: A — y = Ce^(4x)

Q. Find the general solution of the equation dy/dx = 3x^2y.

A. y = Ce^(x^3)
B. y = Ce^(3x^3)
C. y = Ce^(x^3/3)
D. y = Ce^(x^2)

Solution

This is a separable equation. Separating and integrating gives y = Ce^(x^3).

Correct Answer: A — y = Ce^(x^3)

Q. Find the integral of (1/x) dx.

A. ln
B. x
C. + C
D. x + C
. 1/x + C
. e^x + C

Solution

The integral of (1/x) is ln|x| + C, where C is the constant of integration.

Correct Answer: A — ln

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