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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. What is the derivative of f(x) = x^2 * sin(x)? (2023)

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

Solution

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

Correct Answer: A — 2x * sin(x) + x^2 * cos(x)

Q. What is the derivative of f(x) = x^3 * e^x?

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

Solution

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

Correct Answer: A — 3x^2 * e^x + x^3 * e^x

Q. What is 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) + 3x^2
D. 3x^2 * ln(x) + 1

Solution

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

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

Q. What is the derivative of f(x) = x^3 - 4x + 7? (2021)

A. 3x^2 - 4
B. 3x^2 + 4
C. x^2 - 4
D. 3x^2 - 7

Solution

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

Correct Answer: A — 3x^2 - 4

Q. What is the derivative of f(x) = x^3 - 6x^2 + 9x?

A. 3x^2 - 12x + 9
B. 3x^2 - 6x + 9
C. 6x - 12
D. 3x^2 - 9

Solution

The derivative f'(x) = 3x^2 - 12x + 9.

Correct Answer: A — 3x^2 - 12x + 9

Q. What is the derivative of f(x) = x^4 - 6x^2 + 9? (2022)

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

Solution

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

Correct Answer: A — 4x^3 - 12x

Q. What is the derivative of the function f(x) = 3x^2 + 5x - 7? (2021)

A. 3x + 5
B. 6x + 5
C. 6x - 5
D. 3x^2 + 5

Solution

The derivative f'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.

Correct Answer: B — 6x + 5

Q. What is the determinant of a 1x1 matrix [[5]]? (2021)

A. 0
B. 5
C. 10
D. 1

Solution

The determinant of a 1x1 matrix is simply the value of the single element. Therefore, the determinant of [[5]] is 5.

Correct Answer: B — 5

Q. What is the determinant of a 2x2 matrix A = [[a, b], [c, d]]? (2021)

A. ad - bc
B. ab + cd
C. ac + bd
D. ad + bc

Solution

The determinant of a 2x2 matrix is calculated as ad - bc.

Correct Answer: A — ad - bc

Q. What is the determinant of a 2x2 matrix [[a, b], [c, d]]? (2020)

A. ad - bc
B. ab + cd
C. ac - bd
D. bc - ad

Solution

The determinant of a 2x2 matrix is calculated as ad - bc.

Correct Answer: A — ad - bc

Q. What is the determinant of the matrix E = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?

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

Solution

The determinant of E is 0 because the rows are linearly dependent.

Correct Answer: A — 0

Q. What is the determinant of the matrix H = [[1, 1, 1], [1, 2, 3], [1, 3, 6]]?

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

Solution

The determinant can be calculated using the formula for 3x3 matrices. Here, the first column is the same, leading to a determinant of 0.

Correct Answer: A — 0

Q. What is the determinant of the matrix \( E = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{pmatrix} \)? (2023)

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

Solution

The determinant is 0 because the first column is a linear combination of the other columns.

Correct Answer: A — 0

Q. What is the determinant of the matrix \( J = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \)? (2021)

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

Solution

Det(J) = (5*8) - (6*7) = 40 - 42 = -2.

Correct Answer: A — -2

Q. What is the direction of the magnetic field around a current-carrying conductor? (2019)

A. From North to South
B. From South to North
C. Clockwise
D. Counterclockwise

Solution

The direction of the magnetic field around a current-carrying conductor is given by the right-hand rule, which indicates a counterclockwise direction when viewed from the positive current side.

Correct Answer: D — Counterclockwise

Q. What is the directrix of the parabola defined by the equation y^2 = 20x?

A. x = -5
B. x = 5
C. y = 5
D. y = -5

Solution

For the equation y^2 = 4px, p = 5. The directrix is given by x = -p, which is x = -5.

Correct Answer: A — x = -5

Q. What is the distance between the points (0, 0) and (3, 4)?

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

Solution

Using the distance formula: d = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

Q. What is the distance between the points (0, 0) and (8, 6)?

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

Solution

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

Correct Answer: A — 10

Q. What is the distance between the points (0, 0) and (x, y) where x = 3 and y = 4? (2022)

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

Solution

Using the distance formula: d = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

Q. What is the distance between the points (2, 3) and (6, 7)?

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

Solution

Using the distance formula: d = √[(6 - 2)² + (7 - 3)²] = √[16 + 16] = √32 = 4√2 ≈ 5.66.

Correct Answer: A — 5

Q. What is the distance between the points (3, 2) and (3, -2)?

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

Solution

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

Correct Answer: A — 4

Q. What is 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. What is the distance between the points (5, 5) and (1, 1)?

A. 4√2
B. 5√2
C. 6
D. 7

Solution

Using the distance formula: d = √[(1 - 5)² + (1 - 5)²] = √[16 + 16] = √32 = 4√2.

Correct Answer: A — 4√2

Q. What is the distance between the points (6, 8) and (6, 2)?

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

Solution

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

Correct Answer: A — 6

Q. What is the effect called when sound waves spread out after passing through a narrow opening? (2019)

A. Reflection
B. Refraction
C. Diffraction
D. Interference

Solution

The spreading out of sound waves after passing through a narrow opening is known as diffraction.

Correct Answer: C — Diffraction

Q. What is the effect of adding a base to a solution of a weak acid?

A. Increase in pH
B. Decrease in pH
C. No change in pH
D. Increase in temperature

Solution

Adding a base to a weak acid will neutralize some of the acid, increasing the pH.

Correct Answer: A — Increase in pH

Q. What is the effect of adding a base to a solution of hydrochloric acid?

A. Increase in pH
B. Decrease in pH
C. No effect
D. Formation of salt only

Solution

Adding a base to hydrochloric acid will neutralize it, resulting in an increase in pH.

Correct Answer: A — Increase in pH

Q. What is the effect of adding a base to an acidic solution?

A. Increase in pH
B. Decrease in pH
C. No effect
D. Formation of salt only

Solution

Adding a base to an acidic solution increases the pH, making it less acidic.

Correct Answer: A — Increase in pH

Q. What is the effect of adding a strong acid to a solution of a weak base?

A. Increase in pH
B. Decrease in pH
C. No effect
D. Increase in conductivity

Solution

Adding a strong acid to a weak base will decrease the pH of the solution.

Correct Answer: B — Decrease in pH

Q. What is the effect of deforestation on local climate?

A. Increased rainfall
B. Decreased temperature
C. Increased temperature
D. No effect

Solution

Deforestation typically leads to increased temperatures in the local climate due to reduced transpiration and increased solar radiation absorption.

Correct Answer: C — Increased temperature

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