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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 slope of the tangent line to the curve y = x^3 at x = 1? (2019)

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

Solution

The derivative y' = 3x^2. At x = 1, y' = 3(1^2) = 3.

Correct Answer: C — 3

Q. What is the solution of the differential equation dy/dx = y/x?

A. y = Cx
B. y = Cx^2
C. y = C/x
D. y = C ln(x)

Solution

This is separable. Integrating gives y = Cx.

Correct Answer: A — y = Cx

Q. What is the solution to the differential equation dy/dx = 3x^2?

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

Solution

Integrating both sides gives y = x^3 + C, where C is the constant of integration.

Correct Answer: A — x^3 + C

Q. What is the solution to the differential equation dy/dx = 6x?

A. y = 3x^2 + C
B. y = 6x^2 + C
C. y = 2x^2 + C
D. y = 3x + C

Solution

Integrating gives y = (6/2)x^2 + C = 3x^2 + C.

Correct Answer: A — y = 3x^2 + C

Q. What is the solution to the differential equation dy/dx = xy?

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

Solution

This is separable. Separating and integrating gives y = Ce^(x^2/2).

Correct Answer: A — y = Ce^(x^2/2)

Q. What is the solution to the equation 2(x - 3) = 8? (2023)

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

Solution

Expanding gives 2x - 6 = 8. Adding 6 gives 2x = 14, thus x = 7.

Correct Answer: C — 7

Q. What is the solution to the equation 2x - 4 = 10? (2023)

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

Solution

Adding 4 to both sides gives 2x = 14. Dividing by 2 gives x = 7.

Correct Answer: D — 6

Q. What is the solution to the equation 4x + 8 = 24? (2023)

A. 2
B. 4
C. 6
D. 8

Solution

Subtracting 8 from both sides gives 4x = 16. Dividing by 4 gives x = 4.

Correct Answer: C — 6

Q. What is the solution to the equation 4x - 8 = 0?

A. 2
B. 4
C. 0
D. 8

Solution

Adding 8 to both sides gives 4x = 8. Dividing by 4 gives x = 2.

Correct Answer: A — 2

Q. What is the solution to the initial value problem dy/dx = 4y, y(1) = 2?

A. y = 2e^(4x)
B. y = 2e^(4x-4)
C. y = e^(4x)
D. y = 4e^(x)

Solution

The general solution is y = Ce^(4x). Using y(1) = 2, we find C = 2e^(-4).

Correct Answer: B — y = 2e^(4x-4)

Q. What is the specific heat capacity of a substance if 500 J of heat is required to raise the temperature of 2 kg of the substance by 10°C? (2021)

A. 25 J/kg°C
B. 50 J/kg°C
C. 75 J/kg°C
D. 100 J/kg°C

Solution

Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 10°C) = 25 J/kg°C.

Correct Answer: B — 50 J/kg°C

Q. What is the sum of the coefficients in the expansion of (2x - 3)^4?

A. -81
B. 81
C. 0
D. 64

Solution

To find the sum of the coefficients, substitute x = 1: (2*1 - 3)^4 = (-1)^4 = 1. The sum of coefficients is 81.

Correct Answer: B — 81

Q. What is the sum of the coefficients in the expansion of (x + 1)^4?

A. 4
B. 8
C. 16
D. 32

Solution

The sum of the coefficients in the expansion of (x + 1)^4 is (1 + 1)^4 = 2^4 = 16.

Correct Answer: C — 16

Q. What is the sum of the coefficients in the expansion of (x + 1)^8?

A. 256
B. 512
C. 128
D. 64

Solution

The sum of the coefficients in the expansion of (x + 1)^n is given by (1 + 1)^n = 2^n. Here, n=8, so the sum is 2^8 = 256.

Correct Answer: B — 512

Q. What is the sum of the complex numbers z1 = 2 + 2i and z2 = 3 - 4i?

A. 5 - 2i
B. 5 + 2i
C. 1 - 2i
D. 1 + 2i

Solution

To find the sum, we add the real parts and the imaginary parts: (2 + 3) + (2 - 4)i = 5 - 2i.

Correct Answer: A — 5 - 2i

Q. What is the sum of the complex numbers z1 = 2 + 3i and z2 = 4 - 2i?

A. 6 + i
B. 6 + i
C. 2 + 5i
D. 8 + i

Solution

The sum of two complex numbers z1 + z2 = (2 + 3i) + (4 - 2i) = (2 + 4) + (3 - 2)i = 6 + i.

Correct Answer: A — 6 + i

Q. What is the sum of the first five prime numbers?

A. 28
B. 26
C. 30
D. 24

Solution

The first five prime numbers are 2, 3, 5, 7, and 11. Their sum is 2 + 3 + 5 + 7 + 11 = 28.

Correct Answer: A — 28

Q. What is the sum of the interior angles of a hexagon? (2022)

A. 720 degrees
B. 540 degrees
C. 360 degrees
D. 180 degrees

Solution

Sum of interior angles = (n-2) * 180° = (6-2) * 180° = 720 degrees

Correct Answer: A — 720 degrees

Q. What is the sum of the interior angles of a pentagon?

A. 360°
B. 540°
C. 720°
D. 180°

Solution

The sum of the interior angles of a polygon is given by (n-2) * 180°, where n is the number of sides. For a pentagon, n = 5, so (5-2) * 180° = 540°.

Correct Answer: B — 540°

Q. What is the sum of the interior angles of a triangle formed by three intersecting lines?

A. 180 degrees
B. 360 degrees
C. 90 degrees
D. 270 degrees

Solution

The sum of the interior angles of any triangle is always 180 degrees.

Correct Answer: A — 180 degrees

Q. What is the sum of the interior angles of a triangle? (2019)

A. 90 degrees
B. 180 degrees
C. 270 degrees
D. 360 degrees

Solution

The sum of the interior angles of any triangle is always 180 degrees.

Correct Answer: B — 180 degrees

Q. What is the sum of the roots of the equation 2x^2 - 8x + 6 = 0? (2022)

A. 4
B. 6
C. 8
D. 10

Solution

Using Vieta's formulas, the sum of the roots is -(-8)/2 = 4.

Correct Answer: A — 4

Q. What is the sum of the roots of the equation x² - 5x + 6 = 0? (2022)

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

Solution

The sum of the roots is given by -b/a = 5/1 = 5.

Correct Answer: A — 5

Q. What is the sum of the squares of the roots of the equation x^2 - 5x + 6 = 0?

A. 25
B. 19
C. 23
D. 21

Solution

The sum of the squares of the roots is given by (sum of roots)^2 - 2(product of roots). Here, sum = 5, product = 6. So, 5^2 - 2*6 = 25 - 12 = 13.

Correct Answer: B — 19

Q. What is the synonym of 'abundant'?

A. scarce
B. plentiful
C. meager
D. insufficient

Solution

'Abundant' means plentiful or existing in large quantities. Therefore, the synonym is 'plentiful'.

Correct Answer: B — plentiful

Q. What is the synonym of 'candid'?

A. deceitful
B. honest
C. reserved
D. secretive

Solution

'Candid' means truthful and straightforward; frank.

Correct Answer: B — honest

Q. What is the synonym of 'elated'?

A. depressed
B. joyful
C. angry
D. anxious

Solution

'Elated' means in high spirits; extremely happy and excited.

Correct Answer: B — joyful

Q. What is the synonym of 'frugal'?

A. extravagant
B. thrifty
C. wasteful
D. lavish

Solution

'Frugal' means being economical or avoiding waste, making 'thrifty' the synonym.

Correct Answer: B — thrifty

Q. What is the synonym of 'gregarious'?

A. shy
B. sociable
C. reserved
D. antisocial

Solution

'Gregarious' means fond of company; sociable.

Correct Answer: B — sociable

Q. What is the synonym of 'meticulous'?

A. careless
B. thorough
C. negligent
D. sloppy

Solution

'Meticulous' means showing great attention to detail; very careful and precise.

Correct Answer: B — thorough

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