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.
Q. What is the integral of f(x) = 1/x? (2023)
A.
ln
B.
x
C.
+ C
D.
1/x + C
.
x + C
.
e^x + C
Show solution
Solution
The integral of 1/x is ln|x| + C.
Correct Answer:
A
— ln
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Q. What is the integral of the function f(x) = 3x^2? (2021)
A.
x^3 + C
B.
x^3 + 3C
C.
x^3 + 1
D.
3x^3 + C
Show solution
Solution
The integral of 3x^2 is (3/3)x^3 + C = x^3 + C.
Correct Answer:
A
— x^3 + C
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Q. What is the integral of x^n dx, where n ≠ -1? (2023)
A.
(x^(n+1))/(n+1) + C
B.
(x^(n-1))/(n-1) + C
C.
nx^(n-1) + C
D.
x^n + C
Show solution
Solution
The integral of x^n dx is (x^(n+1))/(n+1) + C.
Correct Answer:
A
— (x^(n+1))/(n+1) + C
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Q. What is the integrating factor for the equation dy/dx + 3y = 6?
A.
e^(3x)
B.
e^(-3x)
C.
3e^(3x)
D.
3e^(-3x)
Show solution
Solution
The integrating factor is e^(∫3dx) = e^(3x).
Correct Answer:
A
— e^(3x)
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Q. What is the IUPAC name for CH3-CH2-COOH?
A.
Propanoic acid
B.
Butanoic acid
C.
Acetic acid
D.
Methanoic acid
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Solution
The IUPAC name for CH3-CH2-COOH is propanoic acid, as it has three carbon atoms in the longest chain.
Correct Answer:
A
— Propanoic acid
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Q. What is the IUPAC name for CH3COOH?
A.
Methanol
B.
Ethanol
C.
Acetic acid
D.
Butanoic acid
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Solution
The IUPAC name for CH3COOH is acetic acid.
Correct Answer:
C
— Acetic acid
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Q. What is the latent heat of fusion if 500 g of ice at 0°C absorbs 334,000 J of heat? (2022)
A.
334 J/g
B.
668 J/g
C.
500 J/g
D.
1000 J/g
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Solution
Latent heat of fusion (L) = Q / m = 334,000 J / 500 g = 668 J/g.
Correct Answer:
A
— 334 J/g
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Q. What is the latent heat of fusion of ice if 80 g of ice at 0°C melts to water at 0°C, absorbing 2400 J of heat? (2022)
A.
30 J/g
B.
40 J/g
C.
50 J/g
D.
60 J/g
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Solution
Latent heat of fusion (L) = Q/m = 2400 J / 80 g = 30 J/g.
Correct Answer:
B
— 40 J/g
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Q. What is the latitude of the North Pole?
A.
0°
B.
90°N
C.
90°S
D.
45°N
Show solution
Solution
The North Pole is located at 90°N latitude.
Correct Answer:
B
— 90°N
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Q. What is the latus rectum of the parabola given by the equation y^2 = 12x?
Show solution
Solution
The latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 12, so p = 3, and the latus rectum is 4p = 12.
Correct Answer:
C
— 6
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Q. What is the least common multiple (LCM) of 4 and 6? (2021)
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Solution
LCM of 4 and 6 is 12.
Correct Answer:
A
— 12
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Q. What is the length of an arc of a circle with a radius of 7 cm and a central angle of 60 degrees? (2023)
A.
7π/3 cm
B.
14π/3 cm
C.
14 cm
D.
21 cm
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Solution
Arc length = (θ/360) × 2πr = (60/360) × 2π(7) = (1/6) × 14π = 7π/3 cm.
Correct Answer:
A
— 7π/3 cm
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Q. What is the length of an arc of a circle with radius 5 cm and central angle 60 degrees? (2023)
A.
5π/3 cm
B.
5π/6 cm
C.
5π/12 cm
D.
5π/4 cm
Show solution
Solution
Arc length = (θ/360) × 2πr = (60/360) × 2π(5) = (1/6) × 10π = 5π/6 cm.
Correct Answer:
B
— 5π/6 cm
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Q. What is the length of the altitude from vertex A to side BC in triangle ABC, where AB = 10 cm, AC = 6 cm, and angle A = 90 degrees? (2023)
A.
6 cm
B.
8 cm
C.
10 cm
D.
12 cm
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Solution
In a right triangle, the altitude from the right angle to the hypotenuse is equal to the length of the other side. Thus, the altitude is 6 cm.
Correct Answer:
A
— 6 cm
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Q. What is the length of the altitude from vertex A to side BC in triangle ABC, where AB = 5 cm, AC = 12 cm, and BC = 13 cm? (2023)
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
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Solution
Using Heron's formula, the area is 30 cm². The altitude = (2 * Area) / base = (2 * 30) / 13 = 6 cm.
Correct Answer:
B
— 6 cm
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Q. What is the length of the diagonal of a rectangle with length 6 cm and width 8 cm? (2022)
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
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Solution
The length of the diagonal d of a rectangle can be found using the Pythagorean theorem: d = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the length of the diagonal of a rectangle with sides 3 cm and 4 cm? (2020)
A.
5 cm
B.
7 cm
C.
6 cm
D.
8 cm
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Solution
Diagonal = √(length² + width²) = √(3² + 4²) = √(9 + 16) = √25 = 5 cm
Correct Answer:
A
— 5 cm
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Q. What is the length of the diagonal of a rectangle with sides 6 cm and 8 cm? (2020)
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
Diagonal = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm
Correct Answer:
A
— 10 cm
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Q. What is the length of the diameter of a circle with an area of 50π square units? (2023)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
Show solution
Solution
Area = πr². Given area = 50π, r² = 50, r = √50 = 5√2. Diameter = 2r = 10√2 units.
Correct Answer:
A
— 10 units
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Q. What is the length of the line segment between the points (3, 4) and (7, 1)? (2023)
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Solution
Using the distance formula, length = sqrt((7-3)^2 + (1-4)^2) = sqrt(16 + 9) = 5.
Correct Answer:
A
— 5
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Q. What is the length of the median from the vertex opposite the side of length 10 cm in a triangle with sides 10 cm, 10 cm, and 10 cm? (2023)
A.
5 cm
B.
10 cm
C.
8 cm
D.
7 cm
Show solution
Solution
In an equilateral triangle, the median is equal to the side length, so it is 10 cm.
Correct Answer:
B
— 10 cm
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Q. What is the length of the median from vertex A to side BC in triangle ABC, where AB = 10 cm, AC = 6 cm, and BC = 8 cm? (2023)
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
Using the median formula: m_a = 1/2 * sqrt(2b^2 + 2c^2 - a^2), where a = BC, b = AC, c = AB. m_a = 1/2 * sqrt(2*6^2 + 2*10^2 - 8^2) = 7 cm.
Correct Answer:
C
— 7 cm
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Q. What is the limit: lim (x -> 0) (1 - cos(x))/(x^2)? (2022)
A.
0
B.
1/2
C.
1
D.
Undefined
Show solution
Solution
Using the identity 1 - cos(x) = 2sin^2(x/2), we have lim (x -> 0) (1 - cos(x))/(x^2) = lim (x -> 0) (2sin^2(x/2))/(x^2) = 1/2.
Correct Answer:
B
— 1/2
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Q. What is the limit: lim (x -> 0) (cos(x) - 1)/x^2? (2019)
A.
0
B.
-1/2
C.
1
D.
Undefined
Show solution
Solution
Using the Taylor series expansion for cos(x), we find that lim (x -> 0) (cos(x) - 1)/x^2 = -1/2.
Correct Answer:
B
— -1/2
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Q. What is the limit: lim (x -> 0) (e^x - 1)/x? (2022)
A.
1
B.
0
C.
e
D.
Undefined
Show solution
Solution
Using the derivative of e^x at x = 0, we find that lim (x -> 0) (e^x - 1)/x = 1.
Correct Answer:
A
— 1
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Q. What is the limit: lim (x -> 0) (ln(1 + x)/x)?
A.
1
B.
0
C.
∞
D.
Undefined
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Solution
Using L'Hôpital's Rule, we differentiate the numerator and denominator to find lim (x -> 0) (1/(1 + x)) = 1.
Correct Answer:
A
— 1
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Q. What is the limit: lim (x -> 0) (tan(3x)/x)?
A.
3
B.
0
C.
1
D.
Infinity
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Solution
Using the limit lim (x -> 0) (tan(x)/x) = 1, we have lim (x -> 0) (tan(3x)/x) = 3 * lim (x -> 0) (tan(3x)/(3x)) = 3.
Correct Answer:
A
— 3
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Q. What is the limit: lim (x -> 1) (x^2 - 1)/(x - 1)? (2019)
A.
0
B.
1
C.
2
D.
Undefined
Show solution
Solution
Factoring gives (x - 1)(x + 1)/(x - 1), which simplifies to x + 1. Thus, lim (x -> 1) (x + 1) = 2.
Correct Answer:
C
— 2
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Q. What is the local time at 120°E if it is 6:00 AM at 60°W?
A.
12:00 PM
B.
2:00 PM
C.
4:00 PM
D.
6:00 PM
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Solution
The total difference is 60° + 120° = 180°. This is 12 hours difference. Therefore, 6:00 AM + 12 hours = 6:00 PM.
Correct Answer:
C
— 4:00 PM
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Q. What is the local time at 120°E when it is 3:00 PM at 0° longitude?
A.
6:00 PM
B.
7:00 PM
C.
8:00 PM
D.
9:00 PM
Show solution
Solution
120°E is 120/15 = 8 hours ahead. Therefore, 3:00 PM + 8 hours = 11:00 PM.
Correct Answer:
B
— 7:00 PM
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