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. Evaluate the integral ∫ (5x^4) dx.
A.
x^5 + C
B.
x^5 + 5C
C.
x^5 + 1
D.
5x^5 + C
Show solution
Solution
The integral is (5/5)x^5 + C = x^5 + C.
Correct Answer:
A
— x^5 + C
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Q. Evaluate the integral ∫(0 to 1) (1 - x^2) dx. (2022)
A.
1/3
B.
1/2
C.
2/3
D.
1
Show solution
Solution
∫(0 to 1) (1 - x^2) dx = [x - x^3/3] from 0 to 1 = (1 - 1/3) = 2/3.
Correct Answer:
C
— 2/3
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Q. Evaluate the integral ∫(0 to π) sin(x) dx. (2021)
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Solution
∫(0 to π) sin(x) dx = [-cos(x)] from 0 to π = -(-1 - 1) = 2.
Correct Answer:
C
— 2
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Q. Evaluate the integral ∫(1 to 2) (3x^2 - 4) dx. (2019)
Show solution
Solution
∫(1 to 2) (3x^2 - 4) dx = [x^3 - 4x] from 1 to 2 = (8 - 8) - (1 - 4) = 3.
Correct Answer:
A
— 1
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Q. Evaluate the integral ∫(1 to 3) (3x^2 - 2) dx. (2019)
Show solution
Solution
∫(1 to 3) (3x^2 - 2) dx = [x^3 - 2x] from 1 to 3 = (27 - 6) - (1 - 2) = 20.
Correct Answer:
B
— 12
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Q. Evaluate the integral ∫(1 to 4) (2x + 1) dx. (2021)
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Solution
∫(1 to 4) (2x + 1) dx = [x^2 + x] from 1 to 4 = (16 + 4) - (1 + 1) = 18.
Correct Answer:
B
— 12
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Q. Evaluate the integral ∫(2 to 3) (x^3 - 3x^2 + 2) dx. (2023)
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Solution
∫(2 to 3) (x^3 - 3x^2 + 2) dx = [x^4/4 - x^3 + 2x] from 2 to 3 = (81/4 - 27 + 6) - (16/4 - 8 + 4) = 1.
Correct Answer:
B
— 2
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Q. Evaluate the integral ∫(2x + 3) dx from 1 to 2.
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Solution
The integral evaluates to [x^2 + 3x] from 1 to 2, which gives (4 + 6) - (1 + 3) = 8 - 4 = 4.
Correct Answer:
B
— 7
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Q. Evaluate the integral ∫(2x + 3) dx. (2021)
A.
x^2 + 3x + C
B.
x^2 + 3x
C.
2x^2 + 3x + C
D.
2x^2 + 3x
Show solution
Solution
The integral of (2x + 3) is (2x^2/2) + 3x + C = x^2 + 3x + C.
Correct Answer:
A
— x^2 + 3x + C
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Q. Evaluate the integral ∫(sin x)dx. (2022)
A.
-cos x + C
B.
cos x + C
C.
sin x + C
D.
-sin x + C
Show solution
Solution
The integral of sin x is -cos x + C.
Correct Answer:
A
— -cos x + C
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Q. Evaluate the integral ∫(x^2 - 2x + 1) dx. (2022)
A.
(1/3)x^3 - x^2 + x + C
B.
(1/3)x^3 - x^2 + C
C.
(1/3)x^3 - 2x + C
D.
(1/3)x^3 - x^2 + x
Show solution
Solution
The integral of (x^2 - 2x + 1) is (1/3)x^3 - x^2 + x + C.
Correct Answer:
A
— (1/3)x^3 - x^2 + x + C
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Q. Evaluate the limit lim (x -> 0) (sin(5x)/x) and determine continuity. (2021)
A.
5, Continuous
B.
0, Not continuous
C.
5, Not continuous
D.
0, Continuous
Show solution
Solution
Using the limit property, lim (x -> 0) (sin(kx)/x) = k. Here, k = 5, so the limit is 5, and the function is continuous at x = 0.
Correct Answer:
A
— 5, Continuous
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Q. Evaluate the limit lim (x -> 0) (sin(5x)/x) and determine its continuity.
A.
5, Continuous
B.
0, Continuous
C.
5, Not Continuous
D.
0, Not Continuous
Show solution
Solution
Using the limit property, lim (x -> 0) (sin(5x)/x) = 5. The function is continuous at x = 0.
Correct Answer:
A
— 5, Continuous
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Q. Evaluate the limit lim (x -> 0) (sin(5x)/x). Is the function continuous at x = 0?
A.
5, Continuous
B.
5, Discontinuous
C.
0, Continuous
D.
0, Discontinuous
Show solution
Solution
Using the limit property, lim (x -> 0) (sin(5x)/x) = 5. The function is continuous at x = 0 if defined as f(0) = 5.
Correct Answer:
A
— 5, Continuous
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Q. Evaluate the limit lim (x -> 0) (sin(x)/x) and determine its continuity.
A.
1, Continuous
B.
0, Continuous
C.
1, Discontinuous
D.
0, Discontinuous
Show solution
Solution
The limit lim (x -> 0) (sin(x)/x) = 1. Since the limit exists and equals the function value at x = 0, it is continuous.
Correct Answer:
A
— 1, Continuous
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Q. Evaluate the limit lim (x -> 0) (sin(x)/x). Is the function continuous at x = 0?
A.
1, Continuous
B.
0, Continuous
C.
1, Discontinuous
D.
0, Discontinuous
Show solution
Solution
The limit is 1, and if we define f(0) = 1, then f(x) is continuous at x = 0.
Correct Answer:
A
— 1, Continuous
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Q. Evaluate the limit lim (x -> 3) (x^2 - 9)/(x - 3). Is the function continuous at x = 3? (2021)
A.
0, Yes
B.
0, No
C.
6, Yes
D.
6, No
Show solution
Solution
lim (x -> 3) (x^2 - 9)/(x - 3) = lim (x -> 3) (x + 3) = 6. The function is not defined at x = 3, hence not continuous.
Correct Answer:
C
— 6, Yes
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Q. Evaluate the limit lim x→2 (x^2 - 4)/(x - 2).
A.
0
B.
2
C.
4
D.
Undefined
Show solution
Solution
Using L'Hôpital's Rule, lim x→2 (x^2 - 4)/(x - 2) = lim x→2 (2x)/(1) = 4.
Correct Answer:
C
— 4
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Q. Find the angle between the vectors A = 2i + 2j and B = 2i - 2j. (2022)
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|). A · B = 0, hence θ = 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. Find the angle between the vectors A = i + j and B = 2i + 2j.
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
60 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A| |B|). A · B = 1*2 + 1*2 = 4; |A| = √2, |B| = 2√2. Thus, cos(θ) = 4 / (√2 * 2√2) = 1, θ = 0 degrees.
Correct Answer:
A
— 0 degrees
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Q. Find the angle between the vectors A = i + j and B = i - j.
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
135 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (1 - 1) / (√2 * √2) = 0, θ = 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. Find the angle between the vectors A = i + j and B = j - i. (2022)
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A| |B|). A · B = 0, hence θ = 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. Find the angle θ between the vectors A = i + 2j and B = 2i + 3j if A · B = |A||B|cos(θ).
A.
60°
B.
45°
C.
30°
D.
90°
Show solution
Solution
A · B = 1*2 + 2*3 = 8. |A| = √(1^2 + 2^2) = √5, |B| = √(2^2 + 3^2) = √13. cos(θ) = 8/(√5*√13).
Correct Answer:
B
— 45°
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Q. Find the angle θ between vectors A = 4i + 3j and B = 1i + 2j if A · B = |A||B|cos(θ).
A.
60°
B.
45°
C.
30°
D.
90°
Show solution
Solution
A · B = 4*1 + 3*2 = 10; |A| = √(4^2 + 3^2) = 5; |B| = √(1^2 + 2^2) = √5; cos(θ) = 10/(5√5) = 2/√5; θ = 45°.
Correct Answer:
B
— 45°
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Q. Find the area between the curves y = x and y = x^2 from x = 0 to x = 1.
A.
0.5
B.
1
C.
0.25
D.
0.75
Show solution
Solution
The area between the curves is given by ∫(from 0 to 1) (x - x^2) dx = [x^2/2 - x^3/3] from 0 to 1 = (1/2 - 1/3) = 1/6 = 0.5.
Correct Answer:
A
— 0.5
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Q. Find the area under the curve y = 3x^2 from x = 1 to x = 2.
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Solution
The area under the curve is given by ∫(from 1 to 2) 3x^2 dx = [x^3] from 1 to 2 = (8 - 1) = 7.
Correct Answer:
B
— 6
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Q. Find the coefficient of x^2 in the expansion of (2x - 3)^4.
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Solution
Using the binomial theorem, the coefficient of x^2 in (2x - 3)^4 is given by 4C2 * (2)^2 * (-3)^2 = 6 * 4 * 9 = 216.
Correct Answer:
C
— 54
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Q. Find the coefficient of x^2 in the expansion of (3x - 2)^5.
A.
-60
B.
-90
C.
90
D.
60
Show solution
Solution
The coefficient of x^2 in (3x - 2)^5 is given by 5C2 * (3x)^2 * (-2)^3 = 10 * 9 * (-8) = -720.
Correct Answer:
B
— -90
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Q. Find the coefficient of x^2 in the expansion of (x + 4)^6.
A.
96
B.
144
C.
216
D.
256
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Solution
The coefficient of x^2 is given by C(6, 2)(4)^4 = 15 * 256 = 3840.
Correct Answer:
A
— 96
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Q. Find the coefficient of x^3 in the expansion of (3x - 4)^5.
A.
-540
B.
-720
C.
720
D.
540
Show solution
Solution
The coefficient of x^3 in (3x - 4)^5 is given by 5C3 * (3)^3 * (-4)^2 = 10 * 27 * 16 = -720.
Correct Answer:
B
— -720
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