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. Determine the maximum value of the function f(x) = -x^2 + 6x - 8. (2022)
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Solution
The vertex is at x = -6/(2*(-1)) = 3. The maximum value is f(3) = -3^2 + 6*3 - 8 = 1.
Correct Answer:
B
— 4
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Q. Determine the median of the following numbers: 9, 7, 5, 3, 1.
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Solution
Arrange the numbers: 1, 3, 5, 7, 9. The median is the middle value, which is 5.
Correct Answer:
A
— 5
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Q. Determine the median of the following set: 1, 2, 3, 4, 5, 6, 7, 8. (2020)
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Solution
Arrange the numbers: 1, 2, 3, 4, 5, 6, 7, 8. The median is the average of the 4th and 5th numbers: (4 + 5) / 2 = 4.5.
Correct Answer:
B
— 4.5
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Q. Determine the minimum value of f(x) = x^2 - 6x + 10. (2019)
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Solution
The minimum occurs at x = -b/(2a) = 6/(2*1) = 3. f(3) = 3^2 - 6(3) + 10 = 3.
Correct Answer:
B
— 3
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Q. Determine the minimum value of the function f(x) = x^2 - 4x + 6. (2020)
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Solution
The function is a upward-opening parabola. The minimum occurs at x = -b/(2a) = 4/(2*1) = 2. f(2) = 2^2 - 4(2) + 6 = 2.
Correct Answer:
A
— 2
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Q. Determine the mode of the following data: {1, 2, 2, 3, 4, 4, 4, 5, 5}.
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Solution
The mode is 4, as it appears 3 times, more than any other number.
Correct Answer:
C
— 4
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Q. Determine the slope of the tangent line to f(x) = x^2 at x = 3. (2023)
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Solution
f'(x) = 2x; thus, f'(3) = 2(3) = 6.
Correct Answer:
B
— 6
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Q. Determine the solution of the differential equation dy/dx = y^2 - 1.
A.
y = tan(x + C)
B.
y = 1/(C - x)
C.
y = 1/(C + x)
D.
y = e^(x + C)
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Solution
This is separable. Separating and integrating gives y = 1/(C - x).
Correct Answer:
B
— y = 1/(C - x)
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Q. Determine the x-intercept of the line given by the equation 5x + 2y - 10 = 0. (2023)
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Solution
Setting y = 0 in the equation gives 5x = 10, thus x = 2. The x-intercept is 2.
Correct Answer:
C
— 5
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Q. Determine the y-intercept of the line given by the equation 5x + 2y - 10 = 0. (2021)
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Solution
Setting x = 0 in the equation gives 2y = 10, thus y = 5. The y-intercept is 5.
Correct Answer:
B
— 2
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Q. Differentiate f(x) = 4x^2 * e^x. (2022)
A.
4e^x + 4x^2e^x
B.
4x^2e^x + 4xe^x
C.
4e^x + 2x^2e^x
D.
8xe^x
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Solution
Using the product rule, f'(x) = 4e^x + 4x^2e^x.
Correct Answer:
A
— 4e^x + 4x^2e^x
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Q. Differentiate f(x) = 4x^2 + 3x - 5. (2019)
A.
8x + 3
B.
4x + 3
C.
2x + 3
D.
8x - 3
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Solution
Using the power rule, f'(x) = 8x + 3.
Correct Answer:
A
— 8x + 3
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Q. Differentiate f(x) = 4x^5 - 2x^3 + x. (2022)
A.
20x^4 - 6x^2 + 1
B.
20x^4 - 6x^2
C.
4x^4 - 2x^2 + 1
D.
5x^4 - 2x^2
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Solution
Using the power rule, f'(x) = 20x^4 - 6x^2 + 1.
Correct Answer:
A
— 20x^4 - 6x^2 + 1
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Q. Differentiate f(x) = ln(x^2 + 1). (2022)
A.
2x/(x^2 + 1)
B.
1/(x^2 + 1)
C.
2x/(x^2 - 1)
D.
x/(x^2 + 1)
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Solution
Using the chain rule, f'(x) = 2x/(x^2 + 1).
Correct Answer:
A
— 2x/(x^2 + 1)
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Q. Differentiate f(x) = x^2 * e^x. (2022)
A.
x^2 * e^x + 2x * e^x
B.
2x * e^x + x^2 * e^x
C.
x^2 * e^x + e^x
D.
2x * e^x
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Solution
Using the product rule, f'(x) = x^2 * e^x + 2x * e^x.
Correct Answer:
A
— x^2 * e^x + 2x * e^x
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Q. Differentiate f(x) = x^2 * ln(x).
A.
2x * ln(x) + x
B.
x * ln(x) + 2x
C.
2x * ln(x)
D.
x^2/x
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Solution
Using the product rule, f'(x) = 2x * ln(x) + x.
Correct Answer:
A
— 2x * ln(x) + x
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Q. Differentiate the function f(x) = ln(x^2 + 1).
A.
2x/(x^2 + 1)
B.
2/(x^2 + 1)
C.
1/(x^2 + 1)
D.
x/(x^2 + 1)
Show solution
Solution
Using the chain rule, f'(x) = (1/(x^2 + 1)) * (2x) = 2x/(x^2 + 1).
Correct Answer:
A
— 2x/(x^2 + 1)
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Q. Differentiate the function f(x) = x^2 * e^x.
A.
x^2 * e^x + 2x * e^x
B.
2x * e^x + x^2 * e^x
C.
x^2 * e^x + e^x
D.
2x * e^x + e^x
Show solution
Solution
Using the product rule, f'(x) = (x^2)' * e^x + x^2 * (e^x)' = 2x * e^x + x^2 * e^x.
Correct Answer:
A
— x^2 * e^x + 2x * e^x
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Q. During a global conference, 40% of the attendees were women. If there were 500 attendees, how many were men? (2023)
A.
200
B.
250
C.
300
D.
350
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Solution
Number of women = 40% of 500 = 200. Number of men = 500 - 200 = 300.
Correct Answer:
C
— 300
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Q. During a national celebration, 25% of the attendees are children. If there are 800 attendees, how many are adults? (2020)
A.
600
B.
200
C.
400
D.
300
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Solution
Number of children = 25% of 800 = 0.25 * 800 = 200. Number of adults = 800 - 200 = 600.
Correct Answer:
A
— 600
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Q. During a national event, 25% of the attendees are from outside the country. If there are 800 attendees, how many are from outside the country? (2021)
A.
200
B.
250
C.
300
D.
350
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Solution
Number of attendees from outside = 25% of 800 = 0.25 * 800 = 200.
Correct Answer:
A
— 200
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Q. During a national event, 25% of the attendees are from outside the country. If there are 1,200 attendees, how many are from outside the country?
A.
300
B.
250
C.
400
D.
350
Show solution
Solution
Number of attendees from outside = 25% of 1,200 = 0.25 * 1,200 = 300.
Correct Answer:
A
— 300
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Q. During a national event, 25% of the attendees are from rural areas. If there are 800 attendees, how many are from urban areas?
A.
600
B.
200
C.
400
D.
300
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Solution
Number of attendees from urban areas = 800 * (1 - 0.25) = 800 * 0.75 = 600.
Correct Answer:
A
— 600
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Q. During a national event, 25% of the attendees are students. If there are 1,600 attendees, how many are not students?
A.
1,200
B.
1,000
C.
1,400
D.
1,600
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Solution
Number of non-students = 1,600 * (1 - 0.25) = 1,600 * 0.75 = 1,200.
Correct Answer:
A
— 1,200
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Q. During a national event, 30% of the attendees are from abroad. If there are 1,000 attendees, how many are from abroad? (2021)
A.
300
B.
400
C.
500
D.
600
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Solution
Number of attendees from abroad = 30% of 1,000 = 0.3 * 1,000 = 300.
Correct Answer:
A
— 300
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Q. During a national event, if 70% of the attendees are adults and there are 350 attendees, how many are children?
A.
105
B.
245
C.
70
D.
140
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Solution
Number of adults = 70% of 350 = 0.70 * 350 = 245. Number of children = 350 - 245 = 105.
Correct Answer:
A
— 105
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Q. During a national event, if 70% of the attendees are adults and there are 500 attendees, how many are children? (2022)
A.
150
B.
200
C.
100
D.
250
Show solution
Solution
Number of adults = 70% of 500 = 0.70 * 500 = 350. Number of children = 500 - 350 = 150.
Correct Answer:
B
— 200
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Q. During a peacekeeping mission, 120 soldiers were deployed. If 25% of them were from country A, how many soldiers were from country A?
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Solution
Number of soldiers from country A = 25% of 120 = 0.25 * 120 = 30.
Correct Answer:
C
— 30
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Q. Evaluate the integral ∫ (3x^2 - 4) dx.
A.
x^3 - 4x + C
B.
x^3 - 2x + C
C.
3x^3 - 4x + C
D.
x^3 - 4x
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Solution
The integral evaluates to x^3 - 4x + C, where C is the constant of integration.
Correct Answer:
A
— x^3 - 4x + C
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Q. Evaluate the integral ∫ (4x^3 - 2x) dx.
A.
x^4 - x^2 + C
B.
x^4 - x^2
C.
x^4 - x^2 + 2C
D.
4x^4 - x^2 + C
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Solution
The integral is (4/4)x^4 - (2/2)x^2 + C = x^4 - x^2 + C.
Correct Answer:
A
— x^4 - x^2 + C
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