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. Find the value of x for which the function f(x) = x^3 - 6x^2 + 9x has an inflection point.
Show solution
Solution
To find inflection points, set f''(x) = 0. f''(x) = 6x - 12. Setting 6x - 12 = 0 gives x = 2.
Correct Answer:
B
— 2
Learn More →
Q. Find the value of x where the function f(x) = x^3 - 6x^2 + 9x has a local minimum. (2020)
Show solution
Solution
Setting f'(x) = 3x^2 - 12x + 9 = 0 gives x = 1, 3. Testing shows x = 2 is a local minimum.
Correct Answer:
B
— 2
Learn More →
Q. Find the value of x where the function f(x) = x^3 - 6x^2 + 9x has an inflection point.
A.
x = 1
B.
x = 2
C.
x = 3
D.
x = 0
Show solution
Solution
To find inflection points, set f''(x) = 0. f''(x) = 6x - 12. Setting it to zero gives x = 2.
Correct Answer:
B
— x = 2
Learn More →
Q. For the cubic equation x^3 - 3x^2 + 3x - 1 = 0, which of the following is a root?
Show solution
Solution
By substituting x = 1 into the equation, we find that it satisfies the equation, hence 1 is a root.
Correct Answer:
C
— 1
Learn More →
Q. For the cubic equation x^3 - 3x^2 + 3x - 1 = 0, which of the following is true about its roots?
A.
All roots are real
B.
All roots are complex
C.
One root is real and two are complex
D.
Two roots are real and one is complex
Show solution
Solution
The roots can be found using the Rational Root Theorem and synthetic division, confirming that all roots are real.
Correct Answer:
A
— All roots are real
Learn More →
Q. For the data set 2, 3, 3, 4, 4, 4, 5, 5, what is the mode?
Show solution
Solution
The mode is 4, as it appears 3 times, more than any other number.
Correct Answer:
C
— 4
Learn More →
Q. For the data set: 1, 2, 3, 4, 5, what is the variance? (2022)
Show solution
Solution
Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.
Correct Answer:
B
— 1.5
Learn More →
Q. For the data set: 10, 12, 14, 16, 18, calculate the variance. (2020)
Show solution
Solution
Mean = (10 + 12 + 14 + 16 + 18) / 5 = 14. Variance = [(10-14)² + (12-14)² + (14-14)² + (16-14)² + (18-14)²] / 5 = 8.
Correct Answer:
A
— 8
Learn More →
Q. For the data set: 10, 12, 14, 16, what is the variance? (2019)
Show solution
Solution
Mean = (10 + 12 + 14 + 16) / 4 = 13. Variance = [(10-13)² + (12-13)² + (14-13)² + (16-13)²] / 4 = 2.
Correct Answer:
B
— 4
Learn More →
Q. For the data set: 2, 4, 6, 8, 10, what is the variance? (2023)
Show solution
Solution
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 6. Variance = [(2-6)² + (4-6)² + (6-6)² + (8-6)² + (10-6)²] / 5 = 8.
Correct Answer:
A
— 6
Learn More →
Q. For the data set: 3, 3, 3, 3, 3, what is the variance? (2023)
Show solution
Solution
All values are the same, so variance = 0.
Correct Answer:
A
— 0
Learn More →
Q. For the data set: 5, 7, 9, 11, 13, what is the variance?
Show solution
Solution
Mean = 9. Variance = [(5-9)² + (7-9)² + (9-9)² + (11-9)² + (13-9)²] / 5 = 8.
Correct Answer:
A
— 4
Learn More →
Q. For the data set: 5, 8, 12, 15, 20, what is the median? (2020)
Show solution
Solution
Arranging the numbers: 5, 8, 12, 15, 20. The median is the middle number, which is 12.
Correct Answer:
A
— 12
Learn More →
Q. For the data set: 6, 7, 8, 8, 9, 9, 9, 10, what is the mode?
Show solution
Solution
The mode is 9, as it appears most frequently (three times) in the data set.
Correct Answer:
D
— 9
Learn More →
Q. For the equation x^2 + 2x + 1 = 0, what is the nature of the roots?
A.
Real and distinct
B.
Real and equal
C.
Complex
D.
None of the above
Show solution
Solution
The discriminant is 2^2 - 4(1)(1) = 0, indicating that the roots are real and equal.
Correct Answer:
B
— Real and equal
Learn More →
Q. For the equation x^2 + 4x + k = 0 to have real roots, what must be the condition on k? (2023)
A.
k >= 0
B.
k <= 0
C.
k >= 16
D.
k <= 16
Show solution
Solution
The discriminant must be non-negative: 4^2 - 4*1*k >= 0 leads to 16 - 4k >= 0, thus k <= 4.
Correct Answer:
C
— k >= 16
Learn More →
Q. For the equation x^2 + 6x + k = 0 to have no real roots, what must be the condition on k?
A.
k < 0
B.
k > 0
C.
k = 0
D.
k ≤ 0
Show solution
Solution
The condition for no real roots is that the discriminant must be less than zero: 6^2 - 4*1*k < 0 => 36 < 4k => k > 9.
Correct Answer:
D
— k ≤ 0
Learn More →
Q. For the equation x^3 - 3x^2 + 3x - 1 = 0, how many real roots does it have?
Show solution
Solution
The equation can be factored as (x-1)^3 = 0, which has one real root (x = 1) with multiplicity 3.
Correct Answer:
A
— 1
Learn More →
Q. For the equation x^3 - 4x^2 + 5x - 2 = 0, which of the following is a root? (2023)
Show solution
Solution
By substituting x = 2 into the equation, we find that it satisfies the equation, thus x = 2 is a root.
Correct Answer:
B
— 2
Learn More →
Q. For the equation x^3 - 6x^2 + 11x - 6 = 0, what is the product of the roots? (2019)
Show solution
Solution
The product of the roots of the cubic equation ax^3 + bx^2 + cx + d = 0 is given by -d/a. Here, d = -6 and a = 1, so the product is -(-6)/1 = 6.
Correct Answer:
A
— 6
Learn More →
Q. For the equation x^3 - 6x^2 + 11x - 6 = 0, which of the following is a root?
Show solution
Solution
By substituting x = 2 into the equation, we find that 2 is a root since 2^3 - 6(2^2) + 11(2) - 6 = 0.
Correct Answer:
B
— 2
Learn More →
Q. For the function f(x) = -x^2 + 4x + 1, find the maximum value. (2023)
Show solution
Solution
The maximum occurs at x = -b/(2a) = -4/(-2) = 2. f(2) = -2^2 + 4(2) + 1 = 5.
Correct Answer:
B
— 5
Learn More →
Q. For the function f(x) = 3x^2 - 12x + 7, find the coordinates of the minimum point. (2019)
A.
(2, -5)
B.
(2, -1)
C.
(4, 1)
D.
(4, -5)
Show solution
Solution
The vertex is at x = -(-12)/(2*3) = 2. The minimum value is f(2) = 3(2^2) - 12(2) + 7 = -5. Thus, the coordinates are (2, -5).
Correct Answer:
A
— (2, -5)
Learn More →
Q. For the function f(x) = e^x, what is f''(x)? (2021)
Show solution
Solution
The second derivative f''(x) = d/dx(e^x) = e^x.
Correct Answer:
A
— e^x
Learn More →
Q. For the function f(x) = sin(x) + cos(x), what is f'(π/4)? (2023)
Show solution
Solution
f'(x) = cos(x) - sin(x). At x = π/4, f'(π/4) = cos(π/4) - sin(π/4) = √2/2 - √2/2 = 0.
Correct Answer:
B
— √2
Learn More →
Q. For the function f(x) = sin(x), what is f'(π/2)? (2021)
A.
0
B.
1
C.
-1
D.
undefined
Show solution
Solution
f'(x) = cos(x); f'(π/2) = cos(π/2) = 0.
Correct Answer:
B
— 1
Learn More →
Q. For the function f(x) = x^2 - 6x + 10, what is the minimum value? (2020)
Show solution
Solution
The vertex is at x = 6/2 = 3. The minimum value is f(3) = 3^2 - 6*3 + 10 = 1.
Correct Answer:
B
— 3
Learn More →
Q. For the function f(x) = x^3 - 3x + 2, find the points of discontinuity.
A.
None
B.
x = 1
C.
x = -1
D.
x = 2
Show solution
Solution
f(x) is a polynomial function and is continuous everywhere, hence no points of discontinuity.
Correct Answer:
A
— None
Learn More →
Q. For the function f(x) = { 2x + 1, x < 1; 3, x = 1; x^2, x > 1 }, is f(x) continuous at x = 1?
A.
Yes
B.
No
C.
Only left continuous
D.
Only right continuous
Show solution
Solution
The left limit as x approaches 1 is 3, the right limit is 1, and f(1) = 3. Since the limits do not match, f(x) is discontinuous at x = 1.
Correct Answer:
B
— No
Learn More →
Q. For the function f(x) = { x^2, x < 0; 0, x = 0; x + 1, x > 0 }, is f(x) continuous at x = 0?
A.
Yes
B.
No
C.
Only left continuous
D.
Only right continuous
Show solution
Solution
The left limit as x approaches 0 is 0, the right limit is 1, and f(0) = 0. Since the limits do not match, f(x) is discontinuous at x = 0.
Correct Answer:
B
— No
Learn More →
Showing 781 to 810 of 3872 (130 Pages)
