Q. The equation x^2 - 4x + k = 0 has equal roots when k is equal to:
Show solution
Solution
For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0 leads to k = 4.
Correct Answer:
A
— 4
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Q. The equation x^2 - 4x + k = 0 has no real roots if k is:
A.
< 4
B.
≥ 4
C.
≤ 4
D.
> 4
Show solution
Solution
The discriminant must be less than zero: (-4)^2 - 4*1*k < 0 leads to k > 4.
Correct Answer:
A
— < 4
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Q. The equation x^2 - 6x + 9 = 0 has how many distinct roots?
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Solution
The equation can be factored as (x - 3)(x - 3) = 0, indicating it has one distinct root (a double root).
Correct Answer:
B
— 1
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Q. The equation x^2 - 7x + 10 = 0 has roots that are:
A.
1 and 10
B.
2 and 5
C.
3 and 4
D.
5 and 2
Show solution
Solution
Factoring the equation gives (x - 2)(x - 5) = 0, so the roots are 2 and 5.
Correct Answer:
C
— 3 and 4
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Q. The equation x^3 - 3x^2 + 3x - 1 = 0 has a root at x = 1. What is the multiplicity of this root? (2023)
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Solution
The polynomial can be expressed as (x - 1)^3, indicating that the root x = 1 has a multiplicity of 3.
Correct Answer:
C
— 3
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Q. The equation x^3 - 3x^2 + 3x - 1 = 0 has how many distinct real roots? (2022)
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Solution
The given polynomial can be factored as (x - 1)^3 = 0, which has one distinct real root, x = 1.
Correct Answer:
A
— 1
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Q. The following data represents the number of books read by students in a month: 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the mode?
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Solution
The mode is 3, as it appears most frequently (3 times) in the data set.
Correct Answer:
C
— 3
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Q. The following data represents the number of books read by students in a month: 4, 5, 6, 5, 4, 5, 7, 8, 5. What is the mode?
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Solution
The mode is 5, as it appears 4 times, more than any other number.
Correct Answer:
B
— 5
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Q. The following data set has the numbers: 2, 3, 4, 4, 5, 5, 5, 6, 7. What is the mode of this data set? (2020)
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Solution
The number 5 appears most frequently (3 times), so the mode is 5.
Correct Answer:
B
— 5
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Q. The following data set represents the ages of participants in a survey: 22, 25, 22, 30, 25, 22, 28. What is the mode?
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Solution
The mode is 22, as it appears most frequently (three times) in the data set.
Correct Answer:
A
— 22
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Q. The following data set shows the number of pets owned by families: 2, 3, 2, 4, 3, 2, 5. What is the mode?
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Solution
The mode is 2, as it appears 3 times, which is more than any other number.
Correct Answer:
A
— 2
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Q. The following data shows the number of goals scored by a team in 7 matches: 1, 2, 2, 3, 2, 4, 5. What is the mode?
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Solution
The mode is 2, as it appears 3 times, more than any other number.
Correct Answer:
B
— 2
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Q. The following data shows the number of pets owned by families: 0, 1, 1, 2, 2, 2, 3, 4. What is the mode?
Show solution
Solution
The mode is 2, as it appears most frequently (3 times) in the data set.
Correct Answer:
C
— 2
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Q. The following data shows the number of pets owned by families: 1, 1, 2, 2, 3, 3, 3, 4. What is the mode?
Show solution
Solution
The mode is 3, as it appears most frequently (3 times) in the data set.
Correct Answer:
C
— 3
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Q. The following numbers are given: 8, 3, 5, 12, 7. What is the median?
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Solution
Arrange the numbers: 3, 5, 7, 8, 12. The median is the middle value, which is 7.
Correct Answer:
C
— 8
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Q. The following numbers represent the number of books read by students: 1, 2, 2, 3, 4, 4, 4, 5. What is the mode?
Show solution
Solution
The mode is 4, as it appears three times, which is more than any other number.
Correct Answer:
C
— 4
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Q. The following numbers represent the number of books read by students: 5, 3, 5, 2, 5, 4, 3. What is the mode?
Show solution
Solution
The mode is 5, as it appears 4 times, which is more than any other number.
Correct Answer:
D
— 5
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Q. The following numbers represent the number of games won by a team in a season: 5, 6, 6, 7, 8, 8, 8, 9. What is the mode?
Show solution
Solution
The mode is 8, as it appears most frequently (3 times) in the data set.
Correct Answer:
D
— 8
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Q. The following numbers represent the number of goals scored by a team in 10 matches: 1, 2, 2, 3, 3, 3, 4, 4, 5. What is the mode?
Show solution
Solution
The mode is 3, as it appears most frequently (3 times) in the data set.
Correct Answer:
B
— 3
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Q. The following numbers represent the number of hours studied by students: 1, 2, 2, 3, 3, 4, 4, 4, 5. What is the mode?
Show solution
Solution
The mode is 4, as it appears most frequently (3 times) in the data set.
Correct Answer:
C
— 4
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Q. The following numbers represent the number of hours studied by students: 5, 6, 5, 7, 8, 5, 6. What is the mode?
Show solution
Solution
The mode is 5, as it appears 3 times, more than any other number.
Correct Answer:
A
— 5
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Q. The following numbers represent the number of hours studied by students: 5, 6, 6, 7, 8, 8, 8, 9, 10. What is the mode?
Show solution
Solution
The mode is 8, as it appears most frequently (3 times) in the data set.
Correct Answer:
C
— 8
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Q. The following numbers represent the number of languages spoken by individuals: 1, 2, 2, 3, 3, 3, 4, 5. What is the mode?
Show solution
Solution
The mode is 3, as it appears most frequently (3 times) in the data set.
Correct Answer:
C
— 3
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Q. The following numbers represent the number of pets owned by a group of people: 0, 1, 1, 2, 2, 2, 3. What is the mode?
Show solution
Solution
The number 2 appears 3 times, which is more than any other number, making it the mode.
Correct Answer:
C
— 2
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Q. The following numbers represent the number of pets owned by families: 0, 1, 1, 2, 2, 2, 3, 4. What is the mode?
Show solution
Solution
The mode is 2, as it appears most frequently (3 times) in the data set.
Correct Answer:
C
— 2
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Q. The following numbers represent the scores of a game: 20, 30, 20, 40, 30, 30, 50. What is the mode?
Show solution
Solution
The mode is 30, as it appears three times, more than any other score.
Correct Answer:
B
— 30
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Q. The following numbers represent the scores of a test: 45, 55, 65, 75, 85, 95. What is the median score? (2019)
Show solution
Solution
Arrange the scores: 45, 55, 65, 75, 85, 95. The median is the average of the 3rd and 4th scores: (65 + 75) / 2 = 70.
Correct Answer:
C
— 75
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Q. The following scores were obtained in a quiz: 10, 10, 20, 20, 20, 30, 30, 40. What is the mode?
Show solution
Solution
The mode is 20, as it appears most frequently (3 times) in the data set.
Correct Answer:
B
— 20
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Q. The following scores were recorded in a game: 10, 20, 10, 30, 20, 10, 40. What is the mode?
Show solution
Solution
The mode is 10, as it appears 3 times, which is more than any other score.
Correct Answer:
A
— 10
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Q. The function f(x) = 1/(x-1) is continuous on which of the following intervals?
A.
(-∞, 1)
B.
(1, ∞)
C.
(-∞, ∞)
D.
(-∞, 0)
Show solution
Solution
The function f(x) = 1/(x-1) is discontinuous at x = 1, hence it is continuous on (1, ∞).
Correct Answer:
B
— (1, ∞)
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Showing 1051 to 1080 of 1593 (54 Pages)
Mathematics (NDA) MCQ & Objective Questions
Mathematics plays a crucial role in the NDA exam, as it tests your analytical and problem-solving skills. Practicing Mathematics (NDA) MCQ and objective questions is essential for scoring better in this competitive environment. By focusing on practice questions, you can identify important questions and enhance your exam preparation effectively.
What You Will Practise Here
Algebra: Understanding equations, inequalities, and functions.
Geometry: Key concepts of shapes, angles, and theorems.
Trigonometry: Important ratios, identities, and applications.
Statistics: Basics of mean, median, mode, and standard deviation.
Probability: Fundamental principles and problem-solving techniques.
Calculus: Introduction to limits, derivatives, and integrals.
Mensuration: Formulas for areas and volumes of various shapes.
Exam Relevance
The Mathematics (NDA) syllabus is relevant not only for the NDA exam but also for various other competitive exams like CBSE, State Boards, NEET, and JEE. In these exams, you will often encounter multiple-choice questions that test your understanding of mathematical concepts. Common question patterns include direct application of formulas, problem-solving scenarios, and conceptual understanding, making it essential to practice regularly.
Common Mistakes Students Make
Misinterpreting the question: Students often overlook key details in the problem statement.
Formula errors: Forgetting or misapplying mathematical formulas can lead to incorrect answers.
Calculation mistakes: Simple arithmetic errors can cost valuable marks.
Neglecting units: Failing to consider units in problems involving measurements.
Rushing through questions: Students may skip steps or fail to double-check their work under time pressure.
FAQs
Question: What are the best ways to prepare for Mathematics (NDA) MCQs?Answer: Regular practice with objective questions, understanding key concepts, and solving previous years' papers are effective strategies.
Question: How can I improve my speed in solving Mathematics (NDA) questions?Answer: Time yourself while practicing and focus on solving simpler problems quickly to build speed and confidence.
Start solving Mathematics (NDA) MCQs today to test your understanding and boost your confidence for the exams. Remember, consistent practice is the key to success!
