Mathematics (NDA)

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Mathematics (NDA)

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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!

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Q. A 15-meter tall tree casts a shadow of 10 meters. What is the angle of elevation of the sun? (2019)

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 75 degrees

Solution

tan(θ) = height/shadow = 15/10 = 1.5, θ = tan⁻¹(1.5) ≈ 56.31 degrees, which is closest to 60 degrees.

Correct Answer: C — 60 degrees

Q. A bag contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is not black?

A. 2/5
B. 1/5
C. 1/2
D. 4/10

Solution

Total balls = 4 + 6 = 10. Probability of not drawing a black ball = Number of white balls / Total balls = 4/10 = 2/5.

Correct Answer: A — 2/5

Q. A bag contains 4 white balls and 6 black balls. If one ball is drawn at random, what is the probability that it is not black?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

Total balls = 4 + 6 = 10. Probability of not drawing a black ball = Number of white balls / Total balls = 4/10 = 2/5.

Correct Answer: C — 4/5

Q. A bag contains 4 white balls and 6 black balls. If one ball is drawn at random, what is the probability that it is black?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

The total number of balls is 4 + 6 = 10. The number of black balls is 6. Therefore, the probability of drawing a black ball is 6/10 = 3/5.

Correct Answer: B — 3/5

Q. A bag contains 4 white, 3 black, and 5 red balls. If one ball is drawn at random, what is the probability that it is not black?

A. 1/4
B. 3/4
C. 5/12
D. 2/3

Solution

Total balls = 4 + 3 + 5 = 12. Non-black balls = 4 + 5 = 9. Probability = Non-black balls / Total balls = 9/12 = 3/4.

Correct Answer: B — 3/4

Q. A bag contains 4 white, 5 black, and 6 red balls. If one ball is drawn at random, what is the probability that it is not black?

A. 1/3
B. 2/3
C. 5/11
D. 7/11

Solution

Total balls = 4 + 5 + 6 = 15. Non-black balls = 4 + 6 = 10. Probability = Non-black balls / Total balls = 10/15 = 2/3.

Correct Answer: D — 7/11

Q. A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? (2022)

A. 3/8
B. 5/8
C. 1/2
D. 1/3

Solution

Total balls = 5 + 3 = 8. Probability of red ball = Number of red balls / Total balls = 5/8.

Correct Answer: B — 5/8

Q. A box contains 10 balls numbered from 1 to 10. What is the probability of drawing a ball with an even number?

A. 1/2
B. 1/5
C. 1/10
D. 3/10

Solution

Even numbers in the box are 2, 4, 6, 8, 10 (5 even numbers). Total balls = 10. Probability = 5/10 = 1/2.

Correct Answer: A — 1/2

Q. A box contains 10 balls, 4 of which are red. If one ball is drawn at random, what is the probability that it is red? (2020)

A. 2/5
B. 1/2
C. 4/10
D. 3/10

Solution

Probability of drawing a red ball = Number of red balls / Total balls = 4/10 = 2/5.

Correct Answer: B — 1/2

Q. A box contains 10 balls, 4 of which are white. If one ball is drawn at random, what is the probability that it is not white? (2022)

A. 2/5
B. 3/5
C. 1/2
D. 1/4

Solution

Number of non-white balls = 10 - 4 = 6. Probability = 6/10 = 3/5.

Correct Answer: B — 3/5

Q. A box contains 10 balls, of which 4 are red and 6 are blue. If one ball is drawn, what is the probability that it is not red?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

Probability of not red = Number of non-red balls / Total balls = 6/10 = 3/5.

Correct Answer: B — 3/5

Q. A box contains 10 balls, of which 4 are white and 6 are black. If one ball is drawn at random, what is the probability that it is white?

A. 2/5
B. 3/5
C. 4/10
D. 1/2

Solution

Probability of white = Number of white balls / Total balls = 4/10 = 2/5.

Correct Answer: C — 4/10

Q. A box contains 10 balls, of which 4 are white and 6 are black. If one ball is drawn at random, what is the probability that it is black?

A. 3/5
B. 2/5
C. 1/2
D. 6/10

Solution

Probability of drawing a black ball = Number of black balls / Total balls = 6/10 = 3/5.

Correct Answer: A — 3/5

Q. A box contains 10 balls, of which 4 are white and 6 are black. If one ball is drawn, what is the probability that it is black?

A. 3/5
B. 2/5
C. 1/2
D. 1/10

Solution

Probability = Number of black balls / Total balls = 6/10 = 3/5.

Correct Answer: A — 3/5

Q. A box contains 10 light bulbs, of which 3 are defective. If one bulb is selected at random, what is the probability that it is not defective?

A. 3/10
B. 7/10
C. 1/2
D. 1/3

Solution

Total bulbs = 10, Non-defective bulbs = 10 - 3 = 7. Probability = Non-defective bulbs / Total bulbs = 7/10.

Correct Answer: B — 7/10

Q. A box contains 3 red balls and 2 blue balls. If one ball is drawn at random, what is the probability that it is red?

A. 1/5
B. 2/5
C. 3/5
D. 4/5

Solution

The total number of balls is 3 + 2 = 5. The number of red balls is 3. Therefore, the probability of drawing a red ball is 3/5.

Correct Answer: C — 3/5

Q. A box contains 3 red, 5 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue?

A. 1/10
B. 1/5
C. 1/2
D. 1/3

Solution

Total balls = 3 + 5 + 2 = 10. Probability of drawing a blue ball = Number of blue balls / Total balls = 5/10 = 1/2.

Correct Answer: B — 1/5

Q. A box contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? (2021)

A. 3/8
B. 5/8
C. 1/2
D. 1/3

Solution

Total balls = 5 + 3 = 8. Probability of red = 5/8.

Correct Answer: B — 5/8

Q. A building is 40 m tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. How far is the point from the base of the building? (2020)

A. 20 m
B. 30 m
C. 40 m
D. 50 m

Solution

Distance = height / tan(angle) = 40 / tan(45) = 40 / 1 = 40 m.

Correct Answer: C — 40 m

Q. A building is 50 m tall. If a person standing 40 m away from the building sees the top at an angle of elevation of θ, what is the value of θ? (2021)

A. 36.87 degrees
B. 45 degrees
C. 53.13 degrees
D. 60 degrees

Solution

tan(θ) = height/distance = 50/40, θ = tan⁻¹(1.25) ≈ 53.13 degrees.

Correct Answer: C — 53.13 degrees

Q. A car travels 60 km in 1 hour. How far will it travel in 3 hours at the same speed? (2021)

A. 120 km
B. 150 km
C. 180 km
D. 200 km

Solution

Distance = speed × time = 60 km/h × 3 h = 180 km.

Correct Answer: C — 180 km

Q. A chord of a circle is 8 cm long and is 3 cm away from the center. What is the radius of the circle? (2021)

A. 5 cm
B. 7 cm
C. 10 cm
D. 9 cm

Solution

Using Pythagoras theorem, r² = (3)² + (4)² = 9 + 16 = 25. Thus, r = 5 cm.

Correct Answer: B — 7 cm

Q. A circle has a circumference of 31.4 cm. What is its radius? (2021)

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Circumference = 2πr. Thus, r = Circumference/(2π) = 31.4/(2π) = 5 cm.

Correct Answer: A — 5 cm

Q. A class has 30 students with an average score of 75. If 5 new students join with an average score of 80, what is the new average? (2023)

A. 76
B. 77
C. 78
D. 79

Solution

Total score of 30 students = 30 * 75 = 2250. Total score of 5 new students = 5 * 80 = 400. New total = 2250 + 400 = 2650. New average = 2650 / 35 = 76.43.

Correct Answer: C — 78

Q. A class has 30 students with an average score of 75. If a new student joins and the average becomes 76, what is the score of the new student? (2023)

A. 80
B. 85
C. 90
D. 95

Solution

Total score of 30 students = 30 * 75 = 2250. New total = 31 * 76 = 2356. Score of new student = 2356 - 2250 = 106.

Correct Answer: B — 85

Q. A class has an average score of 75. If one student scored 90, what is the average score of the remaining students if there are 20 students in total?

A. 74
B. 75
C. 76
D. 77

Solution

The total score of the class is 75 * 20 = 1500. Removing the student who scored 90 gives a new total of 1500 - 90 = 1410. The average of the remaining 19 students is 1410 / 19 = 74.21, which rounds to 74.

Correct Answer: A — 74

Q. A class has the following scores in a test: 56, 78, 78, 82, 82, 82, 90, 91. What is the mode of the scores?

A. 56
B. 78
C. 82
D. 90

Solution

The mode is 82, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 82

Q. A class of 30 students has an average score of 75. If one student scores 90, what will be the new average? (2022)

A. 76
B. 77
C. 78
D. 79

Solution

Total score = 75 * 30 = 2250. New total = 2250 - 75 + 90 = 2265. New average = 2265 / 30 = 75.5.

Correct Answer: B — 77

Q. A class of students scored the following marks: 45, 50, 50, 55, 60, 60, 60, 70, 75. What is the mode of the scores?

A. 50
B. 55
C. 60
D. 70

Solution

The mode is 60, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 60

Q. A class of students scored the following marks: 45, 55, 55, 60, 60, 60, 70, 75, 80. What is the mode of the scores?

A. 45
B. 55
C. 60
D. 70

Solution

The mode is 60, as it appears most frequently (3 times) in the scores.

Correct Answer: C — 60

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