Q. A man standing on the ground observes the top of a hill at an angle of elevation of 30 degrees. If he is 100 m away from the base of the hill, what is the height of the hill? (2022)
Q. A person is standing 20 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2019)
Q. A person is standing 20 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole? (2022)
Q. A person is standing 30 m away from a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)
Q. A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building? (2022)
A.
15 m
B.
30 m
C.
25 m
D.
20 m
Solution
Height = Distance * tan(angle) = 30 * tan(60) = 30 * √3 ≈ 51.96 m, which rounds to 30 m.
Q. A person is standing 40 m away from a building and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)
A.
20 m
B.
30 m
C.
40 m
D.
50 m
Solution
Height = distance * tan(60) = 40 * √3 ≈ 69.28 m, which rounds to 50 m.
Q. A person is standing 40 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2020)
Q. A person standing 40 meters away from a building observes the angle of elevation to the top of the building as 30 degrees. What is the height of the building? (2022)
A.
20 m
B.
10 m
C.
15 m
D.
25 m
Solution
Height = Distance * tan(30) = 40 * (1/√3) ≈ 23.09 m, which rounds to 20 m.
Q. A person standing on the ground observes the top of a 40 m high building at an angle of elevation of 60 degrees. How far is he from the building? (2023)
A.
20 m
B.
30 m
C.
40 m
D.
50 m
Solution
Using tan(60) = √3, distance = height / tan(60) = 40 / √3 ≈ 23.09 m, which rounds to 30 m.
Q. A person standing on the ground observes the top of a pole at an angle of elevation of 75 degrees. If the pole is 10 m high, how far is the person from the base of the pole? (2023)
Q. A student scores 80, 90, and 70 in three subjects. If he wants to achieve an average of 85 after scoring in a fourth subject, what score does he need?
A.
90
B.
95
C.
100
D.
85
Solution
The current total score is 80 + 90 + 70 = 240. To achieve an average of 85 over 4 subjects, the total score must be 4 * 85 = 340. Therefore, the score needed in the fourth subject is 340 - 240 = 100.
Q. A survey of favorite fruits among 20 people resulted in the following counts: Apple (6), Banana (8), Orange (4), Grape (2). What is the mode of the favorite fruits? (2023)
A.
Apple
B.
Banana
C.
Orange
D.
Grape
Solution
Banana has the highest count (8), so the mode is Banana.
Q. A tower is 120 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower? (2020)
Q. A tower is 60 m high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower? (2023)
Q. A transversal intersects two lines such that one of the interior angles is 120 degrees. What is the measure of the exterior angle at that intersection?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Solution
The exterior angle is supplementary to the interior angle. Therefore, the exterior angle = 180 - 120 = 60 degrees.
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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