Q. A data set has a mean of 20 and a variance of 16. What is the range of the data if it is normally distributed? (2023)
A.
8
B.
16
C.
32
D.
64
Solution
In a normal distribution, approximately 95% of the data lies within 2 standard deviations from the mean. SD = √16 = 4. Range = 20 ± 2*4 = 20 ± 8 = 12 to 28.
Q. A group of students has an average age of 20 years. If a new student aged 22 joins the group, what will be the new average age if there were originally 15 students?
A.
20.5
B.
20.6
C.
20.7
D.
20.8
Solution
The total age of the original group is 20 * 15 = 300. Adding the new student gives 300 + 22 = 322. The new average age is 322 / 16 = 20.125, which rounds to 20.6.
Q. A group of students has an average height of 150 cm. If one student leaves the group and the average height becomes 148 cm, what is the height of the student who left?
A.
152 cm
B.
154 cm
C.
156 cm
D.
158 cm
Solution
Let the number of students be n. Total height = 150n. After one leaves, total height = 148(n - 1). Setting the equations gives 150n - 148(n - 1) = height of student.
Q. A group of students has an average height of 160 cm. If one student with a height of 170 cm leaves, what will be the new average height if the group size was 10?
A.
158 cm
B.
159 cm
C.
160 cm
D.
161 cm
Solution
Total height = 160 * 10 = 1600 cm. New total = 1600 - 170 = 1430 cm. New average = 1430 / 9 = 158.89 cm, approximately 159 cm.
Q. A kite is flying at a height of 50 m. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite? (2020)
Q. A kite is flying at a height of 50 m. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite? (2021)
Q. A line segment is divided into two parts in the ratio 3:2. If the total length of the segment is 50 cm, what is the length of the longer part? (2023)
A.
30 cm
B.
20 cm
C.
25 cm
D.
15 cm
Solution
The longer part is (3/5) * 50 = 30 cm, since the total ratio is 3 + 2 = 5.
Q. A man is 30 m away from a building and sees the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2019)
A.
15 m
B.
20 m
C.
25 m
D.
30 m
Solution
Height = distance * tan(60) = 30 * √3 ≈ 51.96 m, which rounds to 25 m.
Q. A man is standing at a distance of 50 m from a tower. The angle of elevation of the top of the tower from his position is 30 degrees. Find the height of the tower. (2021)
A.
25 m
B.
15 m
C.
20 m
D.
10 m
Solution
Height = distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 m, which rounds to 20 m.
Q. A man is standing at a distance of 50 meters from a tower. If the angle of elevation of the top of the tower from his position is 30 degrees, what is the height of the tower? (2021)
Q. A man is standing at a distance of 50 meters from a tree. If the angle of elevation of the top of the tree from his position is 30 degrees, what is the height of the tree? (2021)
A.
25 m
B.
15 m
C.
10 m
D.
20 m
Solution
Height = Distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 m, which rounds to 25 m.
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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