Q. In a family with 3 children, what is the probability that at least one of them is a girl?
A.
1/8
B.
1/2
C.
7/8
D.
3/8
Solution
The only scenario where there are no girls is if all three children are boys, which has a probability of (1/2)^3 = 1/8. Therefore, the probability of having at least one girl is 1 - 1/8 = 7/8.
Q. In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a person chosen at random likes either tea or coffee?
A.
1/2
B.
3/5
C.
4/5
D.
1/5
Solution
Using the principle of inclusion-exclusion, P(Tea or Coffee) = P(Tea) + P(Coffee) - P(Both) = (30/50) + (20/50) - (10/50) = 40/50 = 4/5.
Q. In a pair of alternate exterior angles, if one angle measures 120 degrees, what is the measure of the other angle? (2021)
A.
60 degrees
B.
120 degrees
C.
180 degrees
D.
90 degrees
Solution
Alternate exterior angles are equal when two parallel lines are cut by a transversal. Therefore, if one angle is 120 degrees, the other alternate exterior angle is also 120 degrees.
Q. In a right triangle, if one angle is 30 degrees, what is the ratio of the lengths of the sides opposite to the 30 degrees and 60 degrees angles? (2019)
A.
1:√3
B.
1:2
C.
√3:1
D.
2:1
Solution
In a 30-60-90 triangle, the sides opposite the 30 degrees and 60 degrees angles are in the ratio 1:√3.
Q. In a right triangle, if one angle is 45 degrees, what is the measure of the other non-right angle? (2021)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Solution
In a right triangle, the sum of the angles is 180 degrees. If one angle is 45 degrees and the right angle is 90 degrees, the other angle must be 180 - (90 + 45) = 45 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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