Number System Math MCQS With Answers, Binary and Decimal Aptitude MCQs Test Preparation
ECAT Mathematics Number System is the most important for each student appearing in the ECAT (Engineering College Admission Test) test as in this topic you learn about different numbers, including types of numbers and properties of numbers. This concept, if understood well can help you score well in the mathematics section.
A good understanding of the number system is crucial for students with ECAT, as well as advanced studies such as algebra and calculus. This guide contains all the core content, solutions techniques for the problem, followed by MCQs for practice.
Understanding the Number System
In mathematics, the system of numbers is a way of representing and classifying numbers. It includes several types, such as Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers, etc. For ECAT candidates, it is important to have a clear understanding of these types as many MCQs may be based on their properties and interrelations.
1. Types of Numbers
- Natural Numbers (N): The set of all positive integers from 1 to infinity (1, 2, 3, …).
- Whole Numbers (W): All natural numbers including 0 (0, 1, 2, 3, …).
- Integers (Z): A set of whole numbers that includes both positive and negative numbers (-3, -2, -1, 0, 1, 2, 3, …).
- Rational Numbers (Q): Numbers that can be written as p/q (e.g., 1/2, 3/4, 5, −7), where q ≠0 and both p and q are integers.
- Irrational Numbers (Q’): An irrational number that cannot be expressed as a fraction, their decimal expansion is non-repeating, and non-terminating ( e.g. √2, π).
- Real Numbers (R): The complete set of rational and irrational numbers.
2. Binary and Decimal Number Systems
- Decimal System: The standard system of numbers based on 10 (0-9).
- Binary System: A number system based on two digits, 0 and 1, widely used in computing and digital systems.
- Conversion: Converting between binary and decimal systems is a common question type in ECAT mathematics.
Key Properties and Operations
Basic Arithmetic Operations
- Addition (+) and Subtraction (-) are binary operations that follow closure, commutativity, and associativity in real numbers.
- Multiplication (×) is distributive over addition.
- Division (÷) is only defined when the denominator is nonzero.
Special Number Properties
- Even and Odd Numbers: The even no are fully divisible by 2 and odd no are just not.
- Prime Numbers: Number greater than 1 and the numbers that can only be divided by themself are called prime numbers.
- Perfect Squares: The numbers that are the squares of integers (e.g., 4, 9, 16, 25).
- Recurring Decimals: All recurring decimals are rational numbers.
- Multiplicative and Additive Identity: The real number multiplicative identity is 1 and the additive identity is 0.
MCQs Preparation Strategy
To excel in mathematics number system MCQs, follow these strategies:
- Regular Practice: Solve past ECAT papers and timed quizzes.
- Concept Clarity: Focus on definitions, number properties, and conversion techniques.
- Shortcut Methods: Learn quick mental math techniques for faster calculations.
- Formula Review: Memorize key properties of numbers and arithmetic operations.
- Time Management: Practice under timed conditions to improve speed and accuracy.
Sample MCQs for Practice
1. ‘÷’ is
- A binary operation in N
- A binary operation in R\{0} correct
- A binary operation in Qc
- A binary operation in R
2. Every even integer is also
- Natural number
- Irrational number
- Rational number correct
- Whole number
3. √34 is
- A rational number
- An irrational number correct
- A negative integer
- A natural number
4. ‘÷’ is
- A binary operation in R
- A binary operation in Qc
- A binary operation in E
- Not A binary operation in R correct
5. ‘-’ is
- A binary operation in O
- A binary operation in R correct
- Not A binary operation in R
- A binary operation in Qc
6. If n is prim, then√n is
- Natural number
- Rational number
- Whole number
- Irrational number correct
7. √36 is
- An irrational number
- An even integer
- A factor of 26
- A rational number correct
8. ‘.’ Is
- A binary operation in Qc
- Not a binary operation in E
- A binary operation in R correct
- Not a binary operation in R
9. A number that can be written in the form p/q, where p and q are relatively prime integers and q = 0 is called the
- Index number
- Irrational number
- Rational number correct
- Imaginary number
10. ‘+’ is
- Not a binary operation in E
- A binary operation in Qc
- A binary operation in R correct
- Not a binary operation in R
11. Every non-repeating non-terminating decimal is
- none of these
- Irrational number correct
- integer
- Rational number
12. If n is a perfect square, then √n is
- An irrational number
- Always an even integer
- Always an odd integer
- A rational number correct
13. 3 is
- A negative integer
- A rational number correct
- An irrational number
- An odd integer
14. √3 is
- A natural number
- An irrational number correct
- A negative integer
- A rational number
15. Every natural number is also
- negative integer
- rational number correct
- irrational number
- even integer
16. π is
- An irrational number correct
- A rational number
- A whole number
- A natural number
17. The multiplicative identity of real numbers is
- 1correct
- 3
- 0
- 2
18. Every recurring decimal or terminating decimal represents the
- Rational number correct
- Irrational number
- Natural number
- Integer
19. 0 is
- An even integer correct
- An irrational number
- An odd integer
- A natural number
20. If ‘*’ is a binary operation in a set A, then for all a,b Є A,
- A x b Є A
- A*b Є A correct
- A – b Є A
- A + b Є A
21. The additive inverse of 2 is
- 1
- -2 correct
- 0
- 1/2
22. The additive identity of real numbers is
- 1
- 2
- 0
correct - 3
23. Every odd integer is also
- Rational number
correct - Positive integer
- Negative integer
- Irrational number
24. Every integer is also
- natural number
- irrational number
- Whole number
- negative integer
correct
25. ‘÷’ is
- A binary operation in N
- A binary operation in Q – {0}correct
- A binary operation in R
- A binary operation in Qc
Conclusion
In order to shine in the ECAT mathematics section mastering the mathematics number system is essential. Knowing more about the properties of numbers and operations can help improve the efficiency and accuracy of problem-solving.
However, regular practice, understanding each concept thoroughly, and working through MCQs can make a huge difference in the performance on the test. The number system is an important part of ECAT and this subject provide a good foundation before going to higher mathematics with engineering studies. Regular practice is the key to be successful in this subject.