Q. Which of the following numbers is NOT divisible by 7?
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Solution
40 is not divisible by 7, while 21, 28, and 35 are all multiples of 7.
Correct Answer:
D
— 40
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Q. Which of the following numbers is NOT divisible by 8?
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Solution
A number is divisible by 8 if the number formed by its last three digits is divisible by 8. 90 is not divisible by 8.
Correct Answer:
D
— 90
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Q. Which of the following numbers is NOT divisible by 9?
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Solution
A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of the digits of 50 (5 + 0 = 5) is not divisible by 9.
Correct Answer:
D
— 50
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Q. Which of the following numbers is the largest in base-6?
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Solution
In decimal, '54' = 32, '45' = 29, '63' = 39, '36' = 22. '63' is the largest.
Correct Answer:
C
— 63
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Q. Which of the following numbers is the largest in base-8?
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Solution
'72' in base-8 is 58 in decimal, which is larger than the others.
Correct Answer:
D
— 72
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Q. Which of the following numeral systems is most commonly used in digital electronics?
A.
Decimal
B.
Binary
C.
Octal
D.
Hexadecimal
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Solution
The binary system is the most commonly used in digital electronics due to its two-state nature.
Correct Answer:
B
— Binary
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Q. Which of the following numeral systems is not positional?
A.
Decimal
B.
Binary
C.
Roman
D.
Hexadecimal
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Solution
The Roman numeral system is not positional, as it does not use place value to determine the value of digits.
Correct Answer:
C
— Roman
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Q. Which of the following pairs of numbers are congruent modulo 6?
A.
8 and 14
B.
10 and 16
C.
12 and 18
D.
All of the above
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Solution
All pairs have the same remainder when divided by 6: 8 mod 6 = 2, 14 mod 6 = 2; 10 mod 6 = 4, 16 mod 6 = 4; 12 mod 6 = 0, 18 mod 6 = 0.
Correct Answer:
D
— All of the above
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Q. Which of the following pairs of numbers has a GCD of 1?
A.
8 and 12
B.
15 and 28
C.
9 and 27
D.
10 and 20
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Solution
15 and 28 have no common factors other than 1, making their GCD equal to 1.
Correct Answer:
B
— 15 and 28
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Q. Which of the following pairs of numbers has a greatest common divisor (GCD) of 1?
A.
8 and 12
B.
15 and 28
C.
9 and 27
D.
10 and 20
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Solution
15 and 28 are coprime, meaning their GCD is 1.
Correct Answer:
B
— 15 and 28
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Q. Which of the following pairs of numbers has a least common multiple (LCM) of 36?
A.
6 and 12
B.
4 and 9
C.
3 and 18
D.
2 and 18
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Solution
The LCM of 4 and 9 is 36.
Correct Answer:
B
— 4 and 9
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Q. Which of the following pairs of numbers has an HCF of 1? (2023)
A.
8 and 12
B.
15 and 28
C.
9 and 27
D.
14 and 21
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Solution
The HCF of 15 and 28 is 1, making them coprime.
Correct Answer:
B
— 15 and 28
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Q. Which of the following pairs of numbers has an HCF of 6? (2023)
A.
12 and 18
B.
15 and 25
C.
10 and 20
D.
8 and 16
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Solution
The HCF of 12 and 18 is 6, as both numbers are divisible by 6, while the other pairs have higher HCFs.
Correct Answer:
A
— 12 and 18
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Q. Which of the following pairs of numbers has the greatest common factor (GCF) of 1?
A.
8 and 12
B.
15 and 28
C.
9 and 27
D.
14 and 21
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Solution
The GCF of 15 and 28 is 1, making them coprime, while the other pairs share common factors.
Correct Answer:
B
— 15 and 28
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Q. Which of the following statements about base systems is incorrect? (2023)
A.
Base 2 is used in digital electronics.
B.
Base 10 is the most widely used numeral system.
C.
Base 16 can represent more values than base 10.
D.
Base 8 is more efficient than base 2.
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Solution
Base 8 (octal) is not more efficient than base 2 (binary); it simply represents values in a different way.
Correct Answer:
D
— Base 8 is more efficient than base 2.
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Q. Which of the following statements about factors and multiples is correct? (2023)
A.
Every multiple of a number is also a factor of that number.
B.
Factors of a number are always greater than the number itself.
C.
A number can have an infinite number of multiples.
D.
The smallest multiple of any number is always the number itself.
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Solution
A number can have an infinite number of multiples, as you can keep adding the number to itself indefinitely.
Correct Answer:
C
— A number can have an infinite number of multiples.
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Q. Which of the following statements about factors and multiples is incorrect? (2023)
A.
Every multiple of a number is greater than or equal to that number.
B.
A number can have an infinite number of factors.
C.
The product of two numbers is always a multiple of both.
D.
A factor of a number is always greater than the number.
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Solution
A factor of a number is always less than or equal to that number, making the last statement incorrect.
Correct Answer:
D
— A factor of a number is always greater than the number.
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Q. Which of the following statements about factors is incorrect?
A.
Every number has at least two factors.
B.
Factors can be negative.
C.
The number itself is always a factor.
D.
Factors of a prime number are only 1 and the number itself.
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Solution
Every number has at least two factors: 1 and the number itself, but some numbers can have more than two factors.
Correct Answer:
A
— Every number has at least two factors.
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Q. Which of the following statements about multiples is true?
A.
The multiples of a number are infinite.
B.
The multiples of a number are always positive.
C.
The first multiple of any number is the number itself.
D.
All of the above.
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Solution
All statements are true regarding multiples.
Correct Answer:
D
— All of the above.
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Q. Which of the following statements about number systems is true?
A.
Base-10 is the only positional system
B.
Base-2 can represent all integers
C.
Base-16 is less efficient than base-10
D.
Base-5 cannot represent fractions
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Solution
Base-2 can represent all integers, as it is a complete positional system.
Correct Answer:
B
— Base-2 can represent all integers
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Q. Which of the following statements about numeral systems is correct?
A.
All numeral systems are based on the same principles.
B.
Different numeral systems can represent the same value.
C.
The decimal system is the only system used in mathematics.
D.
Base systems are irrelevant in modern computing.
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Solution
Different numeral systems can represent the same value, such as the decimal 10 and binary 1010.
Correct Answer:
B
— Different numeral systems can represent the same value.
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Q. Which of the following statements about numeral systems is incorrect?
A.
Base-10 is the most commonly used system.
B.
Base-16 is used in color codes in web design.
C.
Base-2 is used in human languages.
D.
Base-8 is less common than base-2.
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Solution
Base-2 (binary) is not used in human languages; it is primarily used in computing.
Correct Answer:
C
— Base-2 is used in human languages.
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Q. Which of the following statements about the decimal system is incorrect? (2023)
A.
It is a base 10 system.
B.
It uses digits from 0 to 9.
C.
It is the only system used in mathematics.
D.
It is widely used in everyday life.
Show solution
Solution
The statement that the decimal system is the only system used in mathematics is incorrect; other systems like binary and hexadecimal are also used.
Correct Answer:
C
— It is the only system used in mathematics.
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Q. Which of the following statements about the number 30 is true?
A.
It is a prime number
B.
It has exactly 4 factors
C.
It is a multiple of 5
D.
It is not a composite number
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Solution
30 is a multiple of 5, as it can be expressed as 5 multiplied by 6.
Correct Answer:
C
— It is a multiple of 5
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Q. Which of the following statements can be inferred from the passage about the future of digital sum? (2023)
A.
It will become obsolete with the rise of quantum computing.
B.
It will continue to evolve and integrate with new technologies.
C.
It is likely to be replaced by simpler methods.
D.
It will remain unchanged for the foreseeable future.
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Solution
The passage suggests that digital sum will evolve and integrate with emerging technologies, indicating a promising future.
Correct Answer:
B
— It will continue to evolve and integrate with new technologies.
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Q. Which of the following statements can be inferred from the passage about the importance of digital sum? (2023)
A.
Digital sum is obsolete in today's technology.
B.
Understanding digital sum is crucial for data analysis.
C.
Digital sum has no practical applications.
D.
Only mathematicians need to understand digital sum.
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Solution
The passage suggests that a solid understanding of digital sum is essential for effective data analysis in various fields.
Correct Answer:
B
— Understanding digital sum is crucial for data analysis.
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Q. Which of the following statements is logically consistent with the definition of a factor?
A.
A factor of a number is always greater than the number.
B.
A factor of a number divides the number without leaving a remainder.
C.
A factor can only be a prime number.
D.
A factor is always a multiple of the number.
Show solution
Solution
By definition, a factor divides the number evenly, leaving no remainder.
Correct Answer:
B
— A factor of a number divides the number without leaving a remainder.
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Q. Which of the following statements is logically consistent with the definition of multiples?
A.
Every multiple of 7 is also a multiple of 14.
B.
A number cannot be a multiple of itself.
C.
The sum of two multiples of 3 is always a multiple of 3.
D.
A multiple of 5 is never a multiple of 10.
Show solution
Solution
The sum of two multiples of 3 is always a multiple of 3, as multiples of a number are closed under addition.
Correct Answer:
C
— The sum of two multiples of 3 is always a multiple of 3.
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Q. Which of the following statements is logically consistent with the definition of a multiple?
A.
A multiple of a number is always greater than the number itself.
B.
A multiple of a number can be negative.
C.
A multiple of a number is always an integer.
D.
All of the above.
Show solution
Solution
All statements are true; multiples can be negative, can be equal to the number, and are always integers.
Correct Answer:
D
— All of the above.
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Q. Which of the following statements is logically consistent with the properties of factors?
A.
Every factor of a number is also a multiple of that number.
B.
A number can have an infinite number of factors.
C.
The smallest factor of any number is always 1.
D.
All prime numbers have exactly two factors.
Show solution
Solution
The smallest factor of any number is always 1, as 1 divides every integer.
Correct Answer:
C
— The smallest factor of any number is always 1.
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Showing 571 to 600 of 618 (21 Pages)
Number Systems MCQ & Objective Questions
Understanding number systems is crucial for students preparing for various exams in India. Mastering this topic not only enhances your mathematical skills but also boosts your confidence in tackling objective questions. Practicing MCQs related to number systems helps in identifying important questions and solidifying your exam preparation strategy.
What You Will Practise Here
Types of number systems: Natural, Whole, Integers, Rational, and Irrational numbers
Conversion between different number systems: Decimal, Binary, Octal, and Hexadecimal
Arithmetic operations in various number systems
Properties of numbers: Even, Odd, Prime, and Composite numbers
Understanding place value and significance in different bases
Common number system problems and their solutions
Real-world applications of number systems in technology and computing
Exam Relevance
Number systems are a fundamental part of the curriculum for CBSE, State Boards, NEET, and JEE. Questions related to this topic frequently appear in both objective and subjective formats. Students can expect to encounter problems that require conversions between bases, operations on numbers in different systems, and theoretical questions about properties of numbers. Familiarity with common question patterns will significantly enhance your performance in these exams.
Common Mistakes Students Make
Confusing the conversion process between different number systems
Overlooking the significance of place value in non-decimal systems
Misapplying arithmetic operations when dealing with binary or hexadecimal numbers
Ignoring the properties of numbers, leading to incorrect answers in problem-solving
FAQs
Question: What are the different types of number systems I should know for exams?Answer: You should be familiar with natural numbers, whole numbers, integers, rational numbers, and irrational numbers, as these are commonly tested.
Question: How can I effectively practice number systems for my exams?Answer: Regularly solving Number Systems MCQ questions and objective questions with answers will help reinforce your understanding and improve your speed.
Start solving practice MCQs today to test your understanding of number systems and boost your exam readiness. Remember, consistent practice is the key to success!
