Q. If a number is divided by 15 and gives a remainder of 10, which of the following could be the number?
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Solution
25 gives a remainder of 10 when divided by 15 (15*1 + 10 = 25).
Correct Answer:
A
— 25
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Q. If a number is divided by 15 and gives a remainder of 7, what will be the remainder when this number is divided by 3?
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Solution
The remainder when the number is divided by 3 is 1, since 7 mod 3 = 1.
Correct Answer:
B
— 1
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Q. If a number is divided by 15 and gives a remainder of 8, which of the following numbers will also give the same remainder when divided by 15?
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Solution
23 gives a remainder of 8 when divided by 15.
Correct Answer:
A
— 23
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Q. If a number is divided by 15 and leaves a remainder of 10, what will be the remainder when this number is divided by 5? (2023)
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Solution
Since 10 is greater than 5, the remainder when 10 is divided by 5 is 0.
Correct Answer:
A
— 0
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Q. If a number is divided by 6 and gives a remainder of 2, what will be the remainder when the same number is divided by 3? (2023)
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Solution
If the number gives a remainder of 2 when divided by 6, it will give a remainder of 2 when divided by 3 as well.
Correct Answer:
B
— 1
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Q. If a number is divided by 6 and gives a remainder of 2, what will be the remainder when this number is divided by 3? (2023)
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Solution
Since 2 is less than 3, the remainder when 2 is divided by 3 is 2.
Correct Answer:
A
— 0
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Q. If a number is divided by 8 and gives a remainder of 5, what will be the remainder when this number is divided by 4?
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Solution
The number can be expressed as 8k + 5, which gives a remainder of 1 when divided by 4.
Correct Answer:
B
— 1
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Q. If a number is divided by 8 and leaves a remainder of 5, what will be the remainder when this number is divided by 4? (2023)
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Solution
The number can be expressed as 8k + 5. When divided by 4, the remainder is 5 mod 4 = 1.
Correct Answer:
D
— 3
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Q. If a number is divided by 9 and gives a remainder of 2, which of the following numbers will also give the same remainder when divided by 9?
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Solution
29 gives a remainder of 2 when divided by 9 (9*3 + 2 = 29).
Correct Answer:
C
— 29
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Q. If a number is divisible by 10, which of the following must be true?
A.
It is divisible by 2
B.
It is divisible by 5
C.
It is even
D.
All of the above
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Solution
A number divisible by 10 is always divisible by 2 and 5, and it is also even.
Correct Answer:
D
— All of the above
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Q. If a number is divisible by 12, which of the following must also be true?
A.
It is divisible by 3
B.
It is divisible by 5
C.
It is divisible by 10
D.
It is a prime number
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Solution
A number divisible by 12 is also divisible by both 3 and 4.
Correct Answer:
A
— It is divisible by 3
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Q. If a number is divisible by 15, which of the following must also be true?
A.
It is divisible by 3
B.
It is divisible by 5
C.
It is even
D.
Both 0 and 1 are factors
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Solution
A number divisible by 15 must be divisible by both 3 and 5.
Correct Answer:
A
— It is divisible by 3
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Q. If a number is divisible by 15, which of the following must it also be divisible by?
A.
3
B.
5
C.
15
D.
All of the above
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Solution
A number divisible by 15 is also divisible by both 3 and 5, as 15 is the product of these two primes.
Correct Answer:
D
— All of the above
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Q. If a number is divisible by 4, which of the following must also be true?
A.
It is even
B.
It is divisible by 8
C.
It is divisible by 2
D.
It is a multiple of 10
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Solution
Any number divisible by 4 is even, as 4 itself is an even number.
Correct Answer:
A
— It is even
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Q. If a number is divisible by 4, which of the following must be true?
A.
It ends in 0
B.
It ends in 2
C.
Its last two digits form a number divisible by 4
D.
It is even
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Solution
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Correct Answer:
C
— Its last two digits form a number divisible by 4
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Q. If a number is divisible by 7, which of the following is NOT necessarily true?
A.
It is odd
B.
It is not a prime number
C.
It can be a multiple of 14
D.
It can be a two-digit number
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Solution
A number can be divisible by 7 and still be even, such as 14.
Correct Answer:
A
— It is odd
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Q. If a number is divisible by 8, which of the following must also be true?
A.
It is divisible by 2
B.
It is divisible by 4
C.
It is a multiple of 16
D.
It is a prime number
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Solution
Any number divisible by 8 is also divisible by 4, as 8 is a multiple of 4.
Correct Answer:
B
— It is divisible by 4
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Q. If a number is divisible by 8, which of the following must be true?
A.
It is divisible by 2
B.
It is divisible by 3
C.
It is divisible by 5
D.
It is divisible by 10
Show solution
Solution
A number divisible by 8 is also divisible by 2, as 8 is a multiple of 2.
Correct Answer:
A
— It is divisible by 2
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Q. If a number is divisible by 9, what can be inferred about the sum of its digits?
A.
It is even
B.
It is divisible by 3
C.
It is divisible by 9
D.
It is a prime number
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Solution
A number is divisible by 9 if the sum of its digits is also divisible by 9.
Correct Answer:
C
— It is divisible by 9
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Q. If a number is divisible by both 2 and 3, which of the following is true?
A.
It is divisible by 5
B.
It is divisible by 6
C.
It is odd
D.
It is a prime number
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Solution
A number that is divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer:
B
— It is divisible by 6
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Q. If a number is divisible by both 2 and 3, which of the following must also be true?
A.
It is divisible by 5.
B.
It is divisible by 6.
C.
It is an odd number.
D.
It is a prime number.
Show solution
Solution
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer:
B
— It is divisible by 6.
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Q. If a number is divisible by both 2 and 3, which of the following must it also be divisible by?
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Solution
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer:
B
— 6
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Q. If a number is divisible by both 2 and 5, what can be said about it?
A.
It is odd
B.
It is a multiple of 10
C.
It is a prime number
D.
It is a multiple of 20
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Solution
A number divisible by both 2 and 5 must end in 0, making it a multiple of 10.
Correct Answer:
B
— It is a multiple of 10
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Q. If a number is divisible by both 2 and 5, which of the following must be true?
A.
It is divisible by 10
B.
It is divisible by 15
C.
It is divisible by 20
D.
It is divisible by 25
Show solution
Solution
A number divisible by both 2 and 5 is also divisible by 10, as 10 is the least common multiple of 2 and 5.
Correct Answer:
A
— It is divisible by 10
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Q. If a number is divisible by both 3 and 4, which of the following must also be true?
A.
It is divisible by 12.
B.
It is divisible by 7.
C.
It is divisible by 6.
D.
It is divisible by 9.
Show solution
Solution
The least common multiple of 3 and 4 is 12, so any number divisible by both must also be divisible by 12.
Correct Answer:
A
— It is divisible by 12.
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Q. If a number is divisible by both 3 and 5, which of the following is guaranteed to be true?
A.
It is divisible by 15
B.
It is divisible by 8
C.
It is divisible by 10
D.
It is divisible by 6
Show solution
Solution
A number divisible by both 3 and 5 is also divisible by their least common multiple, which is 15.
Correct Answer:
A
— It is divisible by 15
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Q. If a number is divisible by both 3 and 5, which of the following must also be true?
A.
It is divisible by 15
B.
It is divisible by 8
C.
It is divisible by 10
D.
It is not divisible by 6
Show solution
Solution
A number divisible by both 3 and 5 is also divisible by their LCM, which is 15.
Correct Answer:
A
— It is divisible by 15
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Q. If a number is divisible by both 4 and 6, which of the following must also be true? (2023)
A.
It is divisible by 12.
B.
It is divisible by 24.
C.
It is divisible by 10.
D.
It is not divisible by 2.
Show solution
Solution
The least common multiple of 4 and 6 is 12, so any number divisible by both must also be divisible by 12.
Correct Answer:
A
— It is divisible by 12.
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Q. If a number is divisible by both 5 and 10, which of the following can be concluded?
A.
It is a multiple of 15.
B.
It is a multiple of 20.
C.
It is a multiple of 50.
D.
It is a multiple of 10.
Show solution
Solution
Any number divisible by 10 is also a multiple of 10.
Correct Answer:
D
— It is a multiple of 10.
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Q. If a number is divisible by both 6 and 8, which of the following must it also be divisible by?
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Solution
The least common multiple of 6 and 8 is 24, so any number divisible by both must also be divisible by 24.
Correct Answer:
B
— 24
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Showing 121 to 150 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!
