Q. A number leaves a remainder of 1 when divided by 3 and a remainder of 2 when divided by 5. What is the smallest positive integer that satisfies these conditions? (2023)
A.
6
B.
11
C.
16
D.
21
Solution
The smallest number that satisfies both conditions is 11 (11 % 3 = 2 and 11 % 5 = 1).
Q. A number leaves a remainder of 1 when divided by 5 and a remainder of 2 when divided by 3. What is the smallest positive integer that satisfies these conditions? (2023)
A.
1
B.
5
C.
8
D.
11
Solution
The smallest number that satisfies both conditions is 8 (8 % 5 = 3 and 8 % 3 = 2).
Q. A number leaves a remainder of 4 when divided by 10 and a remainder of 2 when divided by 3. What is the smallest positive integer that satisfies these conditions? (2023)
A.
4
B.
14
C.
24
D.
34
Solution
The smallest number that satisfies both conditions is 14 (14 % 10 = 4 and 14 % 3 = 2).
Q. A number leaves a remainder of 4 when divided by 6. If this number is multiplied by 3, what will be the remainder when the result is divided by 6? (2023)
A.
0
B.
1
C.
2
D.
3
Solution
If the number is 6k + 4, then 3(6k + 4) = 18k + 12, which leaves a remainder of 0 when divided by 6.
Q. A teacher has 48 pencils and 60 erasers. She wants to distribute them equally among students. What is the maximum number of students she can distribute to? (2023)
A.
12
B.
6
C.
8
D.
10
Solution
The HCF of 48 and 60 is 12, which is the maximum number of students she can distribute to equally.
Q. For a number to be divisible by 11, which of the following must be true?
A.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
B.
The number must be even
C.
The number must end in 1
D.
The sum of the digits must be divisible by 11
Solution
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or divisible by 11.
Correct Answer:
A
— The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
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!
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