Q. In a certain number system, the number 12 is represented as 'A' and the number 18 as 'B'. If 'A' is a factor of 'B', which of the following statements is true?
A.
A is greater than B
B.
B is a multiple of A
C.
A and B are equal
D.
A is a multiple of B
Solution
'B' (18) is a multiple of 'A' (12) since 18 can be expressed as 12 multiplied by 1.5.
Q. In a certain number system, the number 12 is represented as 'AB'. If 'A' is a factor of 12 and 'B' is a multiple of 3, which of the following could be the representation of 12?
A.
24
B.
36
C.
48
D.
60
Solution
'A' can be 3 or 4 (factors of 12), and 'B' can be 3, 6, or 9 (multiples of 3). The only combination that fits is 3 and 4, which gives us 24.
Q. In a certain number system, the number 12 is represented as 'AB'. If 'A' is a factor of 12 and 'B' is a multiple of 3, which of the following pairs (A, B) is valid?
A.
(1, 3)
B.
(2, 6)
C.
(3, 9)
D.
(4, 12)
Solution
In this case, A must be a factor of 12 (1, 2, 3, 4, 6, 12) and B must be a multiple of 3 (3, 6, 9, 12). The pair (2, 6) satisfies both conditions.
Q. In a certain number system, the number 12 is represented as 'AB'. If 'A' is a factor of 12 and 'B' is a multiple of 3, which of the following could be the value of 'AB'?
A.
24
B.
36
C.
48
D.
60
Solution
'A' can be 1, 2, 3, 4, 6, or 12 (factors of 12) and 'B' can be 3, 6, 9, 12, etc. The only combination that fits is A=3 and B=12, which gives us 36.
Q. In a class of 60 students, the ratio of boys to girls is 3:2. If the number of boys is increased by 10, what will be the new ratio of boys to girls? (2023)
A.
4:3
B.
5:2
C.
3:2
D.
2:3
Solution
Initially, there are 36 boys and 24 girls. After increasing the boys by 10, there will be 46 boys and 24 girls, giving a new ratio of 46:24, which simplifies to 4:3.
Q. In a class of 60 students, the ratio of boys to girls is 3:2. If the number of boys is increased by 5, what will be the new ratio of boys to girls? (2023)
A.
4:3
B.
5:2
C.
3:2
D.
2:3
Solution
Initially, there are 36 boys and 24 girls. After increasing boys by 5, there will be 41 boys and 24 girls, giving a new ratio of 41:24, which simplifies to approximately 4:3.
Q. In a class of 60 students, the ratio of boys to girls is 3:2. If the number of boys is increased by 10 and the number of girls is decreased by 5, what will be the new ratio of boys to girls? (2023)
A.
2:3
B.
3:2
C.
5:3
D.
4:3
Solution
Initially, there are 36 boys and 24 girls. After the changes, there will be 46 boys and 19 girls. The new ratio is 46:19, which simplifies to approximately 4:3.
Q. In a classroom, if every student has either 2 or 3 pencils, and the total number of pencils is 30, which of the following could be the number of students with 2 pencils?
A.
10
B.
5
C.
15
D.
20
Solution
If there are 10 students with 2 pencils, then there are 10 students with 3 pencils, totaling 30 pencils.
Q. In a classroom, the teacher has 24 pencils and wants to distribute them equally among students. If each student receives a multiple of 3 pencils, how many students can receive pencils?
A.
6
B.
8
C.
4
D.
3
Solution
The multiples of 3 that can divide 24 are 3, 6, 9, and 12. The maximum number of students that can receive pencils is 8 (3 pencils each).
Q. In a classroom, the teacher has 48 pencils and wants to distribute them equally among students. If each student receives a multiple of 4 pencils, what is the maximum number of students that can receive pencils?
A.
12
B.
16
C.
8
D.
6
Solution
The maximum number of students is 12, as 48 ÷ 4 = 12.
Q. In a classroom, the teacher wants to arrange chairs in rows such that each row has the same number of chairs. If there are 48 chairs and the number of rows must be a factor of 48, which of the following is NOT a possible number of rows?
A.
4
B.
6
C.
8
D.
10
Solution
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. 10 is not a factor of 48.
Q. In a classroom, the teacher wants to arrange chairs in rows such that each row has the same number of chairs. If there are 36 chairs, which of the following is NOT a possible number of chairs per row?
A.
1
B.
2
C.
3
D.
5
Solution
5 is not a factor of 36, hence it cannot be a possible number of chairs per row.
Q. In a classroom, the teacher wants to arrange students in groups such that each group has the same number of students. If there are 36 students, which of the following is NOT a possible group size? (2023)
A.
1
B.
2
C.
3
D.
10
Solution
The number 10 is not a factor of 36, hence it cannot be a group size.
Q. In a classroom, the teacher wants to arrange students in rows such that each row has the same number of students. If there are 24 students, which of the following arrangements is NOT possible?
A.
6 rows of 4 students
B.
8 rows of 3 students
C.
12 rows of 2 students
D.
5 rows of 5 students
Solution
5 rows of 5 students would require 25 students, which is not possible with only 24 students.
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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