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!
Q. A certain number when divided by 15 gives a remainder of 8. If this number is multiplied by 2, what will be the remainder when the new number is divided by 15? (2023)
A.
1
B.
2
C.
3
D.
4
Solution
The new number is (original number * 2), which gives a remainder of (8 * 2) = 16, and 16 divided by 15 gives a remainder of 1.
Q. A factory produces two types of widgets. The first type is produced every 12 days and the second every 15 days. How often will both types be produced on the same day? (2023)
A.
30 days
B.
60 days
C.
45 days
D.
75 days
Solution
The LCM of 12 and 15 is 60, so both types will be produced on the same day every 60 days.
Q. A gardener has 36 red roses and 48 yellow roses. He wants to plant them in rows with the same number of each type of rose in each row. What is the maximum number of rows he can plant? (2023)
A.
6
B.
12
C.
18
D.
24
Solution
The HCF of 36 and 48 is 12, which is the maximum number of rows he can plant.
Q. A gardener has 60 red flowers and 90 yellow flowers. What is the largest number of bouquets he can make if each bouquet has the same number of red and yellow flowers? (2023)
A.
15
B.
30
C.
45
D.
60
Solution
The largest number of bouquets is the HCF of 60 and 90, which is 30.
Q. A gardener has two types of plants, one type has a height of 3 feet and the other 5 feet. What is the minimum height at which both types can be tied together? (2023)
A.
15
B.
30
C.
60
D.
45
Solution
The minimum height is the LCM of 3 and 5, which is 15 feet.
Q. A gardener has two types of plants, one type requires watering every 4 days and the other every 6 days. If both types are watered together today, in how many days will they be watered together again? (2023)
A.
12
B.
24
C.
18
D.
30
Solution
The LCM of 4 and 6 is 12. Therefore, they will be watered together again in 12 days.
Q. A group of students can complete a project in 12 days. If 4 more students join, the project can be completed in 8 days. How many students were initially in the group? (2023)
A.
6
B.
8
C.
10
D.
12
Solution
Let the initial number of students be x. The work done is constant, so x * 12 = (x + 4) * 8. Solving gives x = 8.
Q. A group of students can complete a project in 12 days. If 4 more students join, they can complete it in 8 days. How many students were initially in the group?
A.
6
B.
8
C.
10
D.
12
Solution
Let the initial number of students be x. The work done is inversely proportional to the number of days. Setting up the equation gives x = 10.
Q. A number is divided by 11 and gives a remainder of 4. If this number is multiplied by 3, what will be the remainder when the result is divided by 11?
A.
1
B.
2
C.
3
D.
4
Solution
The new number is 3*(11k + 4) = 33k + 12, and 12 mod 11 = 1.
Q. A number is divided by 12 and gives a remainder of 7. If this number is multiplied by 2, what will be the remainder when the new number is divided by 12? (2023)
A.
1
B.
2
C.
3
D.
4
Solution
The new number is (original number * 2) = (12k + 7) * 2 = 24k + 14, which gives a remainder of 2.
Q. A number is divided by 9 and gives a remainder of 2. If this number is multiplied by 3, what will be the remainder when the new number is divided by 9?
A.
0
B.
1
C.
2
D.
3
Solution
The new number is (original number * 3) = (9k + 2) * 3 = 27k + 6, which gives a remainder of 6 when divided by 9.
Q. A number is said to be a multiple of 4 if its last two digits form a number that is divisible by 4. Which of the following numbers is NOT a multiple of 4?
A.
124
B.
256
C.
378
D.
492
Solution
The last two digits of 378 are 78, which is not divisible by 4 (78 ÷ 4 = 19.5). Therefore, 378 is not a multiple of 4.
