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 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 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.
Understanding the concept of Remainders is crucial for students preparing for school exams and competitive tests. Remainders often appear in various mathematical problems, making it essential to practice MCQs and objective questions to enhance your exam readiness. By solving practice questions, you can grasp important concepts and improve your chances of scoring better in exams.
What You Will Practise Here
Definition and significance of Remainders in mathematics
Basic properties of Remainders
Remainders in division and its application
Common formulas related to Remainders
Remainders in polynomial division
Real-life applications of Remainders
Practice with Remainders MCQ questions and objective questions with answers
Exam Relevance
The topic of Remainders is frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to find Remainders in division problems, apply properties, or solve word problems involving Remainders. Understanding the common question patterns will help you tackle these problems effectively during your exams.
Common Mistakes Students Make
Confusing Remainders with Quotients in division
Overlooking the properties of Remainders when solving problems
Misapplying formulas related to Remainders
Failing to interpret word problems correctly
FAQs
Question: What is a Remainder? Answer: A Remainder is the amount left over after division when one number cannot be exactly divided by another.
Question: How can I improve my understanding of Remainders? Answer: Regular practice of Remainders MCQ questions and solving objective questions can significantly enhance your understanding.
Don't wait any longer! Start solving Remainders practice MCQs today to test your understanding and boost your confidence for the upcoming exams.
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