Question
Download Solution PDFA number divided by 11 leaves a remainder 3. What is the remainder when the square of the same number is divided by 11?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A number divided by 11 leaves a remainder of 3.
Formula used:
Let the number be n. Then, n = 11k + 3 for some integer k.
We need to find the remainder when \(n^2\) is divided by 11.
Calculation:
\(n^2\) = \((11k + 3)^2\)
⇒ \(n^2\) = \(121k^2 + 66k + 9\)
⇒ \(n^2 \mod 11\) = \((121k^2 + 66k + 9) \mod 11\)
⇒ \(n^2 \mod 11\) = \((0 + 0 + 9) \mod 11\)
⇒ \(n^2 \mod 11\) = 9
∴ The correct answer is option (3).
Last updated on Jun 5, 2025
-> The UP Police Sub Inspector 2025 Notification will be released by 15th June for 4543 vacancies.
-> A total of 35 Lakh applications are expected this year for the UP Police vacancies..
-> The recruitment is also ongoing for 268 vacancies of Sub Inspector (Confidential) under the 2023-24 cycle.
-> The pay Scale for the post ranges from Pay Band 9300 - 34800.
-> Graduates between 21 to 28 years of age are eligible for this post. The selection process includes a written exam, document verification & Physical Standards Test, and computer typing test & stenography test.
-> Assam Police Constable Admit Card 2025 has been released.