Question
Download Solution PDFThe difference of the squares of two distinct two-digit numbers with one being obtained by reversing the digits of the other is always divisible by
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Let unit digit be y and tens digit be x then the number is 10x + y
If we reverse the digits then the number will be 10y + x
Difference of squares of these two number
= (10x + y)2 - (10y + x)2
= 100x2 + 20xy + y2 - 100y2 - 20xy -x2
= 99x2 - 99y2
= 99(x2 - y2) = 9 × 11(x2 - y2)
So the difference of square is always divisible by 1, 9, 11, 99
Option (4) is correct
Last updated on Jun 5, 2025
-> The NTA has released the CSIR NET 2025 Notification for the June session.
-> The CSIR NET Application Form 2025 can be submitted online by 23rd June 2025
-> The CSIR UGC NET is conducted in five subjects -Chemical Sciences, Earth Sciences, Life Sciences, Mathematical Sciences, and Physical Sciences.
-> Postgraduates in the relevant streams can apply for this exam.
-> Candidates must download and practice questions from the CSIR NET Previous year papers. Attempting the CSIR NET mock tests are also very helpful in preparation.