Assertion: The reverse of the largest number of any number of digit (w...
Assertion Explanation
The assertion states that the reverse of the largest number formed by unique digits is always the smallest number of the same digit length, also with unique digits.
- For example, consider 3-digit numbers formed from unique digits:
- The largest 3-digit number with unique digits is 987.
- The reverse of 987 is 789, which is not the smallest 3-digit number with unique digits. The smallest is 102.
This shows that the assertion is not correct.
Reason Explanation
The reason given is: "101 is the smallest 3-digit number with unique digits which does not change."
- However, this statement is misleading:
- The smallest 3-digit number with unique digits is actually 102, not 101.
- Additionally, 101 is not a valid 3-digit number with unique digits because it repeats the digit '1'.
Therefore, the reason is also incorrect.
Conclusion
Based on the analysis:
- The assertion is incorrect because the reverse of the largest unique-digit number does not yield the smallest unique-digit number.
- The reason is incorrect as it misidentifies the smallest unique-digit number and incorrectly states that 101 does not change.
Thus, the correct option is:
(c) Assertion and Reason both are not correct.