The number of two digit numbers which on being reversed (i.e., their digits exchanged the position) gives out perfect square two digit numbers:

Options

A. 1
B. 4
C. 6
D. 10

Answer

To solve the problem of finding the number of two-digit numbers that, when reversed, result in perfect square two-digit numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Two-Digit Perfect Squares**:
First, we need to identify all the two-digit perfect squares. The perfect squares are obtained by squaring integers. The smallest two-digit perfect square is \(4^2 = 16\) and the largest is \(9^2 = 81\). The two-digit perfect squares are:
- \(16\) (from \(4^2\))
- \(25\) (from \(5^2\))
- \(36\) (from \(6^2\))
- \(49\) (from \(7^2\))
- \(64\) (from \(8^2\))
- \(81\) (from \(9^2\))

2. **Reverse the Digits of Each Perfect Square**:
Next, we will reverse the digits of each of these perfect squares:
- \(16\) reversed is \(61\)
- \(25\) reversed is \(52\)
- \(36\) reversed is \(63\)
- \(49\) reversed is \(94\)
- \(64\) reversed is \(46\)
- \(81\) reversed is \(18\)

3. **Count the Valid Two-Digit Numbers**:
Now, we need to count how many of these reversed numbers are valid two-digit numbers:
- \(61\) (valid)
- \(52\) (valid)
- \(63\) (valid)
- \(94\) (valid)
- \(46\) (valid)
- \(18\) (valid)

All six reversed numbers are valid two-digit numbers.

4. **Conclusion**:
Therefore, the total number of two-digit numbers which, when reversed, give perfect square two-digit numbers is \(6\).

### Final Answer:
The answer is \(6\).

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