A number of decimal system when represented in binary system then its first and last digits are same and the rest digits are also of another kind. Further this number appears to be palindrome of numerals. The numbers is :

Options

A. 57
B. 19
C. 8
D. 9

Answer

To solve the problem, we need to find a decimal number that meets the following criteria when represented in binary:

1. The first and last digits of the binary representation are the same.
2. The rest of the digits are of another kind.
3. The binary representation is a palindrome.

Let's analyze the options provided:

### Step 1: Convert each option to binary

**Option A: 57**
- Decimal: 57
- Binary: 111001

**Option B: 19**
- Decimal: 19
- Binary: 10011

**Option C: 8**
- Decimal: 8
- Binary: 1000

**Option D: 9**
- Decimal: 9
- Binary: 1001

### Step 2: Check if the binary representation is a palindrome

**For Option A (57):**
- Binary: 111001
- Reverse: 100111 (not the same)

**For Option B (19):**
- Binary: 10011
- Reverse: 11001 (not the same)

**For Option C (8):**
- Binary: 1000
- Reverse: 0001 (not the same)

**For Option D (9):**
- Binary: 1001
- Reverse: 1001 (same)

### Step 3: Verify the first and last digit condition

**Option D (9):**
- Binary: 1001
- First digit: 1
- Last digit: 1
- The rest of the digits: 00 (which are of another kind)

### Conclusion
The only option that satisfies all the conditions is **Option D (9)**.

### Final Answer:
The number is **9**.

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