Consider all the six digit numbers that can be formed using the digits 1, 2, 3, 4, 5 and 6, each digit being used exactly once. Each of such six digit numbers have the property that for each digit, not more than two digits smaller than that digit appear to the right of that digit.
Q. A six digit number which does not satisfy the property mentioned above, is :

Options

A. 315426
B. 135462
C. 234651
D. None of these

Answer

To solve the problem, we need to identify which six-digit number formed from the digits 1, 2, 3, 4, 5, and 6 does not satisfy the given property. The property states that for each digit, not more than two digits smaller than that digit can appear to its right.

Let's analyze the options step by step:

### Step 1: Understand the Property
The property requires that for any digit \( n \):
- The number of digits smaller than \( n \) that appear to the right of \( n \) should not exceed 2.

### Step 2: Analyze Each Option
We will check each option one by one to see if they satisfy the property.

#### Option 1: 3, 1, 5, 4, 2, 6
- For 3: Smaller digits to the right are 1 (1 digit) → Satisfies
- For 1: No smaller digits to the right → Satisfies
- For 5: Smaller digits to the right are 4, 2 (2 digits) → Satisfies
- For 4: Smaller digit to the right is 2 (1 digit) → Satisfies
- For 2: No smaller digits to the right → Satisfies
- For 6: Smaller digits to the right are 5, 4, 2, 3, 1 (5 digits) → **Does not satisfy**

#### Option 2: 1, 3, 5, 4, 6, 2
- For 1: No smaller digits to the right → Satisfies
- For 3: Smaller digit to the right is 2 (1 digit) → Satisfies
- For 5: Smaller digits to the right are 4, 2 (2 digits) → Satisfies
- For 4: Smaller digit to the right is 2 (1 digit) → Satisfies
- For 6: Smaller digit to the right is 2 (1 digit) → Satisfies
- All conditions are satisfied.

#### Option 3: 2, 3, 4, 6, 5, 1
- For 2: Smaller digit to the right is 1 (1 digit) → Satisfies
- For 3: Smaller digit to the right is 2 (1 digit) → Satisfies
- For 4: Smaller digit to the right is 2 (1 digit) → Satisfies
- For 6: Smaller digits to the right are 5, 1 (2 digits) → Satisfies
- For 5: Smaller digit to the right is 1 (1 digit) → Satisfies
- All conditions are satisfied.

#### Option 4: 2, 3, 4, 5, 1, 6
- For 2: Smaller digit to the right is 1 (1 digit) → Satisfies
- For 3: Smaller digit to the right is 2 (1 digit) → Satisfies
- For 4: Smaller digit to the right is 2 (1 digit) → Satisfies
- For 5: Smaller digit to the right is 1 (1 digit) → Satisfies
- For 6: Smaller digits to the right are 5, 4, 3, 2, 1 (5 digits) → **Does not satisfy**

### Conclusion
Both Option 1 and Option 4 do not satisfy the property. However, since the question asks for a single six-digit number that does not satisfy the property, we can conclude that:

**The six-digit number which does not satisfy the property is: 3, 1, 5, 4, 2, 6.**