Question

The number of cubic equations that can be formed with the coefficients 0, 3, 2, 4, 5, 6 when repetition of coefficients is allowed, is....

• A. \(720\)
• B. \(1296\)
• C. \(864\)
• D. \(1080\)

Hint:

The leading coefficient cannot be zero, so fill that place first and the remaining places freely.

Answer 1

The Correct Option is D

Step 1: Count all quadruples first.
With 6 numbers and repetition allowed, there are $6^4 = 1296$ ways to choose $(a, b, c, d)$.

Step 2: Remove the bad ones.
The ones with $a = 0$ are not cubic. They number $1 \times 6^3 = 216$.

Step 3: Subtract.
\[ 1296 - 216 = 1080 \]

Final Answer:
Option (D). \[ \boxed{1080} \]