24) What is the duplex of 4763? a) 9526 b) 3674 c) 216 d) 108 e) 54

The concept of "duplex" is used in the Vedic mathematics system and refers to the sum of the squares of the digits of a number plus twice the product of every pair of digits.

To compute the duplex of 4763, we follow these steps:

### Step-by-step calculation of the duplex for the number 4763:

- First, compute the square of the first and last digits and add them up:
  - \( 4^2 = 16 \) (square of 4)
  - \( 3^2 = 9 \) (square of 3)
  - Sum: \( 16 + 9 = 25 \)

- Next, calculate twice the product of the middle digits:
  - \( 2 \times (4 \times 3) = 2 \times 12 = 24 \)
  - \( 2 \times (7 \times 6) = 2 \times 42 = 84 \)
  - \( 2 \times (7 \times 3) = 2 \times 21 = 42 \)
  - \( 2 \times (4 \times 6) = 2 \times 24 = 48 \)

Now, add all these results together:
\[
25 + 24 + 84 + 42 + 48 = 223
\]

The correct answer is not listed among the options, but the duplex of 4763 is **223**.

Do you want further details or have any questions?

Here are some related questions:
1. What is the duplex of 1234?
2. How do you calculate the duplex of a 5-digit number?
3. What is the significance of the duplex method in Vedic mathematics?
4. How does the duplex calculation help in simplifying multiplications?
5. Can the duplex method be extended to decimal numbers?

**Tip:** Duplex can be a quick way to calculate specific sums when used in Vedic mathematics tricks for multiplication.

Learn how to calculate the duplex of the number 4763 using the Vedic Mathematics system. This problem involves squaring digits and multiplying digit pairs. A step-by-step solution is provided, making it suitable for students in Grades 9-12.

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