Assertion : `14^(3)-2744, 24^(3)-13822`
Reason : The digits of number end with 4, then cubes of the number ends with same digit 4.

Options

A. If both asseration and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assartion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the assertion and reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Evaluate the Assertion
The assertion states:
- \( 14^3 = 2744 \)
- \( 24^3 = 13822 \)

First, we will calculate \( 14^3 \):
\[ 14^3 = 14 \times 14 \times 14 \]
Calculating \( 14 \times 14 \):
\[ 14 \times 14 = 196 \]
Now, multiply \( 196 \) by \( 14 \):
\[ 196 \times 14 = 196 \times (10 + 4) = 1960 + 784 = 2744 \]
So, \( 14^3 = 2744 \) is correct.

Next, we will calculate \( 24^3 \):
\[ 24^3 = 24 \times 24 \times 24 \]
Calculating \( 24 \times 24 \):
\[ 24 \times 24 = 576 \]
Now, multiply \( 576 \) by \( 24 \):
\[ 576 \times 24 = 576 \times (20 + 4) = 11520 + 2304 = 13824 \]
So, \( 24^3 = 13824 \), not \( 13822 \). Therefore, the assertion is **false**.

### Step 2: Evaluate the Reason
The reason states:
- If the digits of a number end with 4, then the cube of that number also ends with the digit 4.

To verify this, we can look at the cubes of numbers ending in 4:
- \( 4^3 = 64 \) (ends with 4)
- \( 14^3 = 2744 \) (ends with 4)
- \( 24^3 = 13824 \) (ends with 4)
- \( 34^3 = 39304 \) (ends with 4)

In all cases, the cubes of numbers ending in 4 also end in 4. Therefore, the reason is **true**.

### Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the correct answer is that the assertion is false, but the reason is true.