In each of the following question and equation is presented in four parts with = sign in between parts. The four parts of the equation are lettered (A) (B) ( C) and (D). One of these parts in the equation may be wrong and there by may not yield the same result as the other three parts do. Find out the wrong part. If there is any. If all the four parts are correctly equated and all of them yield the same result, the answer is (E) i.e.,’No,error’.

Options

A. `8^2 div 4^3xx10^2-8`
B. `sqrt2xxsqrt(32)xx9+20`
C. `4^2xx4+2^3xx3`
D. `10^2-2^3`

Answer

To solve the problem, we need to evaluate each of the four parts (A, B, C, and D) of the equation and determine if one of them is incorrect or if all are correct.

Let's denote the four parts as follows:
- (A) \( \frac{8^2}{4^3} \times 10^2 - 8 \)
- (B) \( \sqrt{32} \times 9 + 24^2 \times 4 + 2^3 \times 3 \times 10^2 - 2^3 \)
- (C) \( 4^2 \times 4 + 2^3 \times 3 \)
- (D) \( 10^2 - 2^3 \)

Now, we will calculate the value of each part step by step.

### Step 1: Calculate Part (A)
1. Calculate \( 8^2 = 64 \)
2. Calculate \( 4^3 = 64 \)
3. Calculate \( 10^2 = 100 \)
4. Substitute these values into the expression:
\[ \frac{64}{64} \times 100 - 8 \]
5. Simplify:
\[ 1 \times 100 - 8 = 100 - 8 = 92 \]

### Step 2: Calculate Part (B)
1. Calculate \( \sqrt{32} = 4\sqrt{2} \) (approximately 5.656)
2. Calculate \( 24^2 = 576 \)
3. Calculate \( 2^3 = 8 \)
4. Calculate \( 10^2 = 100 \)
5. Substitute these values into the expression:
\[ 4\sqrt{2} \times 9 + 576 \times 4 + 8 \times 3 \times 100 - 8 \]
6. Calculate:
- \( 4\sqrt{2} \times 9 \approx 22.627 \)
- \( 576 \times 4 = 2304 \)
- \( 8 \times 3 \times 100 = 2400 \)
7. Combine:
\[ 22.627 + 2304 + 2400 - 8 \approx 4698.627 \]

### Step 3: Calculate Part (C)
1. Calculate \( 4^2 = 16 \)
2. Calculate \( 2^3 = 8 \)
3. Substitute these values into the expression:
\[ 16 \times 4 + 8 \times 3 \]
4. Calculate:
- \( 16 \times 4 = 64 \)
- \( 8 \times 3 = 24 \)
5. Combine:
\[ 64 + 24 = 88 \]

### Step 4: Calculate Part (D)
1. Calculate \( 10^2 = 100 \)
2. Calculate \( 2^3 = 8 \)
3. Substitute these values into the expression:
\[ 100 - 8 = 92 \]

### Summary of Results
- (A) = 92
- (B) ≈ 4698.627
- (C) = 88
- (D) = 92

### Conclusion
From the calculations, we see:
- Parts (A) and (D) both yield 92.
- Part (B) yields approximately 4698.627, which is significantly different.
- Part (C) yields 88, which is also different.

Thus, the wrong part is **(B)**.