Which of the following statement (s) is/ are TRUE ?
I. `(0.7)^(2)+(0.07)^(2)+(11.1)^(2) gt 123.8`
II. `(1.12)^(2)+(10.3)^(2)+(1.05)^(2) gt 108.3`

Options

A. Only I
B. Only II
C. Neither I nor II
D. Both I and II

Answer

To determine which of the statements is true, we will evaluate each statement one by one.

### Statement I:
\[ (0.7)^2 + (0.07)^2 + (11.1)^2 > 123.8 \]

1. **Calculate \((0.7)^2\)**:
\[ (0.7)^2 = 0.49 \]

2. **Calculate \((0.07)^2\)**:
\[ (0.07)^2 = 0.0049 \]

3. **Calculate \((11.1)^2\)**:
\[ (11.1)^2 = 123.21 \]

4. **Add the results**:
\[ 0.49 + 0.0049 + 123.21 = 123.7049 \]

5. **Compare with 123.8**:
\[ 123.7049 \not> 123.8 \]
So, Statement I is **FALSE**.

### Statement II:
\[ (1.12)^2 + (10.3)^2 + (1.05)^2 > 108.3 \]

1. **Calculate \((1.12)^2\)**:
\[ (1.12)^2 = 1.2544 \]

2. **Calculate \((10.3)^2\)**:
\[ (10.3)^2 = 106.09 \]

3. **Calculate \((1.05)^2\)**:
\[ (1.05)^2 = 1.1025 \]

4. **Add the results**:
\[ 1.2544 + 106.09 + 1.1025 = 108.4469 \]

5. **Compare with 108.3**:
\[ 108.4469 > 108.3 \]
So, Statement II is **TRUE**.

### Conclusion:
- Statement I is **FALSE**.
- Statement II is **TRUE**.