What approximate value will come in the place of the question mark $(?)$ in the following question? (You are not expected to calculate the exact value.)
$(32.13)^{2} + (23.96)^{2} - (17.11)^{2} = ?$

The value of $\frac{3 \sqrt{2}}{\sqrt{3}+\sqrt{6}}-\frac{4 \sqrt{3}}{\sqrt{6}+\sqrt{2}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}$ is

In an examination,a student was asked to find $\frac{3}{14}$ of a certain number. By mistake,he found $\frac{3}{4}$ of it. His answer was $150$ more than the correct answer. The given number is

The value of: $\sqrt{\frac{0.324 \times 0.081 \times 4.624}{1.5625 \times 0.0289 \times 72.9 \times 64}}$

$4 \frac{1}{2} \times 4 \frac{1}{3} - 8 \frac{1}{3} + 5 \frac{2}{3} = ?$

If the numerator of a fraction is increased by $2$ and the denominator is increased by $3,$ the fraction becomes $\frac{7}{9},$ and if both the numerator and the denominator are decreased by $1,$ the fraction becomes $\frac{4}{5}.$ What is the original fraction?