The correct expression of $5 . \overline{45}$ in the fractional form is

$\frac{1.49 \times 14.9 - 0.51 \times 5.1}{14.9 - 5.1}$

If $a * b = 2a - 3b + ab$,then $3 * 5 + 5 * 3$ is

$\frac{\sqrt{7}}{\sqrt{16+6 \sqrt{7}}-\sqrt{16-6 \sqrt{7}}}$ is equal to

The value of $\frac{3}{1^{2} \cdot 2^{2}}+\frac{5}{2^{2} \cdot 3^{2}}+\frac{7}{3^{2} \cdot 4^{2}}+\frac{9}{4^{2} \cdot 5^{2}}+\frac{11}{5^{2} \cdot 6^{2}}+\frac{13}{6^{2} \cdot 7^{2}}+\frac{15}{7^{2} \cdot 8^{2}}+\frac{17}{8^{2} \cdot 9^{2}}+\frac{19}{9^{2} \cdot 10^{2}}$ is

Which of the following numbers is not a factor of $5^{p} 7^{q}$ where $p \neq 0$ and $q \neq 0$?