Question : If $\frac{1}{N}=\frac{(\sqrt6+\sqrt5)}{(\sqrt6-\sqrt5)}$, what is the value of $N$?

Option 1: $6-\sqrt{30}$

Option 2: $6+\sqrt{30}$

Option 3: $11-2\sqrt{30}$

Option 4: $11+2\sqrt{5}$

Question : If $P=\frac{(\sqrt7-\sqrt6)}{(\sqrt7+\sqrt6)}$, then what is the value of $(P+\frac{1}{P})?$

Option 1: 12

Option 2: 13

Option 3: 24

Option 4: 26

Question : If $\sqrt5=2.236$, then what is the value of $\frac{\sqrt5}{2}+\frac{5}{3\sqrt5}-\sqrt{45}$?

Option 1: – 8.571

Option 2: – 4.845

Option 3: – 2.987

Option 4: – 6.261

Question : If $N=\frac{(\sqrt7-\sqrt3)}{(\sqrt7+\sqrt3)}$, then what is the value of $(N+\frac{1}{N})$?

Option 1: $2\sqrt2$

Option 2: $5$

Option 3: $10$

Option 4: $13$

Question : If $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$, then the value of A is:

Option 1: $\frac{1}{5}$

Option 2: $\frac{3}{10}$

Option 3: $\frac{2}{5}$

Option 4: $\frac{1}{10}$