Question : If $u{_n}=\frac{1}{n}-\frac{1}{n+1}$, then the value of $u{_1} + u{_2}+u{_3}+u{_4}+u{_5}$ is:

Option 1: $\frac{1}{2}$

Option 2: $\frac{1}{3}$

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

Option 4: $\frac{5}{6}$

Question : If $x=(\sqrt{6}-1)^{\frac{1}{3}}$, then the value of $\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right)$ is:

Option 1: $\frac{2 \sqrt{6}-6}{5}$

Option 2: $\frac{4 \sqrt{6}-6}{5}$

Option 3: $\frac{4 \sqrt{6}-6}{3}$

Option 4: $\frac{4 \sqrt{3}-6}{5}$

Question :  If $\sec\theta +\tan\theta = 3$, then what is the value of $\sec \theta-\tan \theta$?

Option 1: $\frac{1}{3}$

Option 2: $6$

Option 3: $\frac{1}{6}$

Option 4: $\frac{1}{5}$

Question : If $6 \sec \theta=10$, then find the value of $\frac{5 \operatorname{cosec} \theta-3 \cot \theta}{4 \cos \theta+3 \sin \theta}$.

Option 1: $\frac{2}{3}$

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

Option 3: $\frac{5}{6}$

Option 4: $\frac{6}{5}$

Question : If $\cos 20°= m$ and $\cos 70°=n$, then the value of $m^2+n^2$:

Option 1: $1$

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

Option 3: $\frac{1}{\sqrt2}$

Option 4: $\frac{1}{2}$

Question : If $\mathrm{N}+\frac{1}{\mathrm{~N}}=\sqrt{3}$, then find the value of $\mathrm{N}^6+\frac{1}{\mathrm{~N}^6}+11$.

Option 1: –11

Option 2: –2

Option 3: 11

Option 4: 9