Question : If $a+\frac{1}{a}=3$, then $a^3+\frac{1}{a^3}$ is:

Option 1: 27

Option 2: 24

Option 3: 18

Option 4: 25

Question : If $p=\frac{5}{18}$, then $27p^{3}–\frac{1}{216}–\frac{9}{2}p^{2}+\frac{1}{4}p$ is equal to:

Option 1: $\frac{4}{27}$

Option 2: $\frac{5}{27}$

Option 3: $\frac{8}{27}$

Option 4: $\frac{10}{27}$

Question : If for a non-zero $x$, $3x^{2}+5x+3=0,$ then the value of $x^{3}+\frac{1}{x^{3}}$ is:

Option 1: $\frac{10}{27}$

Option 2: $-\frac{10}{27}$

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

Option 4: $-\frac{2}{3}$

Question : The value of $2 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}+\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)$ is:

Option 1: $\frac{25}{24}$

Option 2: $\frac{29}{24}$

Option 3: $\frac{35}{24}$

Option 4: $\frac{5}{24}$

Question : The value of $3 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}+\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)$ is:

Option 1: $\frac{55}{24}$

Option 2: $\frac{35}{24}$

Option 3: $\frac{25}{24}$

Option 4: $\frac{5}{24}$

Question : If $\cot \theta=\frac{4}{3}, 0<\theta<\frac{\pi}{2}$, and $5 p \cos ^2 \theta \sin \theta=\cot ^2 \theta$, then the value of $p$ is:

Option 1: $\frac{7}{27}$

Option 2: $\frac{125}{27}$

Option 3: $\frac{5}{27}$

Option 4: $\frac{25}{27}$