Question : If $\small c+\frac{1}{c}=3$, then the value of $\left (c-3 \right )^{7}+\frac{1}{c^{7}}$ is:

Option 1: 2

Option 2: 0

Option 3: 3

Option 4: 1

Question : If $x+\frac{1}{x}=0$, then the value of $x^{5}+\frac{1}{x^{5}}$ is:

Option 1: 2

Option 2:  –1

Option 3: 1

Option 4: 0

Question : If 3 cot A = 4 and A is an acute angle, then find the value of sec A.

Option 1: $\frac{3}{4}$

Option 2: $\frac{5}{4}$

Option 3: $\frac{4}{5}$

Option 4: $\frac{5}{3}$

Question : The value of the expression $\frac{(a-b)^{2}}{(b-c)(c-a)}+\frac{(b-c)^{2}}{(a-b)(c-a)}+\frac{(c-a)^{2}}{(a-b)(b-c)}$ is:

Option 1: $0$

Option 2: $3$

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

Option 4: $2$

Question : If $a^3+b^3=9$ and $a+b=3$, then the value of $\frac{1}a+\frac{1}b$ is:

Option 1: $\frac{1}2$

Option 2: $\frac{3}2$

Option 3: $\frac{5}2$

Option 4:  $–1$