Question : The compound ratio of 3 : 4 and 6 : 7 is 36 : X. Find X.

Option 1: 64

Option 2: 75

Option 3: 56

Option 4: 48

Question : If $x^{2}+\frac{1}{x^{2}}=1$, then, what is the value of $x^{48}+x^{42}+x^{36}+x^{30}+x^{24}+x^{18}+x^{12}+x^{6}+1$?

Option 1: – 9

Option 2: 0

Option 3: 1

Option 4: 9

Question :  If $x^2+\frac{1}{x^2}=7$, then what is the value of $x^3+\frac{1}{x^3}$?

Option 1: 9

Option 2: 18

Option 3: 27

Option 4: 36

Question : If $\small x+y+z=6$ and $xy+yz+zx=10$, then the value of $x^{3}+y^{3}+z^{3}-3xyz$ is:

Option 1: 36

Option 2: 48

Option 3: 42

Option 4: 40

Question : If $x^4+\frac{1}{x^4}=194, x>0$, then find the value of $x^3+\frac{1}{x^3}+x+\frac{1}{x}$

Option 1: 76

Option 2: 66

Option 3: 56

Option 4: 46

Question : What is the value of $x$?
$\frac{3}{2}× \frac{7}{3} ÷ \frac{7}{6}+\frac{1}{4}=\frac{1}{x}$

Option 1: $\frac{7}{12}$

Option 2: $\frac{4}{13}$

Option 3: $\frac{13}{4}$

Option 4: $\frac{6}{7}$