Question : If $\tan x = –\frac{12}{5}$, where $x$ lies in the second quadrant, what is the value of $\sin x-\cot x$?

Option 1: $\frac{209}{156}$

Option 2: $\frac{169}{156}$

Option 3: $\frac{156}{209}$

Option 4: $\frac{144}{169}$

Question : The mean proportional of $a$ and $b$ is $c$. What is the mean proportion of $a^2c$ and $b^2c$?

Option 1: $c$

Option 2: 3$c$

Option 3: $c^3$

Option 4: $c^2$

Question : The mean proportion between 7 and 112 is:

Option 1: 42

Option 2: 28

Option 3: 21

Option 4: 14

Question : Three positive numbers are in the ratio of 4 : 5 : 7, and the sum of their squares is 15,210. Find the sum of the three numbers.

Option 1: 148

Option 2: 156

Option 3: 126

Option 4: 208

Question : Two numbers $x$ and $y$ are such that their mean proportion is 9 and the third proportion is 243. What are the values of $x$ and $y$?

Option 1: 3 and 9

Option 2: 3 and 27

Option 3: 6 and 27

Option 4: 6 and 81