Question : Find 2 numbers such that their mean proportional is 25 and their third proportional is 25.

Option 1: 5 and 5

Option 2: 5 and 25

Option 3: 25 and 125

Option 4: 25 and 25

Question : Find the third proportional to 8 and 20.

Option 1: 25

Option 2: 50

Option 3: 40

Option 4: 64

Question : Find the value of $\frac{\cos^{2}25^\circ-\sin^{2}65^\circ}{\cos^{2}25^\circ+\sin^{2}65^\circ}$

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

Option 2: $1$

Option 3: $–1$

Option 4: $0$

Question : The third proportion of 1.8 and 9 is:

Option 1: 7.5

Option 2: 35

Option 3: 81

Option 4: 45

Question : If $a+b+c=13$ and $a b+b c+c a=45$, find $a^2+b^2+c^2$.

Option 1: 79

Option 2: 65

Option 3: 57

Option 4: 85