Question : The fourth proportional to 8, 32, and 13 is:

Option 1: 39

Option 2: 40

Option 3: 26

Option 4: 52

Question : What is the ratio of the mean proportional between 1.6 and 3.6 and the third proportional of 5 and 8?

Option 1: 2 : 15

Option 2: 5 : 16

Option 3: 3 : 16

Option 4: 4 : 15

Question : If $8 a^3+27 b^3=16$ and $2 a+3 b=4$, then find the value of $16 a^4+81 b^4$.

Option 1: 26

Option 2: 30

Option 3: 28

Option 4: 32

Question : Three numbers are in the ratio 2 : 3 : 4. If the sum of their squares is 1856, the numbers are:

Option 1: 8, 12, and 16

Option 2: 16, 24, and 32

Option 3: 12, 18, and 24

Option 4: None of the above.

Question : Simplify the following expression:
$[(1 + p)(1 + p^2)(1 + p^4)(1 + p^8)(1 + p^{16})(1 - p) - 1]$

Option 1: $-p^{32}$

Option 2: $p^{32}$

Option 3: $(1 + p^{32})$

Option 4: $(1 - p^{32})$