Question : If $ (a-b):(b-c):(c-d) =1:2:3$, then what is the value of $(a + d):c$ ?

Option 1: $1:2$

Option 2: $2:1$

Option 3: $4:1$

Option 4: $3:1$

Question : Three cars travelled a distance in the ratio 1 : 2 : 3. If the ratio of the time of travel is 3 : 2 : 1, then the ratio of their speed is:

Option 1: 3 : 9 : 1

Option 2: 1 : 3 : 9

Option 3: 1 : 2 : 4

Option 4: 4 : 3 : 2

Question : What is the ratio of inradius and circumradius of an equilateral triangle?

Option 1: 1 : 2

Option 2: 1 : 3

Option 3: 1 : 4

Option 4: 3 : 2

Question : If $a^2+b^2=2$ and $c^2+d^2=1$, then the value of $(ad-bc)^2+(ac+bd)^2$ is:

Option 1: $\frac{4}{9}$

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

Option 3: $1$

Option 4: $2$

Question : What is the simplified value of $(3+1)(3^{2}+1)(3^{4}+1)(3^{8}+1)(3^{16}+1)$?

Option 1: $\frac{(3^{32}-1)}{2}$

Option 2: $\frac{(3^{16}-1)}{2}$

Option 3: $\frac{(3^{64}-1)}{2}$

Option 4: $\frac{(3^{128}-1)}{2}$