Question : If $P:Q=1: 3, Q:R=3:4,$ and $R: S=2:1$, then what is the value of $P:S$?

Option 1: $3:1$

Option 2: $2:1$

Option 3: $1:2$

Option 4: $3:2$

Question : If $\cos^{4}\theta-\sin^{4}\theta=\frac{2}{3}$, then the value of $1-2\sin^{2}\theta$ is:

Option 1: $\frac{2}{3}$

Option 2: $\frac{3}{2}$

Option 3: $1$

Option 4: $0$

Question : If $2apq=(p+q)^{2}-(p-q)^{2}$, then the value of $a$ is:

Option 1: 2

Option 2: 1

Option 3: 4

Option 4: 8

Question : If $\sin A+\sin ^2 A=1$, then the value of the expression $\left(\cos ^2 A+\cos ^4 A\right)$ is

Option 1: $\frac{3}{2}$

Option 2: $1$

Option 3: $2$

Option 4: $\frac{1}{2}$

Question : If $p^{3}+3p^{2}+3p=7$, then the value of $p^2+2p$ is:

Option 1: 4

Option 2: 3

Option 3: 5

Option 4: 6