b
\(\frac{1}{f}=(n-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)\)

For the first lens,

\(n=1.5, R_{1}=+14 cm , R_{2}=\infty\)

\(\therefore \frac{1}{f_{1}}=(1.5-1)\left(\frac{1}{14}-\frac{1}{\infty}\right)\)

\(=\frac{0.5}{14}\)

For the second lens,

\(n=1.2, R_{1}=\infty, R_{2}=-14 cm\)

\(\therefore \frac{1}{f_{1}}=(1.2-1)\left(\frac{1}{\infty}-\frac{1}{-14}\right)=\frac{0.2}{14}\)

The focal length of the bi-convex lens is

\(\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}\)

\(=\frac{0.5}{14}+\frac{0.2}{14}=\frac{0.7}{14}=\frac{1}{20}\)

According to thin lens formula,

\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)

Here, \(u=-40 cm , f=20 cm\)

\(\therefore \frac{1}{v}-\frac{1}{-40}=\frac{1}{20}\) or

\(\frac{1}{v}=\frac{1}{20}-\frac{1}{40}\) or

\(v=40 cm\)