d
(d) Number of waves striking the surface per second (or the frequency of the waves reaching surface of the moving target )

\(n' = \frac{{(c + v)}}{\lambda }\)\( = \frac{{\nu (c + v)}}{c}\)

Now these waves are reflected by the moving target

(Which now act as a source). Therefore apparent frequency of reflected second \(n'' = \left( {\frac{c}{{c - v}}} \right)n'\) \( = \nu \left( {\frac{{c + v}}{{c - v}}} \right)\)

The wavelength of reflected wave  \(n = \left( {\frac{c}{{c - v}}} \right)n'\)

The number of beats heard by stationary listener  \( = n'' - \nu  = \nu \left( {\frac{{c + v}}{{c - v}}} \right) - \nu  = \frac{{2\nu v}}{{(c - v)}}\)

Hence option \((a)\, (b)\) and \((c)\) are correct.