d
\(\mathrm{n}_{\mathrm{A}}=425 \mathrm{Hz}, \mathrm{n}_{\mathrm{B}}=?\)

Beat frequency \(x=5\) \(Hz\) which is decreasing \((5 \rightarrow 3)\) after increasing the tension of the string \(B\).

Also tension of string \(\mathrm{B}\) increasing so

\(\mathrm{n}_{\mathrm{B}} \uparrow(\because \mathrm{n} \propto \sqrt{\mathrm{T}})\)

Hence \(\quad \mathrm{n}_{\mathrm{A}}-\mathrm{n}_{\mathrm{B}} \uparrow=x \downarrow \longrightarrow\) correct

\(\mathrm{n}_{\mathrm{B}} \uparrow-\mathrm{n}_{\mathrm{A}}=\mathrm{x} \downarrow  \longrightarrow \text { incorrect }\)

\(\therefore \mathrm{n}_{\mathrm{B}}=\mathrm{n}_{\mathrm{A}}-\mathrm{x}=425-5=420 \mathrm{Hz}\)