\[(a)\;16 \Omega \pm 23 \% ,3 \Omega \pm 6.25 \% \] \[(b)\;3 \Omega \pm 2.3 \%,3 \Omega \pm 6.25 \% \]\[ (c)\;3 \Omega \pm 23 \%,16 \Omega \pm 6.25 \% \] \[ (d)\;16 \Omega \pm 6.25 \%,3 \Omega \pm 23 \%\]

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$R_S=R_1+R_2=16 \Omega$

$R_P=\large\frac{R_1R_2}{R_1+R_2}$$=3 \Omega$

$\large\frac{\Delta R_S}{R_S} $$\times 100$ is $\%$ error in $R_S$

$=\large\frac{1}{16}$$ \times 100=6.25 \%$

$=>R_S=16 \Omega \pm 6.25 \%$

$\large\frac{\Delta R_P}{R_P} $$\times 100$ is $\%$ error in $R_P$

$\bigg(\large\frac{\Delta R_1}{R_1} +\frac{\Delta R_2}{R_2}+\frac{\Delta R_S}{R_S}\bigg)$$ \times 100$

$=\bigg(\large\frac{.5}{4}+\frac{.5}{12}+\frac{1}{16}\bigg) $$ \times 100=23 \%$

$=>R_P=3 \Omega \pm 23 \%$

Hence d is the correct answer.

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