NIMCET 2015 Question Paper with solutions

From the diagram
$\mathit{f}={\mathit{f}}_1{\mathit{f}}_2+{\mathit{f}}_3$ (put value)
$=\left(4,5,6,7,8\right){\mathit{f}}_2+\left(1,6,15\right)=\left(1,6,8,15\right)$
Now, as you know that the number 0,1,2,... 14,15 represent the minterms like ${\mathrm{\Sigma }}_{\mathit{m}}\left(6,8\right)$
(i) If you AND (4, 6) with (4, 5, 6, 7, 8) it will result in (4, 6) but we don't need 4, so option (a) is wrong.
(ii) If you AND (4, 8) with (4, 5, 6, 7, 8) it will result in (4,8) but we don't need 4, so option (b) is wrong.
(iii) If you AND (4, 6, 8) with (4, 5, 6, 7, 8) it will result in (4, 6, 8) but we don't need 4 here too, so option (d)is wrong.
(iv) If you AND (6, 8) with (4, 5, 6, 7, 8) it will result in (6,8) now when OR (6, 8) with (1,6, 15), you get (1,6, 8,15) which is f , so option (c) is correct