NIMCET 2014 Question Paper with solutions

In ΔABC,
a = 2 , b = 4 , ∠C = 60°
cos C = $\frac{{\mathit{a}}^2+{\mathit{b}}^2-{\mathit{c}}^2}{\mathit{a}\mathit{b}}$
cos 60° = $\frac{4+16-{\mathit{c}}^2}{2\times 2\times 4}$
⇒ $\frac{1}{2}$ = $\frac{20-{\mathit{c}}^2}{16}$
⇒ ${\mathit{c}}^2$ = 12
⇒ x = 2 $\sqrt{3}$
now , $\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{A}}{\mathit{a}}$ = $\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{B}}{\mathit{b}}$ = $\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{C}}{\mathit{c}}$
⇒ $\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{A}}{\mathit{a}}$ = $\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{C}}{\mathit{c}}$
⇒ $\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{A}}{2}$ = $\frac{\mathit{s}\mathit{i}\mathit{n}60°}{2\sqrt{3}}$
⇒ sin A = $\frac{1}{2}$
⇒ ∠A = 30°
Now ∠A + ∠B + ∠c = 180°
⇒ 30° + ∠B + 60° = 180°
⇒ ∠B = 90°
∴ ∠A = 30°
and ∠B = 90°