NIMCET 2014 Question Paper with solutions

We have
a = - $4\hat{\mathit{i}}+2\hat{\mathit{j}}$ .... (i)
b = $2\hat{\mathit{i}}+\hat{\mathit{j}}$ ... (ii)
c = $2\hat{\mathit{i}}+3\hat{\mathit{j}}$ ... (iii)
c = ma+nb
From Eqs. (i), (ii), (iii) and (iv),
$2\hat{\mathit{i}}+3\hat{\mathit{j}}$ = m $\left(-4\mathit{i}+2\hat{\mathit{j}}\right)+\mathit{n}\left(2\hat{\mathit{i}}+\hat{\mathit{j}}\right)$
⇒ 2 = - 4m + 2n ... (v)
⇒ 3 = 2n + n ... (vi)
⇒ 2 = - 4m + 6 - 4 m
⇒ 8m = 4 ⇒ m = $\frac{1}{2}$
From Eq. (v). 2 = - 2 + 2n
⇒ n = 2
∴ m + n = $\frac{1}{2}+2$
⇒ m + n = 5/2