NIMCET 2012 Question Paper with solutions

Let A = a + 2b + 3c
B = λb + 4c
C = (2λ - 1) c
Since, A, B, C are non-coplanar vectors.
∴ [A B C] ≠ 0
⇒ $\left|\begin{array}{ccc}1& 2& 3\\ 0& \mathit{\lambda }& 4\\ 0& 0& \left(2\mathit{\lambda }-1\right)\end{array}\right|$ ≠ 0
⇒ 1 . λ . (2λ - 1) ≠ 0
⇒ λ ≠ 0 , $\frac{1}{2}$
Hence, all except two values of λ