NIMCET 2012 Question Paper with solutions

The given system of homogeneous equation
3x + Ky -2z = 0
x + Ky + 3z = 0
2x + 3y-4z = 0
For non-trivial solution
$\left|\begin{array}{ccc}3& \mathit{K}& -2\\ 1& \mathit{K}& 3\\ 2& 3& -4\end{array}\right|$ = 0
⇒ 3 (- 4K - 9) - K (- 4 - 6) + 2 (- 3 + 2K) = 0
⇒ - 12K - 27 + 10K - (+ 6) + 4K = 0
⇒ + 2 K - 33 = 0
∴ K = + $\frac{33}{2}$