NIMCET 2011 — Mathematics PYQ

1. Set up the determinant $D$:

2. Expand the determinant along the first row:

3. Analyze the result:

Since $D=0$, the system either has infinitely many solutions or no solution. We must now check the determinants $D_1,D_2,$ or $D_3$ (Cramer's Rule).

4. Calculate $D_1$ (replace first column with constants 2, 3, 13):

Similarly, checking $D_2$ and $D_3$:

Conclusion:

Since $D=0$ and $D_1=D_2=D_3=0$, the system of equations has infinitely many solutions.

The correct option is (a).