NIMCET 2014 — Mathematics PYQ

Q: How do I solve NIMCET 2014 Mathematics questions?

Practice NIMCET 2014 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of NIMCET Mathematics questions?

NIMCET Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are NIMCET previous year papers available for free?

Yes. Mathem Solvex provides free access to NIMCET previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

NIMCET 2014 — Mathematics PYQ

NIMCET | Mathematics | 2014

Suppose the system of linear equations:

$-2x + y + z = l$

$x - 2y + z = m$

$x + y - 2z = n$

is such that $l + m + n = 0$ , then the system has:

Choose the correct answer:

Explanation

Solution

Concept:

Rouché–Capelli theorem: A system has a solution if $\text{rank}(A) = \text{rank}(A|B)$ .
If $n > \text{rank}(A) = \text{rank}(A|B)$ , there are infinitely many solutions.

Calculation:

Augmented matrix $[A|B]$ is:

[A|B] = \begin{bmatrix} -2 & 1 & 1 & | & l \\ 1 & -2 & 1 & | & m \\ 1 & 1 & -2 & | & n \end{bmatrix}

Applying $R_3 \to R_1 + R_2 + R_3$ :

[A|B] = \begin{bmatrix} -2 & 1 & 1 & | & l \\ 1 & -2 & 1 & | & m \\ 0 & 0 & 0 & | & l + m + n \end{bmatrix}

Since $l + m + n = 0$ , the last row becomes all zeros.

$\text{rank}(A) = \text{rank}(A|B) = 2$ , which is less than the number of variables (3).

Therefore, the system has infinitely many solutions.

Correct Option: 3