NIMCET 2018 — Mathematics PYQ

Q: How do I solve NIMCET 2018 Mathematics questions?

Practice NIMCET 2018 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 2018 — Mathematics PYQ

NIMCET | Mathematics | 2018

Equation of the line perpendicular to x - 2y = 1 and passing through (1, 1) is:

Choose the correct answer:

Explanation

Concept:
- If two lines $y = m_{1} x + c_{1}$ and $y = m_{2} x + c_{2}$ are perpendicular to each other, then $m_{1} \times m_{2} = - 1$ .
- If a point P(a, b) lies on a curve $f (x, y) = 0$ , then $f (a, b) = 0$ .

Calculation:
Let us first find out the slope ( $m_{2}$ ) of the second line.
The equation of the first line is $x - 2 y = 1$ .
It can be written as $y = \frac{1}{2} x - \frac{1}{2}$ . Therefore, $m_{1} = \frac{1}{2}$ .
Now, $m_{1} \times m_{2} = - 1$
$\Rightarrow \frac{1}{2} \times m_{2} = - 1$
$\Rightarrow m_{2} = - 2$
$∴$ The equation of the second line can be written as $y = - 2 x + c$ .
Since this line passes through (1, 1), we must have:
$1 = (- 2) (1) + c$
$\Rightarrow c = 3$ .
Hence, the equation of the line is $y = - 2 x + 3$ .