📚 CBSE Grade-10 Study Guide Open in the Study Guide single page app →
HomeMathematics

Mathematics — CBSE Class 10 board question

Q1. [1]
If the pair of equations $3x - y + 8 = 0$ and $6x - ry + 16 = 0$ represent coincident lines, then the value of $r$ is:
  1. (a) $\frac{1}{2}$
  2. (b) $-\frac{1}{2}$
  3. (c) $2$
  4. (d) $-2$
Previously asked in CBSE board exam
2023 30/2/1 Q6
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer

(c) 2

For coincident lines: $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$

Here, $\dfrac{3}{6} = \dfrac{-1}{-r} = \dfrac{8}{16}$ $\Rightarrow \dfrac{1}{2} = \dfrac{1}{r}$ $\Rightarrow r = 2$

Source: Chapter 3, Section 3.2

Explanation

For coincident lines, all three ratios of coefficients must be equal. Students often make a sign error with the $b$ coefficients — note that $b_1 = -1$ and $b_2 = -r$, so $\frac{-1}{-r} = \frac{1}{r}$. Setting this equal to $\frac{1}{2}$ gives $r = 2$. Verify: $\frac{3}{6} = \frac{-1}{-2} = \frac{8}{16} = \frac{1}{2}$ ✓

If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to Library and find the actual CBSE question paper. The original papers are also available on the CBSE website: cbse.gov.in.
Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.