MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 3

From the official CBSE sample question paper for 2026-27, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · MCQPair of Linear Equations in Two Variables

For what value of $p$ does the pair of Linear equations $4 x + p y + 8 = 0$ and $2 x + 2 y + 2 = 0$ has a unique solution

(A) $p = 4$ only
(B) $p = 2$ only
(C) $p \neq = 4$
(D) $p \neq = 2$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

Open one hint at a time and try again before the next.

Hint 1

Recall the condition on the coefficient ratios for a unique solution.

Hint 2

Compare the ratio of the x-coefficients with the ratio of the y-coefficients.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

A pair of linear equations has a unique solution when $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ .
$\frac{4}{2} \neq = \frac{p}{2} \Rightarrow p \neq = 4$ . Option (C).
1 mark

Answer: p ≠ 4, option (C)

Where the marks are

Applies $a_{1} / a_{2} \neq = b_{1} / b_{2}$ to get p ≠ 4 (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Graphical Method of Solving Linear Equations

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 3

Hints

Step-by-step solution

Revise the chapter

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