The value of 'p' for which the equations px + 3y = p - 3, 12x + py = p has infinitely many solutions is : (A) -6 only (B) 6 only (C) ± 6 (D) Any real number except ± 6

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 6

Set in the CBSE Class 10 board exam of 2025, paper 30/4/1, section A, question 6, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q6 · 1 mark · MCQPair of Linear Equations in Two Variables

The value of ' $p$ ' for which the equations $p x + 3 y = p - 3$ , $12 x + p y = p$ has infinitely many solutions is :

(A) $- 6$ only
(B) $6$ only
(C) $\pm 6$
(D)Any real number except $\pm 6$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/4/1.

Hints

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

Hint 1

Infinitely many solutions: all three ratios equal.

Hint 2

Check both $p = 6$ and $p = - 6$ against the constant-term ratio.

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.

Write as $p x + 3 y - (p - 3) = 0$ , $12 x + p y - p = 0$ . Need $\frac{p}{12} = \frac{3}{p} = \frac{p - 3}{p}$ .
$p^{2} = 36 \Rightarrow p = \pm 6$ ; $\frac{3}{p} = \frac{p - 3}{p} \Rightarrow p = 6$ . So $p = 6$ only, option (B).
1 mark

Answer: $p = 6$ only, option (B)

Where the marks are

Applies $a_{1} / a_{2} = b_{1} / b_{2} = c_{1} / c_{2}$ and gets $p = 6$ (1 mark)

Revise the chapter

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

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 paper2025 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 6

Hints

Step-by-step solution

Revise the chapter

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