MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 21(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section B, question 21(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(a) · 2 marks · Very short answerPair of Linear Equations in Two Variables

Find the value of c for which the following pair of linear equations has infinitely many solutions : $c x + 3 y = c - 3$ , $12 x + cy = c$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

Recall the condition on the ratios of coefficients for a pair of lines to coincide.

Hint 2

Equate the ratios two at a time and solve each equation for c.

Hint 3

Keep only the value common to both equations.

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.

Here $a_{1} = c, b_{1} = 3, c_{1} = c - 3$ and $a_{2} = 12, b_{2} = c, c_{2} = c$ . For infinitely many solutions, $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$ , so $\frac{c}{12} = \frac{3}{c} = \frac{c - 3}{c}$ .
1 mark
From $\frac{c}{12} = \frac{3}{c}$ : $c^{2} = 36$ , so $c = \pm 6$ . From $\frac{3}{c} = \frac{c - 3}{c}$ : $3 c = c^{2} - 3 c$ , i.e. $c^{2} - 6 c = 0$ , so $c = 0$ or $c = 6$ .
½ mark
The only value satisfying both conditions (and $c \neq = 0$ ) is $c = 6$ .
½ mark

Answer: c = 6

Where the marks are

Writes the condition $\frac{c}{12} = \frac{3}{c} = \frac{c - 3}{c}$ (1 mark)
Obtains $c = \pm 6$ and $c = 0, 6$ (½ mark)
Concludes $c = 6$ (½ 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 paper2025 board paper, set 430/2/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 21(a)

Hints

Step-by-step solution

Revise the chapter

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