MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 1

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQPair of Linear Equations in Two Variables

The value of $k$ for which the system of equations $3 x - y + 8 = 0$ and $6 x - k y + 16 = 0$ has infinitely many solutions, is

(A) $- 2$
(B) $2$
(C) $\frac{1}{2}$
(D) $- \frac{1}{2}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

Recall the condition on coefficient ratios for coincident lines.

Hint 2

Equate $\frac{3}{6}$ with $\frac{- 1}{- k}$ .

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.

For infinitely many solutions: $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$ , i.e. $\frac{3}{6} = \frac{- 1}{- k} = \frac{8}{16}$ .
$\frac{1}{k} = \frac{1}{2} \Rightarrow k = 2$ . Option (B).
1 mark

Answer: k = 2, option (B)

Where the marks are

Uses equal ratios of coefficients to get $k = 2$ (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 paper2024 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 1

Hints

Step-by-step solution

Revise the chapter

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