MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 2

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQPair of Linear Equations in Two Variables

The value of k for which the pair of equations $k x = y + 2$ and $6 x = 2 y + 3$ has infinitely many solutions,

(A)is k = 3
(B)does not exist
(C)is k = -3
(D)is k = 4

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

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

Hint 1

Recall the condition on the ratios $a_{1} / a_{2}$ , $b_{1} / b_{2}$ , $c_{1} / c_{2}$ for coincident lines.

Hint 2

Compare $b_{1} / b_{2}$ and $c_{1} / c_{2}$ first. They do not involve $k$ .

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.

Write both equations in standard form: $k x - y - 2 = 0$ and $6 x - 2 y - 3 = 0$ .
For infinitely many solutions we need $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$ , that is $\frac{k}{6} = \frac{- 1}{- 2} = \frac{- 2}{- 3}$ .
Here $\frac{b _{1}}{b _{2}} = \frac{1}{2}$ but $\frac{c _{1}}{c _{2}} = \frac{2}{3}$ , and $\frac{1}{2} \neq = \frac{2}{3}$ whatever $k$ is. So no value of $k$ works: such a $k$ does not exist. Option (B).
1 mark

Answer: k does not exist, option (B)

Where the marks are

Notes that $b_{1} / b_{2} \neq = c_{1} / c_{2}$ , so no k gives infinitely many solutions, option (B) (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 paper2023 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 2

Hints

Step-by-step solution

Revise the chapter

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