MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 2

From the official CBSE sample question paper for 2024-25, 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 system of equations $3 x - k y = 7$ and $6 x + 10 y = 3$ is inconsistent, is

(A) $- 10$
(B) $- 5$
(C) $5$
(D) $7$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Recall the condition on the ratios of the coefficients for parallel lines.

Hint 2

Set $\frac{3}{6}$ equal to $\frac{- k}{10}$ .

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 is inconsistent when $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ .
Here $\frac{3}{6} = \frac{- k}{10}$ , so $- k = 5$ and $k = - 5$ .
1 mark
Check: $\frac{c _{1}}{c _{2}} = \frac{- 7}{- 3} = \frac{7}{3} \neq = \frac{1}{2}$ , so the condition holds. The answer is option (B).

Answer: $k = - 5$ , option (B)

Where the marks are

Uses $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ and obtains $k = - 5$ (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 paperSample paper 2024-25 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2024-25: question 2

Hints

Step-by-step solution

Revise the chapter

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