MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 3

From the official CBSE sample question paper for 2023-24, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · Assertion-reasonCompetency-basedPair of Linear Equations in Two Variables

The lines representing the given pair of linear equations are non-intersecting. Which of the following statements is true?

(A) $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$
(B) $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$
(C) $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$
(D) $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$

Figure in the paper: Two parallel straight lines on a coordinate grid, labelled $a_{1} x + b_{1} y + c_{1} = 0$ (upper line) and $a_{2} x + b_{2} y + c_{2} = 0$ (lower line). See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Non-intersecting lines in a plane are parallel.

Hint 2

Parallel lines have equal slopes but different intercepts.

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.

Non-intersecting lines are parallel, so the pair has no solution (it is inconsistent).
The condition for parallel lines is $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ . Option (B).
1 mark

Answer: $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , option (B)

Where the marks are

States the parallel-lines (no solution) condition, 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)
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 paperSample paper 2023-24 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 3

Hints

Step-by-step solution

Revise the chapter

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