MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2024: question 19

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedPair of Linear Equations in Two Variables

Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) given below.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.

Assertion (A): The pair of linear equations $5 x + 2 y + 6 = 0$ and $7 x + 6 y + 18 = 0$ have infinitely many solutions.

Reason (R): The pair of linear equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ have infinitely many solutions, if $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} = \frac{c _{1}}{c _{2}}$ .

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/4/1.

Hints

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

Hint 1

Compute $\frac{a _{1}}{a _{2}}$ and $\frac{b _{1}}{b _{2}}$ .

Hint 2

If these ratios are unequal, how many solutions are there?

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.

$\frac{a _{1}}{a _{2}} = \frac{5}{7}$ and $\frac{b _{1}}{b _{2}} = \frac{2}{6} = \frac{1}{3}$ . These ratios are not equal, so the pair has a unique solution and the Assertion is false.
1 mark
The Reason states the correct condition for infinitely many solutions, so it is true. The answer is option (D).

Answer: Option (D)

Where the marks are

Compares the ratios to show A is false while R is true (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 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 19

Hints

Step-by-step solution

Revise the chapter

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