MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 13

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section A, question 13, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q13 · 1 mark · MCQPair of Linear Equations in Two Variables

The value of 'k' for which the system of equations $k x + 2 y = 5$ and $3 x + 4 y = 1$ have no solution, is

(A) $k = \frac{3}{2}$
(B) $k \neq = \frac{3}{2}$
(C) $k \neq = \frac{2}{3}$
(D) $k = 15$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

Recall the ratio condition for a pair of parallel lines.

Hint 2

Equate $\frac{k}{3}$ with $\frac{2}{4}$ .

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 no solution, $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , i.e. $\frac{k}{3} = \frac{2}{4} \neq = \frac{5}{1}$ .
$\frac{k}{3} = \frac{1}{2} \Rightarrow k = \frac{3}{2}$ (and $\frac{1}{2} \neq = 5$ holds), so option (A).
1 mark

Answer: $k = \frac{3}{2}$ , option (A)

Where the marks are

Applies the no-solution condition to get $k = \frac{3}{2}$ (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 paper2023 board paper, set 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 13

Hints

Step-by-step solution

Revise the chapter

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