MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 5

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section A, question 5, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q5 · 1 mark · MCQPair of Linear Equations in Two Variables

The value of k for which the system of equations $3 x - 7 y = 1$ and $k x + 14 y = 6$ is inconsistent, is

(A) $- 6$
(B) $\frac{2}{3}$
(C) $6$
(D) $\frac{- 3}{2}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

Inconsistent means the lines are parallel.

Hint 2

Set $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}}$ and solve for $k$ .

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.

For an inconsistent system, $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ .
$\frac{3}{k} = \frac{- 7}{14} = - \frac{1}{2}$ gives $k = - 6$ . Also $\frac{c _{1}}{c _{2}} = \frac{1}{6} \neq = - \frac{1}{2}$ , so the system is indeed inconsistent.
1 mark

Answer: k = −6, option (A)

Where the marks are

Uses the inconsistency condition to get $k = - 6$ (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 paper2025 board paper, set 430/6/1 (Basic): 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 Basic 2025: question 5

Hints

Step-by-step solution

Revise the chapter

More questions from Pair of Linear Equations in Two Variables