If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are not parallel, then k has to be (A) 15/4 (B) ≠ 15/4 (C) any rational number (D) any rational number having 4 as denominator

MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 3

From the official CBSE sample question paper for 2025-26, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · MCQPair of Linear Equations in Two Variables

If the lines given by $3 x + 2 k y = 2$ and $2 x + 5 y + 1 = 0$ are not parallel, then k has to be

(A) $\frac{15}{4}$
(B) $\neq = \frac{15}{4}$
(C)any rational number
(D)any rational number having 4 as denominator

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Two lines that are not parallel intersect in exactly one point.

Hint 2

Compare the ratios of the coefficients of x and of y.

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.

The lines are not parallel exactly when $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ . Here $a_{1} = 3, b_{1} = 2 k, a_{2} = 2, b_{2} = 5$ .
So we need $\frac{3}{2} \neq = \frac{2 k}{5}$ , which gives $4 k \neq = 15$ , i.e. $k \neq = \frac{15}{4}$ . The answer is option (B).
1 mark

Answer: k ≠ 15/4, option (B)

Where the marks are

Applies the condition $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ and gets $k \neq = \frac{15}{4}$ , 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 2025-26 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2025-26: question 3

Hints

Step-by-step solution

Revise the chapter

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