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CBSE Class 10 Mathematics · Ch 3: Pair of Linear Equations in Two Variables

CBSE Class 10 Mathematics · Ch 3: Pair of Linear Equations in Two Variables is an online chapter test in the CBSE Class 10 pattern, covering Pair of Linear Equations in Two Variables. Attempt it on SeatBeat with a timer like the real exam, then see a detailed solution for every question and your score and weak-topic analysis.

30
Questions
20
Minutes
30
Marks
None
Negative marking
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Topics in this test

TopicQuestions
Pair of Linear Equations in Two Variables30

Difficulty: 7 medium · 23 hard

Pair of Linear Equations in Two Variables MCQ questions with answers

The first 3 of 30 questions. Unlock the series for the rest, each with a solution.

  1. Q1. Which of the following pairs of equations does NOT have a unique solution?

    निम्नलिखित में से किस समीकरण युग्म का अद्वितीय हल नहीं है?

    • A. $x + y = 3$ and $x - y = 1$ / $x + y = 3$ और $x - y = 1$
    • B. $x + 2y = 4$ and $2x - y = 3$ / $x + 2y = 4$ और $2x - y = 3$
    • C. $2x + y = 5$ and $4x + 2y = 10$ / $2x + y = 5$ और $4x + 2y = 10$
    • D. $3x - y = 2$ and $x + 2y = 3$ / $3x - y = 2$ और $x + 2y = 3$
    Solution

    In $2x + y = 5$ and $4x + 2y = 10$, we have $\frac{2}{4}=\frac{1}{2}=\frac{5}{10}$, so the lines are coincident with infinitely many solutions, not a unique one.

    $2x + y = 5$ और $4x + 2y = 10$ में $\frac{2}{4}=\frac{1}{2}=\frac{5}{10}$ है, अतः रेखाएँ संपाती हैं और अपरिमित रूप से अनेक हल हैं, अद्वितीय हल नहीं।

  2. Q2. The pair of equations $2x + y = 6$ and $4x + 2y = k$ has no solution for all values of $k$ except:

    समीकरण युग्म $2x + y = 6$ और $4x + 2y = k$ का $k$ के सभी मानों के लिए कोई हल नहीं है, सिवाय:

    • A. every value of $k$ / $k$ के प्रत्येक मान
    • B. $k = 12$
    • C. $k = 3$
    • D. $k = 6$
    Solution

    Here $\frac{2}{4}=\frac{1}{2}=\frac{1}{2}$, so for no solution we need $\frac{6}{k}\neq\frac{1}{2}$, i.e. $k \neq 12$; only at $k = 12$ the lines coincide instead.

    यहाँ $\frac{2}{4}=\frac{1}{2}=\frac{1}{2}$ है, अतः कोई हल न होने के लिए आवश्यक है कि $\frac{6}{k}\neq\frac{1}{2}$, अर्थात् $k \neq 12$; केवल $k = 12$ पर रेखाएँ संपाती हो जाती हैं।

  3. Q3. If $37x + 43y = 123$ and $43x + 37y = 117$, then the value of $x + y$ is:

    यदि $37x + 43y = 123$ और $43x + 37y = 117$ हो, तो $x + y$ का मान है:

    • A. $1$
    • B. $4$
    • C. $3$
    • D. $2$
    Solution

    Adding the two equations gives $80x + 80y = 240$, so $80(x+y) = 240$ and $x + y = 3$.

    दोनों समीकरणों को जोड़ने पर $80x + 80y = 240$ मिलता है, अतः $80(x+y) = 240$ और $x + y = 3$।

Frequently asked questions

How many questions are in the CBSE Class 10 Mathematics · Ch 3: Pair of Linear Equations in Two Variables?

30 questions for 30 marks, to be answered in 20 minutes.

Is there negative marking in the CBSE Class 10 Mathematics · Ch 3: Pair of Linear Equations in Two Variables?

No — wrong answers are not penalised in this test.

Which topics does the CBSE Class 10 Mathematics · Ch 3: Pair of Linear Equations in Two Variables cover?

Pair of Linear Equations in Two Variables (30 questions).

Is the CBSE Class 10 Mathematics · Ch 3: Pair of Linear Equations in Two Variables free?

It is part of the CBSE Class 10 Test Series 2027 — Chapter-wise + Full Tests (26 tests, ₹199). You can first try Hindi · Ch 1: Surdas ke Pad for free.

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