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CBSE Class 9 Mathematics · Ch 2: Introduction to Linear Polynomials

CBSE Class 9 Mathematics · Ch 2: Introduction to Linear Polynomials is an online chapter test in the CBSE Class 9 pattern, covering Introduction to Linear Polynomials. 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
Unlock all 20 tests — ₹99Try English · Ch 1: The Fun They Had free →

Topics in this test

TopicQuestions
Introduction to Linear Polynomials30

Difficulty: 7 medium · 23 hard

Introduction to Linear Polynomials MCQ questions with answers

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

  1. Q1. Consider the following statements about linear polynomials in one variable: I. A linear polynomial has exactly one zero. II. The zero of the polynomial $p(x)=2x+3$ is $\frac{3}{2}$. III. Every linear polynomial can be written as $ax+b$, where $a\neq 0$. Which of these statements are correct?

    एक चर वाले रैखिक बहुपदों के बारे में निम्नलिखित कथनों पर विचार कीजिए: I. एक रैखिक बहुपद का ठीक एक शून्यक होता है। II. बहुपद $p(x)=2x+3$ का शून्यक $\frac{3}{2}$ है। III. प्रत्येक रैखिक बहुपद को $ax+b$ के रूप में लिखा जा सकता है, जहाँ $a\neq 0$। इनमें से कौन-से कथन सही हैं?

    • A. I and III only / केवल I और III
    • B. I and II only / केवल I और II
    • C. II and III only / केवल II और III
    • D. I, II and III / I, II और III
    Solution

    A linear polynomial $ax+b$ with $a\neq 0$ has exactly one zero, so I and III are true; but the zero of $2x+3$ comes from $2x+3=0$, giving $x=-\frac{3}{2}$, so II is wrong.

    $a\neq 0$ वाले रैखिक बहुपद $ax+b$ का ठीक एक शून्यक होता है, अतः I और III सत्य हैं; परंतु $2x+3$ का शून्यक $2x+3=0$ से प्राप्त होता है, जिससे $x=-\frac{3}{2}$ मिलता है, अतः II गलत है।

  2. Q2. The polynomial $p(x)=x^3-2x^2+kx+5$ leaves a remainder of $11$ when divided by $(x-2)$. Using this, what remainder does $p(x)$ leave when it is divided by $(x-3)$?

    बहुपद $p(x)=x^3-2x^2+kx+5$ को $(x-2)$ से विभाजित करने पर शेषफल $11$ प्राप्त होता है। इसका उपयोग करते हुए, जब $p(x)$ को $(x-3)$ से विभाजित किया जाता है, तो शेषफल क्या होगा?

    • A. $23$
    • B. $11$
    • C. $5$
    • D. $17$
    Solution

    By the Remainder Theorem, $p(2)=8-8+2k+5=11$ gives $k=3$, so $p(x)=x^3-2x^2+3x+5$; then $p(3)=27-18+9+5=23$.

    शेषफल प्रमेय के अनुसार, $p(2)=8-8+2k+5=11$ से $k=3$ प्राप्त होता है, अतः $p(x)=x^3-2x^2+3x+5$; तब $p(3)=27-18+9+5=23$।

  3. Q3. Which one of the following is NOT a polynomial?

    निम्नलिखित में से कौन-सा एक बहुपद नहीं है?

    • A. $5x^2 - 3x + 2$
    • B. $7$
    • C. $\sqrt{2}\,x + 1$
    • D. $x^2 + \frac{3}{x}$
    Solution

    $x^2 + \frac{3}{x}$ has the term $\frac{3}{x}=3x^{-1}$ with a negative power, so it is not a polynomial; an irrational coefficient like $\sqrt{2}$ is allowed.

    $x^2 + \frac{3}{x}$ में पद $\frac{3}{x}=3x^{-1}$ है जिसमें ऋणात्मक घात है, अतः यह एक बहुपद नहीं है; $\sqrt{2}$ जैसा अपरिमेय गुणांक मान्य है।

Frequently asked questions

How many questions are in the CBSE Class 9 Mathematics · Ch 2: Introduction to Linear Polynomials?

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

Is there negative marking in the CBSE Class 9 Mathematics · Ch 2: Introduction to Linear Polynomials?

No — wrong answers are not penalised in this test.

Which topics does the CBSE Class 9 Mathematics · Ch 2: Introduction to Linear Polynomials cover?

Introduction to Linear Polynomials (30 questions).

Is the CBSE Class 9 Mathematics · Ch 2: Introduction to Linear Polynomials free?

It is part of the CBSE Class 9 Test Series 2027 — Chapter-wise + Full Tests (20 tests, ₹99). You can first try English · Ch 1: The Fun They Had for free.

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Introduction to Linear Polynomials MCQ Questions with Answers | CBSE Class 9 | SeatBeat