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Bihar Board Class 11 Science Mathematics · Ch 4: Complex Numbers and Quadratic Equations

Bihar Board Class 11 Science Mathematics · Ch 4: Complex Numbers and Quadratic Equations is an online chapter test in the Bihar Board Class 11 Science pattern, covering Complex Numbers and Quadratic Equations. 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
Complex Numbers and Quadratic Equations30

Difficulty: 6 medium · 24 hard

Complex Numbers and Quadratic Equations MCQ questions with answers

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

  1. Q1. If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 - 2x + 4 = 0$, then the value of $\alpha^3 + \beta^3$ is

    यदि $\alpha$ और $\beta$ द्विघात समीकरण $x^2 - 2x + 4 = 0$ के मूल हैं, तो $\alpha^3 + \beta^3$ का मान है

    • A. $40$
    • B. $16$
    • C. $-16$
    • D. $-8$
    Solution

    Here $\alpha+\beta=2$ and $\alpha\beta=4$, so $\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=8-24=-16$.

    यहाँ $\alpha+\beta=2$ और $\alpha\beta=4$ है, इसलिए $\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)=8-24=-16$।

  2. Q2. Which of the following statements about complex numbers is correct?

    सम्मिश्र संख्याओं के बारे में निम्नलिखित में से कौन सा कथन सही है?

    • A. For any two complex numbers $z_1$ and $z_2$, $z_1>z_2$ is always a meaningful statement / किसी भी दो सम्मिश्र संख्याओं $z_1$ और $z_2$ के लिए, $z_1>z_2$ हमेशा एक सार्थक कथन है
    • B. The product of a complex number and its conjugate is always a negative real number / किसी सम्मिश्र संख्या और उसके संयुग्मी का गुणनफल हमेशा एक ऋणात्मक वास्तविक संख्या होता है
    • C. The order relation 'greater than' or 'less than' is not defined for complex numbers unless they are purely real / 'बड़ा है' या 'छोटा है' का क्रम-संबंध सम्मिश्र संख्याओं के लिए परिभाषित नहीं है जब तक वे पूर्णतः वास्तविक न हों
    • D. Every complex number has a unique additive inverse but no multiplicative inverse / प्रत्येक सम्मिश्र संख्या का एक अद्वितीय योगात्मक प्रतिलोम होता है परन्तु गुणात्मक प्रतिलोम नहीं होता
    Solution

    The order relation 'greater than' or 'less than' is defined only for real numbers; it has no meaning for complex numbers unless both are purely real, as stated in the chapter.

    'बड़ा है' या 'छोटा है' का क्रम-संबंध केवल वास्तविक संख्याओं के लिए परिभाषित है; जैसा अध्याय में कहा गया है, यह सम्मिश्र संख्याओं के लिए तब तक अर्थहीन है जब तक दोनों पूर्णतः वास्तविक न हों।

  3. Q3. If $z_1=2-3i$ and $z_2=-1+i$, then $|z_1+z_2|$ equals

    यदि $z_1=2-3i$ और $z_2=-1+i$ हैं, तो $|z_1+z_2|$ बराबर है

    • A. $5$
    • B. $\sqrt2$
    • C. $\sqrt5$
    • D. $\sqrt{13}$
    Solution

    Adding gives $z_1+z_2=1-2i$, and its modulus is $\sqrt{1^2+(-2)^2}=\sqrt5$.

    जोड़ने पर $z_1+z_2=1-2i$ प्राप्त होता है, और इसका मापांक (modulus) $\sqrt{1^2+(-2)^2}=\sqrt5$ है।

Frequently asked questions

How many questions are in the Bihar Board Class 11 Science Mathematics · Ch 4: Complex Numbers and Quadratic Equations?

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

Is there negative marking in the Bihar Board Class 11 Science Mathematics · Ch 4: Complex Numbers and Quadratic Equations?

No — wrong answers are not penalised in this test.

Which topics does the Bihar Board Class 11 Science Mathematics · Ch 4: Complex Numbers and Quadratic Equations cover?

Complex Numbers and Quadratic Equations (30 questions).

Is the Bihar Board Class 11 Science Mathematics · Ch 4: Complex Numbers and Quadratic Equations free?

It is part of the BSEB Class 11 Science Test Series 2027 — Chapter-wise + Full Tests (43 tests, ₹149). You can first try Biology · Ch 1: The Living World for free.

More tests in the BSEB Class 11 Science Test Series 2027 — Chapter-wise + Full Tests

See the full BSEB Class 11 Science Test Series 2027 — Chapter-wise + Full Tests → · Bihar Board Class 11 Science: pattern, notification & syllabus →

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Complex Numbers and Quadratic Equations MCQ | Science