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CBSE Class 11 Science Mathematics · Ch 2: Relations and Functions

CBSE Class 11 Science Mathematics · Ch 2: Relations and Functions is an online chapter test in the CBSE Class 11 Science pattern, covering Relations and Functions. 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
Relations and Functions30

Difficulty: 7 medium · 23 hard

Relations and Functions MCQ questions with answers

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

  1. Q1. Consider the greatest integer function $f(x) = [x]$ and the following statements: (i) $[-3.5] = -3$ (ii) $[-3.5] = -4$ (iii) $[4.9] = 4$ (iv) The range of $f$ is $\mathbb{R}$. Which of the statements are correct?

    महत्तम पूर्णांक फलन $f(x) = [x]$ और निम्नलिखित कथनों पर विचार कीजिए: (i) $[-3.5] = -3$ (ii) $[-3.5] = -4$ (iii) $[4.9] = 4$ (iv) $f$ का परिसर $\mathbb{R}$ है। कौन-से कथन सही हैं?

    • A. (ii), (iii) and (iv) / (ii), (iii) और (iv)
    • B. (i) and (iv) / (i) और (iv)
    • C. (ii) and (iii) / (ii) और (iii)
    • D. (i) and (iii) / (i) और (iii)
    Solution

    $[x]$ is the greatest integer not exceeding $x$, so $[-3.5] = -4$ and $[4.9] = 4$; the range of the greatest integer function is the set of integers $\mathbb{Z}$, not $\mathbb{R}$, so only (ii) and (iii) are correct.

    $[x]$ वह महत्तम पूर्णांक है जो $x$ से अधिक नहीं होता, अतः $[-3.5] = -4$ और $[4.9] = 4$; महत्तम पूर्णांक फलन का परिसर पूर्णांकों का समुच्चय $\mathbb{Z}$ है, न कि $\mathbb{R}$, अतः केवल (ii) और (iii) सही हैं।

  2. Q2. Assertion (A): The domain of the real function $f(x) = \dfrac{1}{x^2 - 3x + 2}$ is $\mathbb{R} - \{1, 2\}$. Reason (R): $x^2 - 3x + 2 = (x - 1)(x - 2)$, which becomes zero at $x = 1$ and $x = 2$. Choose the correct option:

    अभिकथन (A): वास्तविक फलन $f(x) = \dfrac{1}{x^2 - 3x + 2}$ का प्रांत $\mathbb{R} - \{1, 2\}$ है। कारण (R): $x^2 - 3x + 2 = (x - 1)(x - 2)$, जो $x = 1$ और $x = 2$ पर शून्य हो जाता है। सही विकल्प चुनिए:

    • A. A is true but R is false / A सत्य है परंतु R असत्य है
    • B. Both A and R are true and R is the correct explanation of A / A और R दोनों सत्य हैं तथा R, A की सही व्याख्या है
    • C. A is false but R is true / A असत्य है परंतु R सत्य है
    • D. Both A and R are true but R is not the correct explanation of A / A और R दोनों सत्य हैं परंतु R, A की सही व्याख्या नहीं है
    Solution

    The function is undefined only where the denominator is zero; factoring shows that happens at $x = 1$ and $x = 2$, so both statements are true and R correctly explains A.

    फलन केवल वहीं अपरिभाषित होता है जहाँ हर शून्य होता है; गुणनखंडन दर्शाता है कि यह $x = 1$ और $x = 2$ पर होता है, अतः दोनों कथन सत्य हैं और R, A की सही व्याख्या करता है।

  3. Q3. The Cartesian product $A \times A$ has $9$ elements, two of which are $(-1, 0)$ and $(0, 1)$. Then the set $A$ is:

    कार्तीय गुणनफल $A \times A$ में $9$ अवयव हैं, जिनमें से दो $(-1, 0)$ और $(0, 1)$ हैं। तब समुच्चय $A$ है:

    • A. $\{-1, 0\}$
    • B. $\{-1, 0, 1\}$
    • C. $\{-1, 1\}$
    • D. $\{0, 1\}$
    Solution

    Since $A \times A$ has $9 = 3^2$ elements, $n(A) = 3$; the coordinates $-1, 0, 1$ must all belong to $A$, so $A = \{-1, 0, 1\}$.

    चूँकि $A \times A$ में $9 = 3^2$ अवयव हैं, अतः $n(A) = 3$; निर्देशांक $-1, 0, 1$ सभी $A$ से संबंधित होने चाहिए, अतः $A = \{-1, 0, 1\}$।

Frequently asked questions

How many questions are in the CBSE Class 11 Science Mathematics · Ch 2: Relations and Functions?

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

Is there negative marking in the CBSE Class 11 Science Mathematics · Ch 2: Relations and Functions?

No — wrong answers are not penalised in this test.

Which topics does the CBSE Class 11 Science Mathematics · Ch 2: Relations and Functions cover?

Relations and Functions (30 questions).

Is the CBSE Class 11 Science Mathematics · Ch 2: Relations and Functions free?

It is part of the CBSE Class 11 Science Test Series 2027 — Chapter-wise + Full Tests (20 tests, ₹199). You can first try Biology · Ch 1: The Living World for free.

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

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Relations and Functions MCQ Questions with Answers | CBSE Class 11 | SeatBeat