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Bihar Board Class 12 Science Mathematics · Ch 1: Relations and Functions

Bihar Board Class 12 Science Mathematics · Ch 1: Relations and Functions is an online chapter test in the Bihar Board Class 12 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
Attempt this test free

Topics in this test

TopicQuestions
Relations and Functions30

Difficulty: 3 easy · 8 medium · 19 hard

Sample questions with answers

The first 5 questions of this free test.

  1. Q1. On the set $\mathbb{Z}$ of integers, a relation is defined by $a\,R\,b$ if and only if $a-b$ is divisible by $3$. The number of distinct equivalence classes of this relation is

    • A. $3$
    • B. infinitely many
    • C. $2$
    • D. $1$
    Solution

    Integers split according to their remainder on division by $3$ (remainder $0,1$ or $2$), giving exactly $3$ equivalence classes.

  2. Q2. The number of onto functions from the set $\{1,2,3\}$ to the set $\{a,b\}$ is

    • A. $5$
    • B. $6$
    • C. $8$
    • D. $9$
    Solution

    Total functions are $2^{3}=8$; removing the $2$ constant functions (which miss one image) leaves $8-2=6$ onto functions.

  3. Q3. Among the following relations, which one is NOT an equivalence relation?

    • A. 'is perpendicular to' on the set of all lines in a plane
    • B. the universal relation on a set $A$
    • C. the identity relation on a set $A$
    • D. 'is parallel to' on the set of all lines in a plane
    Solution

    The relation 'is perpendicular to' is not reflexive (a line is not perpendicular to itself) and not transitive, so it is not an equivalence relation, while the others are.

  4. Q4. Consider the function $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=x^{3}$ and the statements: (I) $f$ is one-one. (II) $f$ is onto. (III) $f$ is a bijection. Which of the statements are correct?

    • A. Only II and III
    • B. Only I
    • C. I, II and III
    • D. Only I and II
    Solution

    For cubes, $x_1^3=x_2^3\Rightarrow x_1=x_2$ (one-one) and every real has a real cube root (onto), so $f$ is a bijection.

  5. Q5. Assertion (A): The function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x)=x^{2}$ is not one-one. Reason (R): $f(-1)=f(1)=1$ but $-1\neq 1$. Choose the correct option.

    • A. A is false but R is true
    • B. Both A and R are true but R is not the correct explanation of A
    • C. A is true but R is false
    • D. Both A and R are true and R is the correct explanation of A
    Solution

    Two different inputs give the same output, which is exactly why the function fails to be one-one; so R correctly explains A.

Frequently asked questions

How many questions are in the Bihar Board Class 12 Science Mathematics · Ch 1: Relations and Functions?

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

Is there negative marking in the Bihar Board Class 12 Science Mathematics · Ch 1: Relations and Functions?

No — wrong answers are not penalised in this test.

Which topics does the Bihar Board Class 12 Science Mathematics · Ch 1: Relations and Functions cover?

Relations and Functions (30 questions).

Is the Bihar Board Class 12 Science Mathematics · Ch 1: Relations and Functions free?

Yes — this test is free. Create a free SeatBeat account and attempt it online; you get the solutions and your score analysis after submitting.

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