Relations and Functions

Bihar Board Class 12 · Mathematics · 39 past questions

1. Q1 2026 Set A2026 Set C2026 Set D

   What type of a relation is "less than" in the set of real numbers ?

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2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D

   If operation $*$ is defined as $a*b=a^3+b^3$, then $4*(1*2)=$

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3. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2025 Set A2025 Set E2024 Set J2024 Set D2019 Set F2016

   $f : A \to B$ will be an onto function if

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4. Q4 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   If $f:R\to R$, where $f(x)=3x-5$, then $f^{-1}(x) =$

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5. Q5 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2024 Set J2019 Set F

   If the operation $*$ is defined as $a * b = 2a + b$, then $(2 * 3) * 4$ is

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6. Q6 2026 Set A2026 Set H2026 Set E2026 Set B2026 Set F2026 Set J2026 Set D2025 Set A2025 Set E

   If $n(A)=4$ and $n(B)=2$, then $n(A\times B)=$

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7. Q7 2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B2018

   What type of a relation is " Less then" in the set of real numbers ?

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8. Q8 2026 Set H2026 Set E2026 Set C2026 Set F2026 Set J2026 Set D

   If $f:R\to R$; $f(x)=(3-x^3)^{1/3}$, then prove that $(f\circ f)(x)=x$.

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9. Q9 2026 Set J2026 Set B2024 Set D

   If the operation $*$ is defined as $a*b=2a+b$, then $(2*3)*4$ is

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10. Q10 2026 Set J2026 Set B

    If operation $*$ is defined as $a * b = a^3 + b^3$, then $4 * (1 * 2) =$

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11. Q11 2025

    Function $f:N \to N, f(x)=2x$ is

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12. Q12 2025

    A function $f:X \to Y$ is one-one if $x_1,x_2 \in X, f(x_1)=f(x_2) \Rightarrow$

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13. Q13 2025

    A function $f: X \to Y$ invertible if and only if $f$ is

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14. Q14 2025

    If $f(x) = 4-(x-7)^3$ then find $f^{-1}(x)$.

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15. Q15 2025 Set A2025 Set E

    If operation 'o' is defined as $(a\,o\,b)=a^3+b^3$, then $4\,o\,(1\,o\,2)=$

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16. Q16 2025 Set A2025 Set E2021 Set J2021 Set I

    If $f : R \to R$ such that $f(x) = 3x - 4$ then which of the following is $f^{-1}(x)$ ?

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17. Q17 2025 Set A

    If operation 'o' is defined as $(a \circ b) = a^2 + b^2 - ab$, then $(1 \circ 2) \circ 3 =$

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18. Q18 2025 Set A

    Let $A = \{1, 2, 3, \ldots, n\}$. How many bijective functions $f : A \to A$ can be defined ?

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19. Q19 2025 Set E

    If operation 'o' is defined as $(a\,o\,b)=a^2+b^2-ab$, then $(1\,o\,2)\,o\,6=$

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20. Q20 2025 Set E

    Let $A=\{1,2,3,\ldots,n\}$. How many bijective functions $f:A\to A$ can be defined ?

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21. Q21 2024 Set D2024 Set J

    Let $R$ be the relation in the set $N$ given by $R=\{(a,b): a=b-2, b>6\}$. The correct answer in the…

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22. Q22 2023

    If the operation 'o' is defined as a o b = 3a + b then (2 o 3) o 5 =

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23. Q23 2023

    If A={1, 2}, B={a,b,c} then total number of functions from A to B is

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24. Q24 2023

    If A={a, b}, B={1, 2, 3} then total number of one-one functions from A to B is

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25. Q25 2023 Set E

    If the operation 'o' is defined as $a\circ b=3a+b$ then $(2\circ3)\circ5=$

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26. Q26 2023 Set E

    If $A=\{1,2\}$, $B=\{a,b,c\}$ then total number of functions from $A$ to $B$ is

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27. Q27 2023 Set E

    If $A=\{a,b\}$, $B=\{1,2,3\}$ then total number of one-one functions from $A$ to $B$ is

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28. Q28 2021 Set J2021 Set I

    If $A=\{a,b,c\}, B=\{1,2,3\}$ and $f=\{(a,1),(b,2),(c,2)\}$ then what type of a function is $f$?

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29. Q29 2019 Set F

    If $f(x_1)=f(x_2)\Rightarrow x_1=x_2\ \forall\ x_1,x_2\in A$, then what type of a function is $f:A\to B$?

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30. Q30 2019 Set F

    In the set of all straight lines in a plane, the relation R "to be Perpendicular" is -

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31. Q31 2018

    let $\vec{a} = \vec{i} + \vec{j} + 2\vec{k}$ How many binary operation can be defined on this set ?

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32. Q32 2018

    let $\{1,2,3\}$ which of the following function $f : A \to A$ does not an inverse function ?

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33. Q33 2018

    If $A = \{1,2,3\}$ $B = \{6,7,8\}$ and $f : A \to B$ is a function such that $f(x) = x + 5$ then what type of…

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34. Q34 2018

    Examine whether the function $f:R\to R$ is one-one(injective) if $f(x)=x^3,\ x\in R$

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35. Q35 2017

    If $A = \{1,2,3\}$, then how many equivalence relation can be defined on A containing $(1,2)$

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36. Q36 2017

    If $n(A)=3$ and $n(B)=2$ then $n(A\times B)=\ldots\ldots$

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37. Q37 2017

    If $f:R\to R$ such that $f(x)=3x-4$ then which of the following $f^{-1}(x)$?

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38. Q38 2016

    If $y=\sin\left[\cos\left(\tan\left(\sin^{-1}x\right)\right)\right]$, then find $\frac{dy}{dx}$.

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39. Q39 2015

    If $f(x_1) = f(x_2) \Rightarrow x_1 = x_2, x_2 \in A$, then the function $f : A \to R$

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