Relations and Functions

Bihar Board Class 12 · Mathematics · 39 past questions

12 of 39 · show all

1. 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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2. 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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3. Q11 2025

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

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4. 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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5. Q13 2025

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

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6. Q14 2025

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

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7. 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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8. 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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9. 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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10. 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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11. 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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12. 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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