CBSE 2023 · Region 5 · Set 1 · Q36 · 4 marks
An organization conducted bike race under two different categories - Boys and Girls. There were $\displaystyle 28$ participants in all. Among all of them, finally three from category $\displaystyle 1$ and two from category $\displaystyle 2$ were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let $\displaystyle \mathrm{B}=\left\{\mathrm{b}_{1}, \mathrm{b}_{2}, \mathrm{b}_{3}\right\}$ and $\displaystyle \mathrm{G}=\left\{g_{1}, g_{2}\right\}$, where $\displaystyle \mathrm{B}$ represents the set of Boys selected and G the set of Girls selected for the final race.
Based on the above information, answer the following questions :(I)How many relations are possible from B to G ?(II)Among all the possible relations from B to G , how many functions can be formed from B to G ?Let $\displaystyle \mathrm{R}: \mathrm{B} \rightarrow \mathrm{B}$ be defined by $\displaystyle \mathrm{R}=\{(x, \mathrm{y}): x$ and y are students of the same sex\}. Check if $\displaystyle \mathrm{R}$ is an equivalence relation.A function $\displaystyle \mathrm{f}: \mathrm{B} \rightarrow \mathrm{G}$ be defined by $\displaystyle \mathrm{f}=\left\{\left(\mathrm{b}_{1}, \mathrm{~g}_{1}\right),\left(\mathrm{b}_{2}, \mathrm{~g}_{2}\right),\left(\mathrm{b}_{3}, \mathrm{~g}_{1}\right)\right\}$. Check if f is bijective. Justify your answer. Case Study-II
An organization conducted bike race under two different categories - Boys and Girls. There were $\displaystyle 28$ participants in all. Among all of them, finally three from category $\displaystyle 1$ and two from category $\displaystyle 2$ were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let $\displaystyle \mathrm{B}=\left\{\mathrm{b}_{1}, \mathrm{b}_{2}, \mathrm{b}_{3}\right\}$ and $\displaystyle \mathrm{G}=\left\{g_{1}, g_{2}\right\}$, where $\displaystyle \mathrm{B}$ represents the set of Boys selected and G the set of Girls selected for the final race.
Based on the above information, answer the following questions :
(I)
How many relations are possible from B to G ?
(II)
Among all the possible relations from B to G , how many functions can be formed from B to G ?
Let $\displaystyle \mathrm{R}: \mathrm{B} \rightarrow \mathrm{B}$ be defined by $\displaystyle \mathrm{R}=\{(x, \mathrm{y}): x$ and y are students of the same sex\}. Check if $\displaystyle \mathrm{R}$ is an equivalence relation.
A function $\displaystyle \mathrm{f}: \mathrm{B} \rightarrow \mathrm{G}$ be defined by $\displaystyle \mathrm{f}=\left\{\left(\mathrm{b}_{1}, \mathrm{~g}_{1}\right),\left(\mathrm{b}_{2}, \mathrm{~g}_{2}\right),\left(\mathrm{b}_{3}, \mathrm{~g}_{1}\right)\right\}$. Check if f is bijective. Justify your answer. Case Study-II
Marking-scheme solution
(I)
Number of relations $\displaystyle =2^{6}=64$
(II)
Number of possible functions $\displaystyle =2^{3}=8$
(III)
R is an equivalence relation as it is reflexive, symmetric and transitive
Relations and FunctionsTypes of FunctionsApplycase_studymedium
More from Relations and Functions
- Let f: A → B be defined by f(x)=(x-2)/(x-3), where A=R- 3 and B=R- 1. Discuss the bijectivity of the function.2025 · asked 3×
- If f(x)= x + x-1, then which of the following is correct?2025 · asked 3×
- A class-room teacher is keen to assess the learning of her students the concept of "relations" taught to…2025 · asked 3×
- If f: N → W is defined as f(n)=,. then f is:2025 · asked 3×
- If f(x)=-2 x^8, then the correct statement is:2025 · asked 3×
- A function f(x)= 1-x+ x is:2024 · asked 3×
- A school is organizing a debate competition with participants as speakers S= S 1, S 2, S 3, S 4 and these are…2025 · asked 3×
- For real x, let f(x)=x^3+5 x+1. Then:2025 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.