Let A ={1,2,3, ldots ldots, 10} and B=left{frac{m}{n}: m, n ∈ A, m

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1.Set Theory

hard

Let $A =\{1,2,3, \ldots \ldots, 10\}$ and $B=\left\{\frac{m}{n}: m, n \in A, m < n \text { and } \operatorname{gcd}(m, n)=1\right\} . $Then $n(B)$ is equal to :

A$31$

B$36$

C$37$

D$29$

(JEE MAIN-2025)

Solution

$A=\{1,2, \ldots .10\}$
$\begin{array}{l} B \left\{\frac{ m }{ n }= m , n \in A , m < n , \operatorname{gcd}( m , n )=1\right\} \\ n ( B )\end{array}$
$n=2 \quad\left\{\frac{1}{2}\right\}$
$n=3 \quad\left\{\frac{1}{3}, \frac{2}{3}\right\}$
$n=4 \quad\left\{\frac{1}{4}, \frac{3}{4}\right\}$
$n=5 \quad\left\{\frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5}\right\}$
$n=6 \quad\left\{\frac{1}{6}, \frac{5}{6}\right\}$
$n=7 \quad\left\{\frac{1}{7}, \frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7}\right\}$
$n=8 \quad\left\{\frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8}\right\}$
$n=9 \quad\left\{\frac{1}{9}, \frac{2}{9}, \frac{4}{9}, \frac{5}{9}, \frac{7}{9}, \frac{8}{9}\right\}$
$n=10 \quad\left\{\frac{1}{10}, \frac{3}{10}, \frac{7}{10}, \frac{9}{10}\right\}$
$n(B)=31$

Standard 11

Mathematics

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:

$\{ x:x$ is a student of class $\mathrm{XI}$ of your school $\} \ldots \{ x:x$ student of your school $\} $

easy

Let $A =\{1,2,3, \ldots \ldots, 10\}$ and $B=\left\{\frac{m}{n}: m, n \in A, m < n \text { and } \operatorname{gcd}(m, n)=1\right\} . $Then $n(B)$ is equal to :

Solution

Similar Questions

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$\left[ { – 23,5} \right)$

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$\{ x:x$ is a student of class $\mathrm{XI}$ of your school $\} \ldots \{ x:x$ student of your school $\} $

Let $A =\{1,2,3, \ldots \ldots, 10\}$ and $B=\left\{\frac{m}{n}: m, n \in A, m < n \text { and } \operatorname{gcd}(m, n)=1\right\} . $Then $n(B)$ is equal to :

Solution

Similar Questions

Write the following intervals in set-builder form : $\left[ { – 23,5} \right)$

State whether each of the following set is finite or infinite : The set of letters in the English alphabet

Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: $ 4\, ……… \, A $

Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: $ 8\, …….\, A $

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces: $\{ x:x$ is a student of class $\mathrm{XI}$ of your school $\} \ldots \{ x:x$ student of your school $\} $

Write the following intervals in set-builder form :

$\left[ { – 23,5} \right)$

State whether each of the following set is finite or infinite :

The set of letters in the English alphabet

Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:

$ 4\, ……… \, A $

Let $A=\{1,2,3,4,5,6\} .$ Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:

$ 8\, …….\, A $

Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:

$\{ x:x$ is a student of class $\mathrm{XI}$ of your school $\} \ldots \{ x:x$ student of your school $\} $