Number of positive integral solution of the e | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\begin{aligned} xyx &=90=2,3^{2}, 5^{1} \ 	ext { Let } x &=2^{ x _{1}} 3^{ y _{1}} 5^{ Z _{1}} \ y &=2^{ x _{1}} 3^{ y _{2}} 5^{ z _{2

Vedclass · Accepted Answer

$54$

Vedclass · Answer

$\begin{aligned} xyx &=90=2,3^{2}, 5^{1} \ 	ext { Let } x &=2^{ x _{1}} 3^{ y _{1}} 5^{ Z _{1}} \ y &=2^{ x _{1}} 3^{ y _{2}} 5^{ z _{2}} \ z &=2^{ x _{3}} 3^{ y _{3}} 5^{ z _{3}} \end{aligned}$

$x _{1}+ x _{2}+ x _{3}=1 ightarrow\left(\begin{array}{c}1+3-1 \ 3-1\end{array}ight)=\left(\begin{array}{l}3 \ 2\end{array}ight)=3$

$y _{1}+ y _{2}+ y _{3}=2 ightarrow\left(\begin{array}{c}2+3-1 \ 3-1\end{array}ight)=\left(\begin{array}{c}4 \ 2\end{array}ight)=6$

$z _{1}+ z _{2}+ z _{3}=1 ightarrow\left(\begin{array}{c}1+3-1 \ 3-1\end{array}ight)=\left(\begin{array}{l}3 \ 2\end{array}ight)=3$

$3,6,3=54 ways$

Number of positive integral solution of the equation $xyz = 90$ is equal to :-

Similar Questions

Out of $6$ boys and $4$ girls, a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys

If $P(n,r) = 1680$ and $C(n,r) = 70$, then $69n + r! = $

The number of seven digit positive integers formed using the digits $1,2,3$ and $4$ only and sum of the digits equal to $12$ is $...........$.

On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are $20$ students in the class, then the total number of greeting cards exchanged by the students is

If $n$ is even and the value of $^n{C_r}$ is maximum, then $r = $