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  4. The number of values of ' r ' satisfying the equation, 39 C3 r-1- 39 Cr2= 39 Cr2-1- 39 C3 r is :

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Q. The number of values of ' $r$ ' satisfying the equation, ${ }^{39} C_{3 r-1}-{ }^{39} C_{r^2}={ }^{39} C_{r^2-1}-{ }^{39} C_{3 r}$ is :

Binomial Theorem

Solution:

${ }^{39} C _{3 r -1}-{ }^{39} C _{ r ^2}={ }^{39} C _{ r ^2-1}-{ }^{39} C _{3 r } $
$\Rightarrow{ }^{39} C _{3 r -1}+{ }^{39} C _{3 r }={ }^{39} C _{ r ^2-1}+{ }^{39} C _{ r ^2}$
${ }^{40} C _{3 r }={ }^{40} C _{ r ^2}$
$r ^2=3 r$ or $ r =0,3$