The number of ordered pairs ( mathrm{r}, math | vedclass

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Question

$6 	imes^{35} \mathrm{C}_{\mathrm{r}}=\left(\mathrm{k}^{2}-3ight)^{36} \mathrm{C}_{\mathrm{r}+1}$

$k^{2}-3>0 \Rightarrow k^{2}>3$

$\mat

Vedclass · Accepted Answer

$4$

Vedclass · Answer

$6 	imes^{35} \mathrm{C}_{\mathrm{r}}=\left(\mathrm{k}^{2}-3ight)^{36} \mathrm{C}_{\mathrm{r}+1}$

$k^{2}-3>0 \Rightarrow k^{2}>3$

$\mathrm{k}^{2}-3=\frac{6 \mathrm{	imes}^{35} \mathrm{C}_{\mathrm{r}}}{^{36} \mathrm{C}_{\mathrm{r}+1}}=\frac{\mathrm{r}+1}{6}$

Possible values of $\mathrm{r}$ for integral values of $\mathrm{k},$ are

$r=5,35$

number of ordered pairs are $4$

$(5,2),(5,-2),(35,3),(35,-3)$

The number of ordered pairs ( $\mathrm{r}, \mathrm{k}$ ) for which $6 \cdot ^{35} \mathrm{C}_{\mathrm{r}}=\left(\mathrm{k}^{2}-3\right)\cdot{^{36} \mathrm{C}_{\mathrm{r}+1}}$. where $\mathrm{k}$ is an integer, is

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