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Permutations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSPermutations2 Marks
Question
Find x in the following.
$\frac{1}{4!}+\frac{1}{5!}=\frac{\text{x}}{6!}$
✓

Answer

We have,
$\frac{1}{4!}+\frac{1}{5!}=\frac{\text{x}}{6!}$
$\Rightarrow​​​​​​​​\frac{1}{4!}+\frac{1}{4\times5!}=\frac{\text{x}}{6\times5\times4!}$
$\Rightarrow4!\times\bigg[\frac{1}{4!}+\frac{1}{5\times4!}\bigg]=\frac{\text{x}}{30}$
$\Rightarrow1+\frac{1}{58}=\frac{\text{x}}{30}$
$\Rightarrow\frac{6}{5}=\frac{\text{x}}{30}$
$\Rightarrow\frac{\text{x}}{30}=\frac{6}{5}$
$\Rightarrow\text{x}=\frac{6\times30}{5}$
$\Rightarrow6\times6$
$\Rightarrow\text{x}= 36$
Hence, $\text{x}= 36$

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