Q97 / 150 · MHT CET 2021 (20 Sep Shift 2) · Mathematics

If $\frac{\mathrm{n} !}{2 !(\mathrm{n}-2) !}$ and $\frac{\mathrm{n} !}{4 !(\mathrm{n}-4) !}$ are in the ratio $2: 1$, then $\mathrm{n}=$

A
6
B
4
Correct answer
C
5
D
3

Solution

We have $\frac{n !}{2 !(n-2) !} \times \frac{4 !(n-4) !}{n !}=\frac{2}{1}$ $$ \therefore \frac{(4 \times 3)}{(n-2)(n-3)}=2 \Rightarrow n^2-5 n+6=6 $$

Hence, the correct answer is option: 'C'.

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