Question

The total number of combinations of 2n different things taken any one or more at a time and total number of combinations of n different things taken one or more at a time is in the ratio 65: 1, then the value of n is equal to

• A. $4$
• B. $5$
• C. $6$
• D. None of these

Answer 1

Answer: (C)

$6$

$\frac{2^{2n}-1}{2^n-1}$ = $\frac{65}{1}$ Put $2^n$ = t
$t^2$ - 1 = 65t - 65
or $t^2$ - 65t + 65 = 0 or (t - 64) (t - 1) = 0
$\therefore$ $2^n$ = $2^6$ = $2^0$
$\therefore$ n = 6 $\Rightarrow$ (c)