If ^ 2017 C_0 + ^ 2017 C_1 + ^ 2017 C_2+......+ ^ 2017 C_ 1008 = … - Vidyadip

MCQ

If $^{2017}C_0 + ^{2017}C_1 + ^{2017}C_2+......+ ^{2017}C_{1008} = \lambda ^2 (\lambda > 0),$ then remainder when $\lambda $ is divided by $33$ is-

A
$8$
B
$13$
C
$17$
✓
$25$

✓

Answer

Correct option: D.

$25$

d
${\,^{2017}}{C_0} + {\,^{2017}}{C_1} + ......{\,^{2017}}{C_{1008}} = {2^{2016}} = {\lambda ^2}$

$\lambda = {2^{1008}}\,\,\,\,\, \Rightarrow \,\,\,{8.32^{201}} = 8{\left( {33 - 1} \right)^{201}} = - 8 = 25$

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