Question
Question: If (1 + x – 2x<sup>2</sup>)<sup>6</sup> = 1 + C<sub>1</sub>x+ C<sub>2</sub>x<sup>2</sup> ……C<sub>12<...
If (1 + x – 2x2)6 = 1 + C1x+ C2x2 ……C12x12 then the value of C2 +C4 + C6 +…….C12 is
A
30
B
32
C
31
D
None of these
Answer
31
Explanation
Solution
Put x = 1 in equation …..(i)
O = 1 + C1 + C2 +…….C12………(ii)
Now put x = –1 in equation (i);
26 = 1– C1 + C2 – C3 +……….C12 x12……(iii)
Adding (i) & (ii)
26 = 2(1 + c2 + c4+……….c12)
\ c2 + c4 + c6 + ………..c12 = 31