Home
Class 12
MATHS
If (1+x-2x^2)^(20)=a0a1x=a2x^2+a3x^3++a(...

If `(1+x-2x^2)^(20)=a_0a_1x=a_2x^2+a_3x^3++a_(40)x^(40),` then find the value of `a_1+a_3+a_5++a_(39)dot`

A

0

B

`(3^(10)-1)/(2)`

C

`3^(10)`

D

`4^(10)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `(1+x+x^(2))^(10)(1-x+x^(2))^(10)`
`=a_(0)+a_(1)x+a_(2)x^(2)+…..+a_(40)x^(40)`
It can be seen that the expansion does not contain any term containing odd power.
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 9

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 8

    VMC MODULES ENGLISH|Exercise MATHMATICS (SECTION 2)|5 Videos

  • PERMUTATION & COMBINATION

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|50 Videos

Similar Questions

Explore conceptually related problems

If (1+x-2x^2)^(20)=a_0+a_1x+a_2x^2+a_3x^3++a_(40)x^(40), then find the value of a_1+a_3+a_5++a_(39)dot

If (1+x-2x^2)^(20)=a_0+a_1x+a_2x^2+a_3x^3+...+a_(40)x^(40), then find the value of a_1+a_3+a_5+...+a_(39)dot

If (1+x+2x^(2))^(20) = a_(0) + a_(1)x^(2) "……" + a_(40)x^(40) , then find the value of a_(0) + a_(1) + a_(2) + "……" + a_(38) .

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

If (1+x-2x^2)^6=1+a_1x+a_2x^(2)++a_(12)x^(12), then find the value of a_2+a_4+a_6++a_(12)dot

If (1 + x+ 2x^(2))^(20) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(40) x^(40) . The value of a_(0) + a_(2) + a_(4) + …+ a_(38) is

If (1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x^(2n), find the value of a_0+a_3+a_6++ ,n in Ndot

If (1-x+x^2)^n=a_0+a_1x+a_2x^2+ .........+a_(2n)x^(2n),\ find the value of a_0+a_2+a_4+........+a_(2n)dot

If (1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x_(2n), find the value of a_0+a_6++ ,n in Ndot

If (1+x+x^(2))^(20) = a_(0) + a_(1)x^(2) "……" + a_(40)x^(40) , then following questions. The value of a_(0) + 3a_(1) + 5a_(2) + "……" + 81a_(40) is