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Find the coefficient of x4 in the expansion of (1+x+x2+x3)11.

0 4 Views | Posted 3 months ago
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  • 1 Answer

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    Answered by

    Vishal Baghel | Contributor-Level 10

    3 months ago

    This is a Short Answer Type Questions as classified in NCERT Exemplar
    Sol:

    Given  expression  is  (1+x+x2+x3)11                           = [ ( 1 + x ) + x 2 ( 1 + x ) ] 1 1 = [ ( 1 + x ) ( 1 + x 2 ) ] 1 1                           = ( 1 + x ) 1 1 . ( 1 + x 2 ) 1 1 Expanding  the  above  expression,  we  get                   ( C 0 1 1 + C 1 1 1 x + C 2 1 1 x 2 + C 3 1 1 x 3 + C 4 1 1 x 4 + … ) . ( C 0 1 1 + C 1 1 1 x 2 + C 2 1 1 x 4 + … ) = ( 1 + 1 1 x + 5 5 x 2 + 1 6 5 x 3 + 3 3 0 x 4 + … ) . ( 1 + 1 1 x 2 + 5 5 x 4 + … ) C o l l e c t i n g     t h e     t e r m s     c o n t a i n i n g     x 4 ,     w e     g e t ( 5 5 + 6 0 5 + 3 3 0 ) x 4 = 9 9 0 x 4 H e n c e ,     t h e     c o e f f i c i e n t     o f     x 4 = 9 9 0

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