The value of ∑ r = 1 15 r 2 15 C r 15 C r − 1 is equal to:

The value of ∑r=115r215Cr15Cr−1 is equal to:
  1. 1240
  2. 560
  3. 1085
  4. 680

Solution

Given ∑ r=1 15 r 2 ( 15 C r 15 C r−1 )

Here 15Cr15Cr-1=16-rr

∑ r=1 15 r 2 ( 15 C r 15 C r−1 ) =   ∑ r=1 15 r 2 16-rr

= ∑ r=1 15 r 16-r

=16  ∑ r=1 15 r -  ∑ r=1 15 r 2

=16 ×15 ×162-15 ×31 ×166

=8 ×15 ×16-5 ×8 ×31

=1920-1240=680

Asked in: JEE Main 2016 (09 Apr Online)

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