If the constant term, in binomial expansion of 2 x r + 1 x 2 10 is 180 , then r is equal to ____________.

Step-by-step solution

The general term in the binomial expansion of a + b n is C R n a n - R b R . Thus, the general term in the expansion of 2 x r + 1 x 2 10 is = C R 10 2 x r 10 - R 1 x 2 R = C R 10 2 10 - R x r 10 - R x - 2 R Given, the constant term in the expansion is 180 ⇒ C R 10 · 2 10 - R = 180       … 1 And ( 10 - R ) r - 2 R = 0 ⇒ r = 2 R 10 - R ⇒ r = 2 ( R - 10 ) 10 - R + 20 10 - R ⇒ r = - 2 + 20 10 - R         … 2 Since R is positive integer less tha