JEE Main202118 Mar 2021Morning ShiftMathematicsBinomial TheoremActual
Let 1 + x + 2 x 2 20 = a 0 + a 1 x + a 2 x 2 + … + a 40 x 40 , then a 1 + a 3 + a 5 + … + a 37 is equal to
Options
- A2 20 2 20 - 21
- B2 19 2 20 - 21
- C2 19 2 20 + 21
- D2 20 2 20 + 21
Correct answer
B. 2 19 2 20 - 21
Step-by-step solution
Given 1 + x + 2 x 2 20 = a 0 + a 1 x + … + a 40 x 40 Put x = 1 we get, a 0 + a 1 + a 2 + … + a 40 = 4 20 Put x = - 1 we get, a 0 - a 1 + a 2 + … . + a 40 = 2 20 ⇒ a 1 + a 3 + … . + a 39 = 4 20 - 2 20 2 ⇒ a 1 + a 3 + … + a 37 = 2 39 - 2 19 - a 39 Here a 39 = 20 ! ( 2 ) 19 × 1 19 ! = 20 × 2 19 ⇒ a 1 + a 3 + … + a 37 = 2 19 2 20 - 1 - 20 = 2 19 2 20 - 21