JEE Main202125 Jul 2021Morning ShiftMathematicsBinomial TheoremActual
The term independent of x in the expansion of x + 1 x 2 / 3 - x 1 / 3 + 1 - x - 1 x - x 1 / 2 10 , where x ≠ 0 , 1 is equal to
Correct answer
0
Step-by-step solution
x + 1 x 2 / 3 - x 1 / 3 + 1 - x - 1 x - x 1 / 2 10 x 1 / 3 + 1 x 2 / 3 - x 1 / 3 + 1 x 2 / 3 - x 1 / 3 + 1 - x 1 / 2 + 1 x 1 / 2 - 1 x 1 / 2 x 1 / 2 - 1 10 = x 1 / 3 + 1 - x 1 / 2 + 1 x 1 / 2 10 = x 1 / 3 - 1 x 1 / 2 10 Now the r + 1 th Term T r + 1 = C r 10 x 1 / 3 10 - r · - 1 x 1 / 2 r T r + 1 = C r 10 x 1 / 3 10 - r · x - r / 2 - 1 r For independent term 10 - r 3 - r 2 = 0 ⇒ r = 4 ⇒ T 5 = C 4 10 - 1 4 = 10 × 9 × 8 × 7 4 × 3 × 2 × 1 = 210