If the coefficients of x - 2 and x - 4 , in the expansion of x 1 3 + 1 2 x 1 3 18 , x > 0 , are m and n respectively, then m n is equal to

Step-by-step solution

We have, x 1 3 + 1 2 x 1 3 18 , x > 0 General term, T r + 1 = 18 C r x 1 3 18 - r 1 2 x 1 3 r = 18 C r   x 6 - 2 r 3 1 2 r Now, 6 - 2 r 3 = - 2 ⇒ r = 12 and, 6 - 2 r 3 = - 4 ⇒ r = 15 Hence, m n = Coefficient of   x - 2 Coefficient of   x - 4 = C 12 18 2 12 C 15 18 2 15 = 18 ! 6 ! . 12 ! 18 ! 3 ! . 15 ! × 2 3 = 15 × 14 × 13 6 × 5 × 4 × 2 3 = 182