If 3 6 4 4 k is the term, independent of x , in the binomial expansion of x 4 - 12 x 2 12 , then k is equal to

Step-by-step solution

Given that x 4 - 12 x 2 12 r t h term of an expression is T r + 1   = C r n x n - r y r T r + 1 = C r 12 x 4 12 - r - 12 x 2 r = C r 12 1 4 12 - r ( - 12 ) r · x 12 - r - 2 r ⇒    12 - 3 r = 0 ⇒    r = 4 So term independent from x is T 5 = C 4 12 · 1 4 8 · 3 4 · 4 4 = C 4 12 · 3 4 4 4 We know that C r n = n ! n - r ! r ! = 55 × 3 6 4 4 They given that it is = k   3 6 4 4 So required value of   k   =   55 .