Q: Which of the following is/are true in the expansion of (x + 2y + 3z)12
(A) The number of terms in the expansion is 91
(B) The sum of all the coefficient in the expansion is 126
(C) The number of terms in the expansion is 36
(D) The sum of all the coefficient in the expansion is 612
Sol. (x + 2y + 3z)12
= 12C0 (x + 2y)12 (3z)0 + 12C1 (x + 2y)11 (3z)1 + ….+ 12C12 (x + 2y)0 (3z)12
= 13 + 12 + 11 + …….1 = 91
Sum of coefficients = (1 + 2 + 3)12 = 612
Hence (A) and (D) are the correct answer.