Question
Mathematics Question on Trigonometric Identities
If sum of the coefficients of x7 and x4 in the expansion of (x2a−bx)11 is zero, then
A
(A) ab = 1
B
(B) a = b
C
(C) ab = -1
D
(D) a+b = 0
Answer
(A) ab = 1
Explanation
Solution
Explanation:
Tr+1=11Cr(x2a)11−r(−bx)r=11Cr(−1)rar−11brx22−3rFor coefficient of x4 and x7, we put 22−3r=4 and 22−3r=7⇒r=6 and r=5We are given11C6(−1)6a−5b6+11C5(−1)5a−6b5=0⇒b6a5=b5a6⇒ab=1