Binomial TheoremHard
Question
If in the expansion of (1+ x)m (1 - x)n, the coefficients of x and x2 are 3 and - 6respectively, then m is
Options
A.6
B.9
C.12
D.24
Solution
(1 + x)m (1 - x)n = 
= 1 + (m - n)x +
x2 + ....
term containing power of x ≥ 3.
Now, m - n = 3 ....(i)
(∵ coefficient of x = 3 given)
and
m(m - 1) + n(n - 1) - mn = - 6
⇒ m(m -1) + n(n -1) - 2mn = - 12
⇒ m2 - m + n2 - n - 2mn = - 12
⇒ (m - n)2 - (m + n) = - 12
⇒ m+ n = 9 + 12 = 21 ......(ii)
On solving Eqs. (i) and (ii) , we get
m = 12
= 1 + (m - n)x +
x2 + .... term containing power of x ≥ 3.
Now, m - n = 3 ....(i)
(∵ coefficient of x = 3 given)
and
m(m - 1) + n(n - 1) - mn = - 6⇒ m(m -1) + n(n -1) - 2mn = - 12
⇒ m2 - m + n2 - n - 2mn = - 12
⇒ (m - n)2 - (m + n) = - 12
⇒ m+ n = 9 + 12 = 21 ......(ii)
On solving Eqs. (i) and (ii) , we get
m = 12
Create a free account to view solution
View Solution FreeMore Binomial Theorem Questions
Find numerically greatest term in the expansion of (2 + 3 x)9, when x = 3/2....If (1 + x)10 = a0 + a1x + a2x2 +......+ a10x10, then value of (a0 - a2 + a4 - a6 + a8 - a10)2 + (a1 - a3 + a5 - a7 + a9)...The sum of the coefficients in the expansion of (a + 2b + c)10 is -...The value of m, for which the coefficients of the (2m + 1)th and (4m + 5)th terms in the expansion of (1 + x)10 are equa...The sum (r + 1) Cr2 is equal to :...