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
The sum of the series (12 + 1). 1! + (22 + 1). 2! + (32 + 1). 3! + ....... + (n2 + 1). n! is -...If the coefficients of x7 & x8 in the expansion of are equal, then the value of n is -...In the expansion of (71/3 + 111/9)6561, the number of terms free from radicals is:...Given positive integers r > 1, n > 2and the coefficient of (3r) th and (r + 2) th term in the binomial expansion of (1 +...If recursion polynomials Pk(x) are defined as P1(x) = (x - 2)2, P2 (x) = ((x - 2)2 - 2)2 P3 (x) = ((x - 2)2 - 2)2 - 2)2 ...