CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 8 – Binomial Theorem Maths
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Solution 11:
It is known that
T C a b
r1
n nr r
r
Assuming that
.
r 1 th
Tr
1
term, , in the binomial expansion of n
r 1 th
n
x occurs in the
2n
2
2
1
1 n r r n r
r r r
T C x C x
Comparing the indices of x
Therefore, the coefficient of
2n
C
n
in
n
x
n
x
and in
2 n ! 2 n ! 2 n !
2 ....... 1
n! 2 n n ! n! n! n!
Assuming that
n
x
occurs in the
2 1
n
T C x C x
2n
2
1
1 n k k
k
k k k
Comparing the indices of x
Therefore, the coefficient of
in
a
b
term of the expansion of 2
Tr
1
, we obtain r n
in the expansion of 2
n
x
k 1 th
and in
1 x
n
is
1 x
term of the expansion of 2 1
Tk
1
, we obtain k n
1
x
n
n
x in the expansion of 2 1
2n
1
2n
1 ! 2n
1 !
Cn
n! 2n 1 n ! n! n 1 !
1
2
2 n. 2n 1 ! 2 n ! 2 n !
....... 2
2 n. n! n 1 ! 2. n! n! 2
n!
From (1) and (2) , it is observed that
1
2
C
2n
2n
1
n
C
2
C
2n
2n
1
n
n
C
Therefore, the coefficient of
expansion of 2 1
Hence proved.
n
1
x
n
.
n
x expansion of
1 x 2
n
is
1
x
n
n
is given by
, we obtain
, we obtain
is twice the coefficient of
n
x in the
Question 12:
Find a positive value of m for which the coefficient of
Solution 12:
It is known that
1
th
1 x
2
x in the expansion
r term, T , in the binomial expansion of a
b n
r 1
m
is 6.
is given by
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