CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 8 – Binomial Theorem Maths
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Question 13:
Show that
Solution 13:
n 1
9 8n
9
In order to show that
where k is some natural number
By Binomial Theorem,
is divisible by 64, whenever n is a positive integer.
n 1
9 8n
9
2
m m m m m m
0 1 2
m
1 a C C a C a ....
C a
For
a 8 and
mn1
, we obtain
is divisible by 64, it has to be prove that,
n1 n1 n1 n1 2 n1
n1
C0 C1 C2 C n 1
18 8 8 .... 8
1
n1 2 n1 n1 n1
9 1 n 1 8 8 C2 C3 8 .... C
1
8 n
n
1
n1 n1 n1 n1
9 9 8n 64 C2 C3 8 .... C
1
8 n
n
1
n1 n1 n1 n1
9 8n 9 64 k, where k C2 C3 8 .... C
1
8 n
n
Thus,
n 1
9 8n
9
is divisible by 64, whenever n is a positive integer.
n 1
9 8n 9 64
is a natural number
k
,
Question 14:
Prove that
n
r0
r n
3 C 4
Solution 14:
By Binomial Theorem,
n
r0
C a b a b
n nr r
r
By putting
n
r0
n
C
n
r0
r
b 3
r
and
1 3 13
n r r n
r n
3 C 4
Hence proved.
r
n
n
n
a 1 in the above equation, we obtain
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