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NDA Math Binomial Theorem
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© examsnet.com
Question : 11
Total: 50
Consider the expansion of
(
1
+
x
)
n
.
Let
p
,
q
,
r
and
s
be the coefficients of first, second,
n
th and
(
n
+
1
)
th terms respectively. What is
(
p
s
+
q
r
)
equal to?
[NDA-II 2021]
1
+
2
n
1
+
2
n
2
1
+
n
2
1
+
4
n
Validate
Solution:
👈: Video Solution
(c) Given,
(
1
+
x
)
n
In the above expansion,
(
r
+
1
)
th term
T
r
+
1
=
n
C
r
x
r
∴
T
1
=
n
C
0
x
∘
,
T
2
=
n
C
1
x
′
p
=
1
...(i)
∴
n
C
1
=
q
n
=
q
T
n
=
n
C
n
−
1
x
n
−
1
,
T
n
+
1
=
n
C
n
x
n
∴
r
=
n
...(iii)
∴
s
=
1
.
.
.
(iv)
∴
(
p
s
+
q
r
)
=
1
⋅
1
+
n
⋅
n
=
1
+
n
2
=
(
1
+
n
2
)
Hence, option (c) is correct.
© examsnet.com
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