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Manipal Entrance Test 2018 Math Paper
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© examsnet.com
Question : 63
Total: 70
The first three terms in the expansion of
(
1
+
a
x
)
n
(
n
≠
0
)
are
1
,
6
x
and
16
x
2
.
Then, the values of
a
and
n
are respectively
2 and 9
3 and 2
2
3
and 9
3
2
and 6
Validate
Solution:
∵
(
1
+
a
x
)
n
=
1
+
a
x
n
+
n
(
n
−
1
)
2
!
(
a
x
)
2
+
.
.
.
.
Given that,
a
x
n
=
6
x
⇒
a
n
=
6
...(i)
⇒
a
2
n
(
n
−
1
)
2
=
16
...(ii)
On solving Eqs. (i) and (ii), we get
a
=
2
3
and
n
=
9
© examsnet.com
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