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UPSC NDA Math Model Paper 7
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© examsnet.com
Question : 26
Total: 120
The number of triangles which can be formed by using the vertices of a regular polygon of (n + 3) sides is 220. Then the value of n is:
10
8
11
9
Validate
Solution:
Here,number of triangle
=
220
Number of triangle formed by
n
+
3
sides will be
n
+
3
C
3
∴
n
+
3
C
3
=
220
(
n
+
3
)
!
3
!
n
!
=
220
⇒
(
n
+
3
)
×
(
n
+
2
)
×
(
n
+
1
)
3
×
2
=
220
⇒
(
n
+
3
)
×
(
n
+
2
)
×
(
n
+
1
)
=
1320
Now, if we put
n
=
9
, we get
12
×
11
×
10
=
1320
∴
n
=
9
© examsnet.com
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