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KVPY SA Exam 2015 Question Paper
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© examsnet.com
Question : 2
Total: 80
If n is the smallest natural number such that n + 2n + 3n + ....+ 99n is a perfect square, then the number of digits in
n
2
is
1
2
3
more than 3
Validate
Solution:
n
+
2
n
+
3
n
+
.
.
.
+
99
n
=
k
2
⇒
n
99.100
2
=
k
2
⇒
n
.99
.50
=
k
2
⇒
n
.9
.11
.25
.2
=
k
2
So
n
=
11.2
=
22
n
2
=
484
No. of digits in
n
2
=
3.
© examsnet.com
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