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AP EAMCET Engineering 17 Sep 2020 Shift 2 Paper
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© examsnet.com
Question : 17
Total: 160
On an
n
×
n
chessboard, the total number of rectangles which are not squares is
350.
Then number of white squares on the chessboard is ______
32
50
18
72
Validate
Solution:
Number of rectangles in a chess board (including squares)
=
Σ
n
3
=
n
2
(
n
+
1
)
2
4
Number of squares in a chess board
=
Σ
n
2
=
n
(
n
+
1
)
(
2
n
+
1
)
6
So, Number of rectangles which are not squares
=
Σ
n
3
−
Σ
n
2
=
n
2
(
n
+
1
)
2
4
−
n
(
n
+
1
)
(
2
n
+
1
)
6
=
350
⇒
n
(
n
+
1
2
)
(
n
(
n
+
1
)
2
−
2
n
+
1
3
)
=
350
⇒
n
(
n
+
1
2
)
(
3
n
2
+
3
n
−
4
n
−
2
6
)
=
350
⇒
n
(
n
+
1
)
(
3
n
2
−
n
−
2
)
=
350
×
6
×
2
⇒
n
(
n
+
1
)
(
3
n
2
−
3
n
+
2
n
−
2
)
=
350
×
6
×
2
⇒
n
(
n
+
1
)
(
3
n
(
n
−
1
)
+
2
(
n
−
1
)
=
350
×
6
×
2
⇒
n
(
n
+
1
)
(
n
−
1
)
(
3
n
+
2
)
=
350
×
6
×
2
⇒
(
n
−
1
)
n
(
n
+
1
)
(
3
n
+
2
)
=
5
×
6
×
7
×
20
By comparison we get
∴
n
=
6
Hence, total number of black and white squares
=
n
×
n
=
6
×
6
=
36
Half of there are white
=
36
2
=
18
squares.
© examsnet.com
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