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KVPY SX SB Exam 2015 Question Paper
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© examsnet.com
Question : 1
Total: 120
PART I
MATHEMATICS
The number of ordered pairs (x, y) of real numbers that satisfy the simultaneous equations
x
+
y
2
=
x
2
+
y
=
12
is
0
1
2
4
Validate
Solution:
x
+
y
2
=
x
2
+
y
=
12
curve (1)
x
+
y
2
=
12
y
2
=
−
(
x
−
12
)
Intersection on x-axis (12, 0)
Intersection on y-axis
(
0
,
±
√
12
)
curve (2)
x
2
+
y
=
12
x
2
=
−
(
y
−
12
)
Intersection on x-axis =
(
±
√
12
,
0
)
Intersection on y-axis = (0, 12)
four intersection
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