KVPY SX SB Exam 2015 Question Paper

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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

Solution:

x + y^2 = x^ 2 + y = 12

curve (1)

x + y^2 = 12

^ 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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