KVPY SA Exam 2018 Question Paper

Question : 1 of 80

Marks: +1, -0

The number of pairs (a, b) of positive real numbers satisfying 1 and

a^2 + b^2 > 1

0
1
2
more than 2

Validate

Solution:

Let

a^2 = m

b^2 = N

then m > 0 and N > 0
Now given condition is

M + N > 1 \and M^2 + N^2 < 1

(M,N) lies inside circle

x^2 + y^2 < 1

and above line x + y > 1
⇒ (M, N) lies in shaded region and number of points in shaded region are infinite, so number of pair (a,b) are also infinite.

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