KVPY 2020-21 SA Exam Previous Papers

Question : 1 of 80

Marks: +1, -0

PART-I : MATHEMATICS

Let [x] be the greatest integer less than or equal to x, for a real number x. Then the equation

[x^2] = x + 1

has

Solution:

[x^2] = x + 1

...(i)
(i) ⇒ x is an integer ...(ii)

x^2 -{x^2} = x + 1

x^2 -x -1 = {x^2}

...(iii)
(iii)

⇒ x^2 -x -1 < 1 ⇒ -1 < x < 2

...(iv)
(ii) & (iv) ⇒ possible values of x are 0 & 1.
But 0 and 1 do not satisfy (i).
⇒ No solution

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