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KVPY 2020-21 SA Exam Previous Papers
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© examsnet.com
Question : 1
Total: 80
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
Two solutions
One solution
No solution
More than two solutions
Validate
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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