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Let f : R → R be defined as [ ] [ ] ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ≥ − < ≤ π + < ≤ − + < = − 2 x , c e 2 x 1 )], x [sin( b 1 x 0 ] 1 x [ ae 0 x e ) x ( f x x x Where a , b , c ∈ R and [ t ] denotes greatest integer less than or equal to t . Then, which of the following statements is true?

1. There exists a , b , c ∈ R such that ƒ is continuous on R
2. If ƒ is discontinuous at exactly one point, then a + b + c = 1
3. If ƒ is discontinuous at exactly one point, then a + b + c ≠ 1
4. ƒ is discontinuous at atleast two points, for any values of a , b and c

Correct answer: If ƒ is discontinuous at exactly one point, then a + b + c ≠ 1

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