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JEE Main 28 June 2022 Shift 1 Solved Paper

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Question : 8

Total: 90

Let f:R→R be defined as
f(x)=[

[ex],	x<0
aex+[x−1],	0≤x<1
b+[sin(πx)],	1≤x<2
[e−x]−c,	x≥2.

where a,b,c∈R and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?

[28-Jun-2022-Shift-1]

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

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