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Limits Continuity and Differentiability question

2022 · 28 Jun · Shift 1 · Q29

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JEE Main
Mathematics
Limits Continuity and Differentiability
2022 · 28 Jun · Shift 1 · Q29

Limits Continuity and Differentiability question

2022 · 28 Jun · Shift 1 · Q29

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let f : R

\to

R be defined as

f(x) = \left\{ \begin{matrix} [e^x], & x \lt 0 \\ ae^x + [x - 1], & 0 \le x \lt 1 \\ b + [\sin(\pi x)], & 1 \le x \lt 2 \\ [e^{-x}] - c, & x \ge 2 \end{matrix} \right.

where a, b, c

\in

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

A
There exists a, b, c $\in$ R such that f is continuous on R.
B
If f is discontinuous at exactly one point, then a + b + c = 1
C
If f is discontinuous at exactly one point, then a + b + c $e$ 1
D
f is discontinuous at at least two points, for any values of a, b and c

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