Let f(x)=\{\table0 {, },\text{if },-1 \\leq x

F is continuous function in [–1, 1]

F is discontinuous function in [–1, 1]

WBJEE 2021 Math Solved Paper

CATEGORY - III (Q66 to Q75)

Carry 2 marks each and one or more option(s) is/are correct. If all correct answers are not marked and no incorrect answer is marked then score = 2 × number of correct answers marked  actual number of correct answers. If any wrong option is marked or if any combination including a wrong option is marked, the answer will considered wrong, but there is no negative marking for the same and zero marks will be awarded.

Question : 72 of 75

Marks: +1, -0

Let f(x)={

0,	if	−1≤x<0
1,	if	x=0
2,	if	0<x≤1

and let F(x)=

∫

−1

f(t)dt,−1≤x≤1, then

F is continuous function in [–1, 1]
F is discontinuous function in [–1, 1]
F'(x) exists at x = 0
F'(x) does not exists at x = 0

Validate

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2x,	0<x≤1