1

JEE Main 2021 (Online) 16th March Morning Shift

Numerical

+4

-1

If $$\mathop {\lim }\limits_{x \to 0} {{a{e^x} - b\cos x + c{e^{ - x}}} \over {x\sin x}} = 2$$, then a + b + c is equal to ____________.

Your input ____

2

JEE Main 2021 (Online) 25th February Evening Shift

Numerical

+4

-1

A function f is defined on [$$-$$3, 3] as

$$f(x) = \left\{ {\matrix{ {\min \{ |x|,2 - {x^2}\} ,} & { - 2 \le x \le 2} \cr {[|x|],} & {2 < |x| \le 3} \cr } } \right.$$ where [x] denotes the greatest integer $$ \le $$ x. The number of points, where f is not differentiable in ($$-$$3, 3) is ___________.

$$f(x) = \left\{ {\matrix{ {\min \{ |x|,2 - {x^2}\} ,} & { - 2 \le x \le 2} \cr {[|x|],} & {2 < |x| \le 3} \cr } } \right.$$ where [x] denotes the greatest integer $$ \le $$ x. The number of points, where f is not differentiable in ($$-$$3, 3) is ___________.

Your input ____

3

JEE Main 2021 (Online) 25th February Evening Shift

Numerical

+4

-1

If $$\mathop {\lim }\limits_{x \to 0} {{ax - ({e^{4x}} - 1)} \over {ax({e^{4x}} - 1)}}$$ exists and is equal to b, then the value of a $$-$$ 2b is __________.

Your input ____

4

JEE Main 2021 (Online) 25th February Morning Slot

Numerical

+4

-1

The number of points, at which the function

f(x) = | 2x + 1 | $$-$$ 3| x + 2 | + | x

f(x) = | 2x + 1 | $$-$$ 3| x + 2 | + | x

^{2}+ x $$-$$ 2 |, x$$\in$$R is not differentiable, is __________.Your input ____

Questions Asked from Limits, Continuity and Differentiability (Numerical)

Number in Brackets after Paper Indicates No. of Questions

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