JEE Main 2020 (Online) 2nd September Evening Slot | Limits, Continuity and Differentiability Question 104 | Mathematics

JEE Main 2020 (Online) 2nd September Evening Slot

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to 0} {\left( {\tan \left( {{\pi \over 4} + x} \right)} \right)^{{1 \over x}}}$$ is equal to :

$$e$$

$$e$$²

JEE Main 2020 (Online) 2nd September Morning Slot

MCQ (Single Correct Answer)

-1

If a function f(x) defined by

$$f\left( x \right) = \left\{ {\matrix{ {a{e^x} + b{e^{ - x}},} & { - 1 \le x < 1} \cr {c{x^2},} & {1 \le x \le 3} \cr {a{x^2} + 2cx,} & {3 < x \le 4} \cr } } \right.$$

be continuous for some $$a$$, b, c $$ \in $$ R and f'(0) + f'(2) = e, then the value of of $$a$$ is :

$${e \over {{e^2} - 3e - 13}}$$

$${1 \over {{e^2} - 3e + 13}}$$

$${e \over {{e^2} - 3e + 13}}$$

$${e \over {{e^2} + 3e + 13}}$$

JEE Main 2020 (Online) 9th January Evening Slot

MCQ (Single Correct Answer)

-1

Let [t] denote the greatest integer $$ \le $$ t and $$\mathop {\lim }\limits_{x \to 0} x\left[ {{4 \over x}} \right] = A$$.
Then the function, f(x) = [x²]sin($$\pi $$x) is discontinuous, when x is equal to :

$$\sqrt {A + 1} $$

$$\sqrt {A + 5} $$

$$\sqrt {A + 21} $$

$$\sqrt {A} $$

JEE Main 2020 (Online) 9th January Evening Slot

MCQ (Single Correct Answer)

-1

Let a function ƒ : [0, 5] $$ \to $$ R be continuous, ƒ(1) = 3 and F be defined as :

$$F(x) = \int\limits_1^x {{t^2}g(t)dt} $$ , where $$g(t) = \int\limits_1^t {f(u)du} $$

Then for the function F, the point x = 1 is :

a point of inflection.

a point of local maxima.

a point of local minima.

not a critical point.

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