1
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {\left( {\tan \left( {{\pi \over 4} + x} \right)} \right)^{{1 \over x}}}$$ is equal to :
A
2
B
1
C
$$e$$
D
$$e$$2
2
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-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 :
A
$${e \over {{e^2} - 3e - 13}}$$
B
$${1 \over {{e^2} - 3e + 13}}$$
C
$${e \over {{e^2} - 3e + 13}}$$
D
$${e \over {{e^2} + 3e + 13}}$$
3
JEE Main 2020 (Online) 9th January Evening Slot
+4
-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 :
A
$$\sqrt {A + 1}$$
B
$$\sqrt {A + 5}$$
C
$$\sqrt {A + 21}$$
D
$$\sqrt {A}$$
4
JEE Main 2020 (Online) 9th January Evening Slot
+4
-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
a point of inflection.
B
a point of local maxima.
C
a point of local minima.
D
not a critical point.
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