1
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to a} {{{{\left( {a + 2x} \right)}^{{1 \over 3}}} - {{\left( {3x} \right)}^{{1 \over 3}}}} \over {{{\left( {3a + x} \right)}^{{1 \over 3}}} - {{\left( {4x} \right)}^{{1 \over 3}}}}}$$ ($$a$$ $$ \ne $$ 0) is equal to :
A
$$\left( {{2 \over 9}} \right){\left( {{2 \over 3}} \right)^{{1 \over 3}}}$$
B
$$\left( {{2 \over 3}} \right){\left( {{2 \over 9}} \right)^{{1 \over 3}}}$$
C
$${\left( {{2 \over 3}} \right)^{{4 \over 3}}}$$
D
$${\left( {{2 \over 9}} \right)^{{4 \over 3}}}$$
2
JEE Main 2020 (Online) 3rd September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let [t] denote the greatest integer $$ \le $$ t. If for some
$$\lambda $$ $$ \in $$ R - {1, 0}, $$\mathop {\lim }\limits_{x \to 0} \left| {{{1 - x + \left| x \right|} \over {\lambda - x + \left[ x \right]}}} \right|$$ = L, then L is equal to :
A
1
B
2
C
0
D
$${1 \over 2}$$
3
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to 0} {\left( {\tan \left( {{\pi \over 4} + x} \right)} \right)^{{1 \over x}}}$$ is equal to :
A
2
B
1
C
$$e$$
D
$$e$$2
4
JEE Main 2020 (Online) 2nd September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${e \over {{e^2} + 3e + 13}}$$
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