1
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
Let $$f:\left( {0,\infty } \right) \to \left( {0,\infty } \right)$$ be a differentiable function such that f(1) = e and
$$\mathop {\lim }\limits_{t \to x} {{{t^2}{f^2}(x) - {x^2}{f^2}(t)} \over {t - x}} = 0$$. If f(x) = 1, then x is equal to :
A
$${1 \over e}$$
B
e
C
$${1 \over 2e}$$
D
2e
2
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
The function
$$f(x) = \left\{ {\matrix{ {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} \cr {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| > 1} \cr } } \right.$$ is :
A
continuous on R–{–1} and differentiable on R–{–1, 1}
B
both continuous and differentiable on R–{1}
C
both continuous and differentiable on R–{–1}
D
continuous on R–{1} and differentiable on R–{–1, 1}
3
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
$$\mathop {\lim }\limits_{x \to a} {{{{\left( {a + 2x} \right)}^{{1 \over 3}}} - {{\left( {3x} \right)}^{{1 \over 3}}}} \over {{{\left( {3a + x} \right)}^{{1 \over 3}}} - {{\left( {4x} \right)}^{{1 \over 3}}}}}$$ ($$a$$ $$\ne$$ 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
$${\left( {{2 \over 9}} \right)^{{4 \over 3}}}$$
4
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
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
$${1 \over 2}$$
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