1
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Let f : R $$\to$$ R be a function defined by
f(x) = max {x, x2}. Let S denote the set of all points in R, where f is not differentiable. Then :
A
{0, 1}
B
{0}
C
$$\phi$$(an empty set)
D
{1}
2
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
For all twice differentiable functions f : R $$\to$$ R,
with f(0) = f(1) = f'(0) = 0
A
f''(x) $$\ne$$ 0, at every point x $$\in$$ (0, 1)
B
f''(x) = 0, for some x $$\in$$ (0, 1)
C
f''(0) = 0
D
f''(x) = 0, at every point x $$\in$$ (0, 1)
3
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {{x\left( {{e^{\left( {\sqrt {1 + {x^2} + {x^4}} - 1} \right)/x}} - 1} \right)} \over {\sqrt {1 + {x^2} + {x^4}} - 1}}$$
A
is equal to 0.
B
is equal to $$\sqrt e$$.
C
is equal to 1.
D
does not exist.
4
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
If the function
$$f\left( x \right) = \left\{ {\matrix{ {{k_1}{{\left( {x - \pi } \right)}^2} - 1,} & {x \le \pi } \cr {{k_2}\cos x,} & {x > \pi } \cr } } \right.$$ is
twice differentiable, then the ordered pair (k1, k2) is equal to :
A
$$\left( {{1 \over 2},-1} \right)$$
B
(1, 1)
C
(1, 0)
D
$$\left( {{1 \over 2},1} \right)$$
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