1
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
If f : R $$\to$$ R is a function defined by f(x)= [x - 1] $$\cos \left( {{{2x - 1} \over 2}} \right)\pi$$, where [.] denotes the greatest integer function, then f is :
A
continuous for every real x
B
discontinuous at all integral values of x except at x = 1
C
discontinuous only at x = 1
D
continuous only at x = 1
2
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}
3
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)
4
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.
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