1
JEE Main 2021 (Online) 25th February Morning Slot
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{n \to \infty } {\left( {1 + {{1 + {1 \over 2} + ........ + {1 \over n}} \over {{n^2}}}} \right)^n}$$ is equal to :
A
$${{1 \over 2}}$$
B
1
C
0
D
$${{1 \over e}}$$
2
JEE Main 2021 (Online) 24th February Morning Slot
MCQ (Single Correct Answer)
+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
3
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+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}
4
JEE Main 2020 (Online) 6th September Evening Slot
MCQ (Single Correct Answer)
+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)
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