1
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
The value of $$\mathop {\lim }\limits_{h \to 0} 2\left\{ {{{\sqrt 3 \sin \left( {{\pi \over 6} + h} \right) - \cos \left( {{\pi \over 6} + h} \right)} \over {\sqrt 3 h\left( {\sqrt 3 \cosh - \sinh } \right)}}} \right\}$$ is :
A
$${4 \over 3}$$
B
$${2 \over 3}$$
C
$${3 \over 4}$$
D
$${2 \over {\sqrt 3 }}$$
2
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
Let f be any function defined on R and let it satisfy the condition : $$|f(x) - f(y)|\, \le \,|{(x - y)^2}|,\forall (x,y) \in R$$

If f(0) = 1, then :
A
f(x) can take any value in R
B
$$f(x) < 0,\forall x \in R$$
C
$$f(x) > 0,\forall x \in R$$
D
$$f(x) = 0,\forall x \in R$$
3
JEE Main 2021 (Online) 25th February Morning Slot
+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
$${{1 \over e}}$$
4
JEE Main 2021 (Online) 24th February Morning Slot
+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
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