1
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
If $$f(x) = [x] - \left[ {{x \over 4}} \right]$$ ,x $$\in$$ 4 , where [x] denotes the greatest integer function, then
A
Both $$\mathop {\lim }\limits_{x \to 4 - } f(x)$$ and $$\mathop {\lim }\limits_{x \to 4 + } f(x)$$ exist but are not equal
B
f is continuous at x = 4
C
$$\mathop {\lim }\limits_{x \to 4 + } f(x)$$ exists but $$\mathop {\lim }\limits_{x \to 4 - } f(x)$$ does not exist
D
$$\mathop {\lim }\limits_{x \to 4 - } f(x)$$ exists but $$\mathop {\lim }\limits_{x \to 4 + } f(x)$$ does not exist
2
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
If the function $$f(x) = \left\{ {\matrix{ {a|\pi - x| + 1,x \le 5} \cr {b|x - \pi | + 3,x > 5} \cr } } \right.$$
is continuous at x = 5, then the value of a – b is :-
A
$${2 \over {\pi - 5 }}$$
B
$${2 \over {5 - \pi }}$$
C
$${-2 \over {\pi + 5 }}$$
D
$${2 \over {\pi + 5 }}$$
3
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
Let ƒ(x) = 15 – |x – 10|; x $$\in$$ R. Then the set of all values of x, at which the function, g(x) = ƒ(ƒ(x)) is not differentiable, is :
A
{10,15}
B
{5,10,15,20}
C
{10}
D
{5,10,15}
4
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
If the function ƒ defined on , $$\left( {{\pi \over 6},{\pi \over 3}} \right)$$ by $$f(x) = \left\{ {\matrix{ {{{\sqrt 2 {\mathop{\rm cosx}\nolimits} - 1} \over {\cot x - 1}},} & {x \ne {\pi \over 4}} \cr {k,} & {x = {\pi \over 4}} \cr } } \right.$$\$ is continuous, then k is equal to
A
1
B
1 / $$\sqrt 2$$
C
$${1 \over 2}$$
D
2
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