1
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}
2
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
3
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
Let ƒ : R $$\to$$ R be a differentiable function satisfying ƒ'(3) + ƒ'(2) = 0.
Then $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + f(3 + x) - f(3)} \over {1 + f(2 - x) - f(2)}}} \right)^{{1 \over x}}}$$ is equal to
A
e
B
e2
C
e–1
D
1
4
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
Let ƒ : [–1,3] $$\to$$ R be defined as

$$f(x) = \left\{ {\matrix{ {\left| x \right| + \left[ x \right]} & , & { - 1 \le x < 1} \cr {x + \left| x \right|} & , & {1 \le x < 2} \cr {x + \left[ x \right]} & , & {2 \le x \le 3} \cr } } \right.$$

where [t] denotes the greatest integer less than or equal to t. Then, ƒ is discontinuous at:
A
only three points
B
four or more points
C
only two points
D
only one point
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