1
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
For each t $$\in$$ R , let [t] be the greatest integer less than or equal to t

Then  $$\mathop {\lim }\limits_{x \to 1^ + } {{\left( {1 - \left| x \right| + \sin \left| {1 - x} \right|} \right)\sin \left( {{\pi \over 2}\left[ {1 - x} \right]} \right)} \over {\left| {1 - x} \right|.\left[ {1 - x} \right]}}$$
A
equals $$-$$ 1
B
equals 1
C
equals 0
D
does not exist
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
Let  $$f\left( x \right) = \left\{ {\matrix{ {\max \left\{ {\left| x \right|,{x^2}} \right\}} & {\left| x \right| \le 2} \cr {8 - 2\left| x \right|} & {2 < \left| x \right| \le 4} \cr } } \right.$$

Let S be the set of points in the interval (– 4, 4) at which f is not differentiable. Then S
A
equals $$\left\{ { - 2, - 1,1,2} \right\}$$
B
equals $$\left\{ { - 2, - 1,0,1,2} \right\}$$
C
equals $$\left\{ { - 2,2} \right\}$$
D
is an empty set
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
For each x$$\in$$R, let [x] be the greatest integer less than or equal to x.

Then $$\mathop {\lim }\limits_{x \to {0^ - }} \,\,{{x\left( {\left[ x \right] + \left| x \right|} \right)\sin \left[ x \right]} \over {\left| x \right|}}$$ is equal to :
A
$$-$$ sin 1
B
1
C
sin 1
D
0
4
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
Let f : R $$\to$$ R be a function defined as
$$f(x) = \left\{ {\matrix{ 5 & ; & {x \le 1} \cr {a + bx} & ; & {1 < x < 3} \cr {b + 5x} & ; & {3 \le x < 5} \cr {30} & ; & {x \ge 5} \cr } } \right.$$

Then, f is
A
continuous if a = 0 and b = 5
B
continuous if a = –5 and b = 10
C
continuous if a = 5 and b = 5
D
not continuous for any values of a and b
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