1
JEE Advanced 2018 Paper 2 Offline
+3
-1
Let $${f_1}:R \to R,\,{f_2}:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R,\,{f_3}:( - 1,{e^{\pi /2}} - 2) \to R$$ and $${f_4}:R \to R$$ be functions defined by

(i) $${f_1}(x) = \sin (\sqrt {1 - {e^{ - {x^2}}}} )$$,

(ii) $${f_2}(x) = \left\{ \matrix{ {{|\sin x|} \over {\tan { - ^1}x}}if\,x \ne 0,\,where \hfill \cr 1\,if\,x = 0 \hfill \cr} \right.$$

the inverse trigonometric function tan$$-$$1x assumes values in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$,

(iii) $${f_3}(x) = [\sin ({\log _e}(x + 2))]$$, where for $$t \in R,\,[t]$$ denotes the greatest integer less than or equal to t,

(iv) $${f_4}(x) = \left\{ \matrix{ {x^2}\sin \left( {{1 \over x}} \right)\,if\,x \ne 0 \hfill \cr 0\,if\,x = 0 \hfill \cr} \right.$$
LIST-I LIST-II
P. The function $$f_1$$ is 1. NOT continuous at $$x = 0$$
Q. The function $$f_2$$ is 2. continuous at $$x = 0$$ and NOT differentiable at $$x = 0$$
R. The function $$f_3$$ is 3. differentiable at $$x = 0$$ and its derivative is NOT continuous at $$x = 0$$
S. The function $$f_4$$ is 4. differentiable at $$x = 0$$ and its derivative is continuous at $$x = 0$$
A
P $$\to$$ 2 ; Q $$\to$$ 3 ; R $$\to$$ 1 ; S $$\to$$ 4
B
P $$\to$$ 4 ; Q $$\to$$ 1 ; R $$\to$$ 2 ; S $$\to$$ 3
C
P $$\to$$ 4 ; Q $$\to$$ 2 ; R $$\to$$ 1 ; S $$\to$$ 3
D
P $$\to$$ 2 ; Q $$\to$$ 1 ; R $$\to$$ 4 ; S $$\to$$ 3
2
JEE Advanced 2017 Paper 2 Offline
+3
-1
If f : R $$\to$$ R is a twice differentiable function such that f"(x) > 0 for all x$$\in$$R, and $$f\left( {{1 \over 2}} \right) = {1 \over 2}$$, f(1) = 1, then
A
f'(1) $$\le$$ 0
B
f'(1) > 1
C
0 < f'(1) $$\le$$ $${1 \over 2}$$
D
$${1 \over 2}$$ < f'(1) $$\le$$ 1
3
IIT-JEE 2012 Paper 1 Offline
+3
-1

If $$\mathop {\lim }\limits_{x \to \infty } \left( {{{{x^2} + x + 1} \over {x + 1}} - ax - b} \right) = 4$$, then

A
a = 1, b = 4
B
a = 1, b = $$-$$4
C
a = 2, b = $$-$$3
D
a = 2, b = 3
4
IIT-JEE 2012 Paper 1 Offline
+3
-1

Let $$f(x) = \left\{ {\matrix{ {{x^2}\left| {\cos {\pi \over x}} \right|,} & {x \ne 0} \cr {0,} & {x = 0} \cr } } \right.$$

x$$\in$$R, then f is

A
differentiable both at x = 0 and at x = 2.
B
differentiable at x = 0 but not differentiable at x = 2.
C
not differentiable at x = 0 but differentiable at x = 2.
D
differentiable neither at x = 0 nor at x = 2.
EXAM MAP
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