1
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : [0, $$\infty $$) $$ \to $$ R be a continuous function such that

$$f(x) = 1 - 2x + \int_0^x {{e^{x - t}}f(t)dt} $$ for all x $$ \in $$ [0, $$\infty $$). Then, which of the following statement(s) is (are) TRUE?
A
The curve y = f(x) passes through the point (1, 2)
B
The curve y = f(x) passes through the point (2, $$-$$1)
C
The area of the region $$\{ (x,y) \in [0,1] \times R:f(x) \le y \le \sqrt {1 - {x^2}} \} $$ is $${{\pi - 2} \over 4}$$
D
The area of the region $$\{ (x,y) \in [0,1] \times R:f(x) \le y \le \sqrt {1 - {x^2}} \} $$ is $${{\pi - 1} \over 4}$$
2
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
If $$I = \sum\nolimits_{k = 1}^{98} {\int_k^{k + 1} {{{k + 1} \over {x(x + 1)}}} dx} $$, then
A
$$I > {\log _e}99$$
B
$$I < {\log _e}99$$
C
$$I < {{49} \over {50}}$$
D
$$I > {{49} \over {50}}$$
3
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
If the line x = $$\alpha $$ divides the area of region R = {(x, y) $$ \in $$R2 : x3 $$ \le $$ y $$ \le $$ x, 0 $$ \le $$ x $$ \le $$ 1} into two equal parts, then
A
2$$\alpha $$4 $$-$$ 4$$\alpha $$2 + 1 =0
B
$$\alpha $$4 + 4$$\alpha $$2 $$-$$ 1 =0
C
$${1 \over 2} < \alpha < 1$$
D
0 < $$\alpha $$ $$ \le $$ $${1 \over 2}$$
4
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Let
$$f\left( x \right) = \mathop {\lim }\limits_{n \to \infty } {\left( {{{{n^n}\left( {x + n} \right)\left( {x + {n \over 2}} \right)...\left( {x + {n \over n}} \right)} \over {n!\left( {{x^2} + {n^2}} \right)\left( {{x^2} + {{{n^2}} \over 4}} \right)....\left( {{x^2} + {{{n^2}} \over {{n^2}}}} \right)}}} \right)^{{x \over n}}},$$ for

all $$x>0.$$ Then
A
$$f\left( {{1 \over 2}} \right) \ge f\left( 1 \right)$$
B
$$f\left( {{1 \over 3}} \right) \le f\left( {{2 \over 3}} \right)$$
C
$$\,f'\left( 2 \right) \le 0$$
D
$$\,{{f'\left( 3 \right)} \over {f\left( 3 \right)}} \ge {{f'\left( 2 \right)} \over {f\left( 2 \right)}}$$
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