1
JEE Advanced 2016 Paper 2 Offline
+3
-1
The value of $$\int\limits_{-{\pi \over 2}}^{{\pi \over 2}} {{{{x^2}\cos x} \over {1 + {e^x}}}dx}$$ is equal to
A
$${{{\pi ^2}} \over 4} - 2$$
B
$${{{\pi ^2}} \over 4} + 2$$
C
$${\pi ^2} - {e^{{\pi \over 2}}}$$
D
$${\pi ^2} + {e^{{\pi \over 2}}}$$
2
JEE Advanced 2016 Paper 2 Offline
+3
-1
Area of the region

$$\left\{ {\left( {x,y} \right) \in {R^2}:y \ge \sqrt {\left| {x + 3} \right|} ,5y \le x + 9 \le 15} \right\}$$

is equal to
A
$${1 \over 6}$$
B
$${4 \over 3}$$
C
$${3 \over 2}$$
D
$${5 \over 3}$$
3
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
$$\,{{f'\left( 3 \right)} \over {f\left( 3 \right)}} \ge {{f'\left( 2 \right)} \over {f\left( 2 \right)}}$$
4
JEE Advanced 2016 Paper 2 Offline
+3
-0
Football teams $${T_1}$$ and $${T_2}$$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $${T_1}$$ winning, drawing and losing a game against $${T_2}$$ are $${1 \over 2},{1 \over 6}$$ and $${1 \over 3}$$ respectively. Each team gets $$3$$ points for a win, $$1$$ point for a draw and $$0$$ point for a loss in a game. Let $$X$$ and $$Y$$ denote the total points scored by teams $${T_1}$$ and $${T_2}$$ respectively after two games.

$$\,\,\,\,P\,\left( {X > Y} \right)$$ is

A
$${1 \over 4}$$
B
$${5 \over 12}$$
C
$${1 \over 2}$$
D
$${7 \over 12}$$
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