1
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
$${5 \over 3}$$
2
JEE Advanced 2013 Paper 1 Offline
+4
-1
The area enclosed by the curves $$y = \sin x + {\mathop{\rm cosx}\nolimits}$$ and $$y = \left| {\cos x - \sin x} \right|$$ over the interval $$\left[ {0,{\pi \over 2}} \right]$$ is
A
$$4\left( {\sqrt 2 - 1} \right)$$
B
$$2\sqrt 2 \left( {\sqrt 2 - 1} \right)$$
C
$$2\left( {\sqrt 2 + 1} \right)$$
D
$$2\sqrt 2 \left( {\sqrt 2 + 1} \right)$$
3
IIT-JEE 2011 Paper 1 Offline
+4
-1
Let the straight line $$x=b$$ divide the area enclosed by
$$y = {\left( {1 - x} \right)^2},y = 0,$$ and $$x=0$$ into two parts $${R_1}\left( {0 \le x \le b} \right)$$ and
$${R_2}\left( {b \le x \le 1} \right)$$ such that $${R_1} - {R_2} = {1 \over 4}.$$ Then $$b$$ equals
A
$${3 \over 4}$$
B
$${ 1\over 2}$$
C
$${1 \over 3}$$
D
$${1 \over 4}$$
4
IIT-JEE 2011 Paper 2 Offline
+4
-1
Let f $$:$$$$\left[ { - 1,2} \right] \to \left[ {0,\infty } \right]$$ be a continuous function such that
$$f\left( x \right) = f\left( {1 - x} \right)$$ for all $$x \in \left[ { - 1,2} \right]$$

Let $${R_1} = \int\limits_{ - 1}^2 {xf\left( x \right)dx,}$$ and $${R_2}$$ be the area of the region bounded by $$y=f(x),$$ $$x=-1,$$ $$x=2,$$ and the $$x$$-axis. Then

A
$${R_1} = 2{R_2}$$
B
$${R_1} = 3{R_2}$$
C
$${2R_1} = {R_2}$$
D
$${3R_1} = {R_2}$$
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