IIT-JEE 2012 Paper 1 Offline | JEE Advanced Year Wise Previous Years Questions

IIT-JEE 2012 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let $$S$$ be the area of the region enclosed by $$y = {e^{ - {x^2}}}$$, $$y=0$$, $$x=0$$, and $$x=1$$; then

$$S \ge {1 \over e}$$

$$S \ge 1 - {1 \over e}$$

$$S \le {1 \over 4}\left( {1 + {1 \over {\sqrt e }}} \right)$$

$$S \le {1 \over {\sqrt 2 }} + {1 \over {\sqrt e }}\left( {1 - {1 \over {\sqrt 2 }}} \right)$$

IIT-JEE 2012 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

If $$y(x)$$ satisfies the differential equation $$y' - y\,tan\,x = 2x\,secx$$ and $$y(0)=0,$$ then

$$y\left( {{\pi \over 4}} \right) = {{{\pi ^2}} \over {8\sqrt 2 }}$$

$$y'\left( {{\pi \over 4}} \right) = {{{\pi ^2}} \over {18}}$$

$$y\left( {{\pi \over 3}} \right) = {{{\pi ^2}} \over 9}$$

$$y'\left( {{\pi \over 3}} \right) = {{4\pi } \over 3} + {{2{\pi ^2}} \over {3\sqrt 3 }}$$

IIT-JEE 2012 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

A ship is fitted with three engines $${E_1},{E_2}$$ and $${E_3}$$. The engines function independently of each other with respective probabilities $${1 \over 2},{1 \over 4}$$ and $${1 \over 4}$$. For the ship to be operational at least two of its engines must function. Let $$X$$ denote the event that the ship is operational and Let $${X_1},{X_2}$$ and $${X_3}$$ denote respectively the events that the engines $${E_1},{E_2}$$ and $${E_3}$$ are functioning. Which of the following is (are) true?

$$P\left[ {X_1^c|X} \right] = {3 \over {16}}$$

$$P$$ [exactly two engines of the ship are functioning $$\left. {|X} \right] = {7 \over 8}$$

$$P\left[ {X|{X_2}} \right] = {5 \over {16}}$$

$$P\left[ {X|{X_1}} \right] = {7 \over {16}}$$

IIT-JEE 2012 Paper 1 Offline

MCQ (Single Correct Answer)

-1

The point $$P$$ is the intersection of the straight line joining the points $$Q(2, 3, 5)$$ and $$R(1, -1, 4)$$ with the plane $$5x-4y-z=1.$$ If $$S$$ is the foot of the perpendicular drawn from the point $$T(2, 1, 4)$$ to $$QR,$$ then the length of the line segment $$PS$$ is

$${{1 \over {\sqrt 2 }}}$$

$${\sqrt 2 }$$

$$2$$

$${2\sqrt 2 }$$

PREVIOUS NEXT