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1

### JEE Advanced 2013 Paper 2 Offline

MCQ (Single Correct Answer)
A line $$L:y=mx+3$$ meets $$y$$-axis at $$(E, 3)$$ and the are of the parabola $${y^2} = 16x,$$ $$0 \le y \le 6$$ at the point $$F\left( {{x_0},{y_0}} \right)$$. The tangent to the parabola at $$F\left( {{x_0},{y_0}} \right)$$ intersects the $$y$$-axis at $$G\left( {0,{y_1}} \right)$$. The slope $$m$$ of the line $$L$$ is chosen such that the area of the triangle $$EFG$$ has a local maximum.

Match List $$I$$ with List $$II$$ and select the correct answer using the code given below the lists:

List $$I$$
P.$$\,\,\,m =$$
Q.$$\,\,\,$$Maximum area of $$\Delta EFG$$ is
R.$$\,\,\,$$ $${y_0} =$$
S.$$\,\,\,$$ $${y_1} =$$

List $$II$$
1.$$\,\,\,$$ $${1 \over 2}$$
2.$$\,\,\,$$ $$4$$
3.$$\,\,\,$$ $$2$$
4.$$\,\,\,$$ $$1$$

A
$$P = 4,Q = 1,R = 2,S = 3$$
B
$$P = 3,Q = 4,R = 1,S = 2$$
C
$$P = 1,Q = 3,R = 2,S = 4$$
D
$$P = 1,Q = 3,R = 4,S = 2$$
2

### IIT-JEE 2012 Paper 1 Offline

MCQ (Single Correct Answer)
The ellipse $${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ is inscribed in a rectangle $$R$$ whose sides are parallel to the coordinate axes. Another ellipse $${E_2}$$ passing through the point $$(0, 4)$$ circumscribes the rectangle $$R$$. The eccentricity of the ellipse $${E_2}$$ is
A
$${{\sqrt 2 } \over 2}$$
B
$${{\sqrt 3 } \over 2}$$
C
$${{1 \over 2}}$$
D
$${{3 \over 4}}$$
3

### IIT-JEE 2011 Paper 2 Offline

MCQ (Single Correct Answer)
Let $$P(6, 3)$$ be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at the point $$P$$ intersects the $$x$$-axis at $$(9, 0)$$, then the eccentricity of the hyperbola is
A
$$\sqrt {{5 \over 2}}$$
B
$$\sqrt {{3 \over 2}}$$
C
$${\sqrt 2 }$$
D
$${\sqrt 3 }$$
4

### IIT-JEE 2011 Paper 2 Offline

MCQ (Single Correct Answer)
Let $$(x, y)$$ be any point on the parabola $${y^2} = 4x$$. Let $$P$$ be the point that divides the line segment from $$(0, 0)$$ to $$(x, y)$$ in the ratio $$1 : 3$$. Then the locus of $$P$$ is
A
$${x^2} = y$$
B
$${y^2} = 2x$$
C
$${y^2} = x$$
D
$${x^2} = 2y$$

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NEET

Class 12