1
JEE Advanced 2014 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$a, r, s, t$$ be nonzero real numbers. Let $$P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)$$ and $$S\,\,\left( {a{s^2},2as} \right)$$ be distinct points on the parabola $${y^2} = 4ax$$. Suppose that $$PQ$$ is the focal chord and lines $$QR$$ and $$PK$$ are parallel, where $$K$$ is the point $$(2a,0)$$

The value of $$r$$ is

A
$$ - {1 \over t}$$
B
$${{{t^2} + 1} \over t}$$
C
$$ {1 \over t}$$
D
$${{{t^2} - 1} \over t}$$
2
JEE Advanced 2014 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$a, r, s, t$$ be nonzero real numbers. Let $$P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)$$ and $$S\,\,\left( {a{s^2},2as} \right)$$ be distinct points on the parabola $${y^2} = 4ax$$. Suppose that $$PQ$$ is the focal chord and lines $$QR$$ and $$PK$$ are parallel, where $$K$$ is the point $$(2a,0)$$

If $$st=1$$, then the tangent at $$P$$ and the normal at $$S$$ to the parabola meet at a point whose ordinate is

A
$${{{{\left( {{t^2} + 1} \right)}^2}} \over {2{t^3}}}$$
B
$${{a{{\left( {{t^2} + 1} \right)}^2}} \over {2{t^3}}}$$
C
$${{a{{\left( {{t^2} + 1} \right)}^2}} \over {{t^3}}}$$
D
$${{a{{\left( {{t^2} + 2} \right)}^2}} \over {{t^3}}}$$
3
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
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
$$P = 1,Q = 3,R = 4,S = 2$$
4
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$PQ$$ be a focal chord of the parabola $${y^2} = 4ax$$. The tangents to the parabola at $$P$$ and $$Q$$ meet at a point lying on the line $$y=2x+a$$, $$a>0$$.

Length of chord $$PQ$$ is

A
$$7a$$
B
$$5a$$
C
$$2a$$
D
$$3a$$
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