1

JEE Advanced 2014 Paper 2 Offline

MCQ (Single Correct Answer)
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)
The common tangents to the circle $${x^2} + {y^2} = 2$$ and the parabola $${y^2} = 8x$$ touch the circle at the points $$P, Q$$ and the parabola at the points $$R$$, $$S$$. Then the area of the quadrilateral $$PQRS$$ is
A
$$3$$
B
$$6$$
C
$$9$$
D
$$15$$
3

JEE Advanced 2013 Paper 2 Offline

MCQ (Single Correct Answer)
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 $$y=2x+a$$, $$a>0$$.

If chord $$PQ$$ subtends an angle $$\theta $$ at the vertex of $${y^2} = 4ax$$, then tan $$\theta = $$

A
$${2 \over 3}\sqrt 7 $$
B
$${-2 \over 3}\sqrt 7 $$
C
$${2 \over 3}\sqrt 5 $$
D
$${-2 \over 3}\sqrt 5 $$
4

JEE Advanced 2013 Paper 2 Offline

MCQ (Single Correct Answer)
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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