1
JEE Advanced 2019 Paper 2 Offline
+3
-1
Let the circles

C1 : x2 + y2 = 9 and C2 : (x $$-$$ 3)2 + (y $$-$$ 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x $$-$$ h)2 + (y $$-$$ k)2 = r2 satisfies the following conditions :

(i) Centre of C3 is collinear with the centres of C1 and C2.

(ii) C1 and C2 both lie inside C3 and

(iii) C3 touches C1 at M and C2 at N.

Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be a tangent to the parabola x2 = 8$$\alpha$$y.

There are some expression given in the List-I whose values are given in List-II below.

Which of the following is the only INCORRECT combination?
A
(III), (R)
B
(IV), (S)
C
(I), (P)
D
(IV), (U)
2
JEE Advanced 2019 Paper 2 Offline
+3
-1
Let the circle C1 : x2 + y2 = 9 and C2 : (x $$-$$ 3)2 + (y $$-$$ 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x $$-$$ h)2 + (y $$-$$ k)2 = r2 satisfies the following conditions :

(i) centre of C3 is collinear with the centers of C1 and C2.

(ii) C1 and C2 both lie inside C3, and

(iii) C3 touches C1 at M and C2 at N.

Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be a tangent to the parabola x2 = 8$$\alpha$$y.

There are some expression given in the List-I whose values are given in List-II below.

Which of the following is the only CORRECT combination?
A
(II), (T)
B
(I), (S)
C
(II), (Q)
D
(I), (U)
3
JEE Advanced 2017 Paper 1 Offline
+3
-1
By appropriately matching the information given in the three columns of the following table.

Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.

Column - 1 Column - 2 Column - 3
(i) $${x^2} + {y^2} = a$$ $$my = {m^2}x + a$$ $$\left( {{a \over {{m^2}}},\,{{2a} \over m}} \right)$$
(ii) $${x^2}{a^2}{y^2} = {a^2}]$$ $$y = mx + a\sqrt {{m^2} + 1}$$ $$\left( {{{ - ma} \over {\sqrt {{m^2} + 1} }},\,{a \over {\sqrt {{m^2} + 1} }}} \right)$$
(iii) $${y^2} = 4ax$$ $$y = mx + \sqrt {{a^2}{m^2} - 1}$$ $$\left( {{{ - {a^2}m} \over {\sqrt {{a^2}{m^2} + 1} }},\,{1 \over {\sqrt {{a^2}{m^2} + 1} }}} \right)$$
(iv) $${x^2} - {a^2}{y^2} = {a^2}$$ $$y = mx + \sqrt {{a^2}{m^2} + 1}$$ $$\left( {{{ - {a^2}m} \over {\sqrt {{a^2}{m^2} - 1} }},\,{{ - 1} \over {\sqrt {{a^2}{m^2} - 1} }}} \right)$$
If a tangent to a suitable conic (Column 1) is found to be y = x + 8 and its point of contact is (8, 16), then which of the following options is the only CORRECT combination?
A
(III) (i) (P)
B
(I) (ii) (Q)
C
(II) (iv) (R)
D
(III) (ii) (Q)
4
JEE Advanced 2014 Paper 2 Offline
+3
-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
$${{{t^2} - 1} \over t}$$
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