1

JEE Advanced 2019 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let the circles

C

(i) Centre of C

(ii) C

(iii) C

Let the line through X and Y intersect C

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?

C

_{1}: x^{2}+ y^{2}= 9 and C_{2}: (x $$-$$ 3)^{2}+ (y $$-$$ 4)^{2}= 16, intersect at the points X and Y. Suppose that another circle C_{3}: (x $$-$$ h)^{2}+ (y $$-$$ k)^{2}= r^{2}satisfies the following conditions :(i) Centre of C

_{3}is collinear with the centres of C_{1}and C_{2}.(ii) C

_{1}and C_{2}both lie inside C_{3}and(iii) C

_{3}touches C_{1}at M and C_{2}at N.Let the line through X and Y intersect C

_{3}at Z and W, and let a common tangent of C_{1}and C_{3}be a tangent to the parabola x^{2}= 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?

2

JEE Advanced 2019 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let the circle C

(i) centre of C

(ii) C

(iii) C

Let the line through X and Y intersect C

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?

_{1}: x^{2}+ y^{2}= 9 and C_{2}: (x $$-$$ 3)^{2}+ (y $$-$$ 4)^{2}= 16, intersect at the points X and Y. Suppose that another circle C_{3}: (x $$-$$ h)^{2}+ (y $$-$$ k)^{2}= r^{2}satisfies the following conditions :(i) centre of C

_{3}is collinear with the centers of C_{1}and C_{2}.(ii) C

_{1}and C_{2}both lie inside C_{3}, and(iii) C

_{3}touches C_{1}at M and C_{2}at N.Let the line through X and Y intersect C

_{3}at Z and W, and let a common tangent of C_{1}and C_{3}be a tangent to the parabola x^{2}= 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?

3

JEE Advanced 2017 Paper 1 Offline

MCQ (Single Correct Answer)

+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.

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?

4

JEE Advanced 2014 Paper 2 Offline

MCQ (Single Correct Answer)

+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

Questions Asked from Parabola (MCQ (Single Correct Answer))

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