1

JEE Advanced 2018 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$, where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60$$^\circ $$ at one of its vertices N. Let the area of the $$\Delta $$LMN be $$4\sqrt 3 $$.

List - I | List - II | ||
---|---|---|---|

P. | The length of the conjugate axis of H is | 1. | 8 |

Q. | The eccentricity of H is | 2. | $${4 \over {\sqrt 3 }}$$ |

R. | The distance between the foci of H is | 3. | $${2 \over {\sqrt 3 }}$$ |

S. | The length of the latus rectum of H is | 4. | 4 |

2

JEE Advanced 2018 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Let S be the circle in the XY-plane defined the equation x

Let E

^{2}+ y^{2}= 4.Let E

_{1}E_{2}and F_{1}F_{2}be the chords of S passing through the point P_{0}(1, 1) and parallel to the X-axis and the Y-axis, respectively. Let G_{1}G_{2}be the chord of S passing through P_{0}and having slope$$-$$1. Let the tangents to S at E_{1}and E_{2}meet at E_{3}, then tangents to S at F_{1}and F_{2}meet at F_{3}, and the tangents to S at G_{1}and G_{2}meet at G_{3}. Then, the points E_{3}, F_{3}and G_{3}lie on the curve3

JEE Advanced 2018 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Let S be the circle in the XY-plane defined the equation x

Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve

^{2}+ y^{2}= 4.Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve

4

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) | $${x^2} - {a^2}{y^2} = {a^2}$$ | $$y = mx + \sqrt {{a^2}{m^2} + 1} $$ | $$\left( {{{ - {a^2}m} \over {\sqrt {{a^2}{m^2} - 1} }},\,{{ - 1} \over {\sqrt {{a^2}{m^2} - 1} }}} \right)$$ |

For $$a = \sqrt 2 $$, if a tangent is drawn to a suitable conic (Column 1) at the point of contact ($$-$$1, 1), then which of the following options is the only CORRECT combination for obtaining its equation?

Questions Asked from Conic Sections (MCQ (Single Correct Answer))

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