1

JEE Advanced 2023 Paper 1 Online

MCQ (More than One Correct Answer)

+4

-2

Let $T_1$ and $T_2$ be two distinct common tangents to the ellipse $E: \frac{x^2}{6}+\frac{y^2}{3}=1$ and the parabola $P: y^2=12 x$. Suppose that the tangent $T_1$ touches $P$ and $E$ at the points $A_1$ and $A_2$, respectively and the tangent $T_2$ touches $P$ and $E$ at the points $A_4$ and $A_3$, respectively. Then which of the following statements is(are) true?

2

JEE Advanced 2019 Paper 1 Offline

MCQ (More than One Correct Answer)

+4

-1

Define the collections {E

$${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$

R

En : ellipse $${{{x^2}} \over {a_n^2}} + {{{y^2}} \over {b_n^2}} = 1$$ of the largest area inscribed in $${R_{n - 1}},n > 1$$;

R

Then which of the following options is/are correct?

_{1}, E_{2}, E_{3}, ...} of ellipses and {R_{1}, R_{2}, R_{3}.....} of rectangles as follows :$${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$

R

_{1}: rectangle of largest area, with sides parallel to the axes, inscribed in E_{1};En : ellipse $${{{x^2}} \over {a_n^2}} + {{{y^2}} \over {b_n^2}} = 1$$ of the largest area inscribed in $${R_{n - 1}},n > 1$$;

R

_{n}: rectangle of largest area, with sides parallel to the axes, inscribed in E_{n}, n > 1.Then which of the following options is/are correct?

3

JEE Advanced 2018 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-1

Consider two straight lines, each of which is tangent to both the circle x

^{2}+ y^{2}= (1/2) and the parabola y^{2}= 4x. Let these lines intersect at the point Q. Consider the ellipse whose centre is at the origin O(0, 0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is $$\sqrt 2 $$, then which of the following statement(s) is (are) TRUE?4

JEE Advanced 2015 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-1

Let $${E_1}$$ and $${E_2}$$ be two ellipses whose centres are at the origin. The major axes of $${E_1}$$ and $${E_2}$$ lie along the $$x$$-axis and the $$y$$-axis, respectively. Let $$S$$ be the circle $${x^2} + {\left( {y - 1} \right)^2} = 2$$. The straight line $$x+y=3$$ touches the curves $$S$$, $${E_1}$$ and $${E_2}$$ at $$P, Q$$ and $$R$$ respectively. Suppose that $$PQ = PR = {{2\sqrt 2 } \over 3}$$. If $${e_1}$$ and $${e_2}$$ are the eccentricities of $${E_1}$$ and $${E_2}$$, respectively, then the correct expression(s) is (are)

Questions Asked from Ellipse (MCQ (Multiple Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

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