1
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Morning Slot

Equation of a common tangent to the parabola y2 = 4x and the hyperbola xy = 2 is
A
x + y + 1 = 0
B
4x + 2y + 1 = 0
C
x – 2y + 4 = 0
D
x + 2y + 4 = 0

Explanation

Let the equation of tangent to parabola

y2 = 4x be y = mx + $${1 \over m}$$

It is also a tangent to hyperbola xy = 2

$$ \Rightarrow $$  x$$\left( {mx + {1 \over m}} \right)$$ = 2

$$ \Rightarrow $$  x2m + $${x \over m}$$ $$-$$ 2 = 0

D = 0 $$ \Rightarrow $$   m = $$-$$ $${1 \over 2}$$

So tangent is 2y + x + 4 = 0
2
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Morning Slot

If tangents are drawn to the ellipse x2 + 2y2 = 2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve :
A
$${{{x^2}} \over 2} + {{{y^2}} \over 4} = 1$$
B
$${1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1$$
C
$${1 \over {4{x^2}}} + {1 \over {2{y^2}}} = 1$$
D
$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$

Explanation

Equation of general tangent on ellipse

$${x \over {a\,\sec \theta }} + {y \over {b\cos ec\theta }} = 1$$

$$a = \sqrt 2 ,\,\,b = 1$$

$$ \Rightarrow {x \over {\sqrt 2 \sec \theta }} + {y \over {\cos ec\theta }} = 1$$

Let the midpoint be (h, k)

$$h = {{\sqrt 2 \sec \theta } \over 2} \Rightarrow \cos \theta = {1 \over {\sqrt 2 h}}$$

and $$k = {{\cos ec\theta } \over 2} \Rightarrow \sin \theta = {1 \over {2k}}$$

$$ \because $$  $${\sin ^2}\theta + {\cos ^2}\theta = 1$$

$$ \Rightarrow $$  $${1 \over {2{h^2}}} + {1 \over {4{k^2}}} = 1$$

$$ \Rightarrow $$  $${1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1$$
3
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Evening Slot

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :
A
$${{13} \over 6}$$
B
2
C
$${{13} \over 12}$$
D
$${{13} \over 8}$$

Explanation

2b = 5 and 2ae = 13

b2 = a2(e2 $$-$$ 1) $$ \Rightarrow $$  $${{25} \over 4}$$ = $${{169} \over 4}$$ $$-$$ a2

$$ \Rightarrow $$  a $$=$$ 6 $$ \Rightarrow $$  e $$=$$ $${{13} \over {12}}$$
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Evening Slot

Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it ?
A
$$\left( {4\sqrt 2 ,2\sqrt 3 } \right)$$
B
$$\left( {4\sqrt 3 ,2\sqrt 3 } \right)$$
C
$$\left( {4\sqrt 3 ,2\sqrt 2 } \right)$$
D
$$\left( {4\sqrt 2 ,2\sqrt 2 } \right)$$

Explanation

$${{2{b^2}} \over a} = 8$$ and 2ae $$=$$ 2b

$$ \Rightarrow $$  $${b \over a}$$ = e and 1 $$-$$ e2 = e2 $$ \Rightarrow $$ e $$=$$ $${1 \over {\sqrt 2 }}$$

$$ \Rightarrow $$  b = 4$$\sqrt 2 $$ and a $$=$$ 8

So equation of ellipse is $${{{x^2}} \over {64}} + {{{y^2}} \over {32}} = 1$$

Questions Asked from Conic Sections

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Name Indicates No of Questions
AIEEE 2002 (1)
keyboard_arrow_right
AIEEE 2003 (2)
keyboard_arrow_right
AIEEE 2004 (2)
keyboard_arrow_right
AIEEE 2005 (3)
keyboard_arrow_right
AIEEE 2006 (3)
keyboard_arrow_right
AIEEE 2007 (3)
keyboard_arrow_right
AIEEE 2008 (2)
keyboard_arrow_right
AIEEE 2009 (1)
keyboard_arrow_right
AIEEE 2010 (1)
keyboard_arrow_right
AIEEE 2011 (1)
keyboard_arrow_right
AIEEE 2012 (2)
keyboard_arrow_right
JEE Main 2013 (Offline) (2)
keyboard_arrow_right
JEE Main 2014 (Offline) (2)
keyboard_arrow_right
JEE Main 2015 (Offline) (3)
keyboard_arrow_right
JEE Main 2016 (Offline) (2)
keyboard_arrow_right
JEE Main 2016 (Online) 9th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2016 (Online) 10th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2017 (Offline) (2)
keyboard_arrow_right
JEE Main 2017 (Online) 8th April Morning Slot (5)
keyboard_arrow_right
JEE Main 2017 (Online) 9th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2018 (Offline) (2)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Evening Slot (2)
keyboard_arrow_right
JEE Main 2018 (Online) 16th April Morning Slot (3)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Morning Slot (4)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Evening Slot (4)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Morning Slot (3)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Evening Slot (3)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Evening Slot (3)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Evening Slot (3)
keyboard_arrow_right
JEE Main 2020 (Online) 7th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 7th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 8th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 8th January Evening Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 9th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 9th January Evening Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 2nd September Evening Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Morning Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Evening Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 4th September Morning Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 4th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 5th September Morning Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 5th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 6th September Morning Slot (2)
keyboard_arrow_right
JEE Main 2020 (Online) 6th September Evening Slot (2)
keyboard_arrow_right
JEE Main 2021 (Online) 24th February Morning Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 24th February Evening Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th February Morning Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th February Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Morning Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 17th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 22th July Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Morning Shift (3)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Morning Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 26th August Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 26th August Evening Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 27th August Morning Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 27th August Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 31st August Morning Shift (2)
keyboard_arrow_right

EXAM MAP

Joint Entrance Examination

JEE Advanced JEE Main

Graduate Aptitude Test in Engineering

GATE CE GATE ECE GATE ME GATE IN GATE EE GATE CSE GATE PI

Medical

NEET