1
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 8th April Morning Slot

Consider an ellipse, whose center is at the origin and its major axis is along the x-axis. If its eccentricity is $${3 \over 5}$$ and the distance between its foci is 6, then the area (in sq. units) of the quadrilatateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :
A
8
B
32
C
80
D
40

Explanation

e = 3/5 & 2ae = 6  $$ \Rightarrow $$   a = 5

$$ \because $$   b2 = a2 (1 $$-$$ e2)

$$ \Rightarrow $$   b2 = 25(1 $$-$$ 9/25)


$$ \Rightarrow $$   b = 4

$$ \therefore $$   area of required quadrilateral

= 4(1/2 ab) = 2ab = 40
2
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 9th April Morning Slot

If y = mx + c is the normal at a point on the parabola y2 = 8x whose focal distance is 8 units, then $$\left| c \right|$$ is equal to :
A
$$2\sqrt 3 $$
B
$$8\sqrt 3 $$
C
$$10\sqrt 3 $$
D
$$16\sqrt 3 $$

Explanation

c = $$-$$ 29m $$-$$ 9m3

a = 2

Given (at2 $$-$$ a)2 + 4a2t2 = 64

$$ \Rightarrow $$   (a(t2 + 1)) = 8

$$ \Rightarrow $$   t2 + 1 = 4 $$ \Rightarrow $$ t2 = 3

$$ \Rightarrow $$   t = $$\sqrt 3 $$

$$ \therefore $$   c = 2at(2 + t2)

= $$2\sqrt 3 \left( 5 \right)$$

$$\left| c \right|$$ = 10$$\sqrt 3 $$
3
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 9th April Morning Slot

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, −1) and (−2, 2) is :
A
$${1 \over 2}$$
B
$${2 \over {\sqrt 5 }}$$
C
$${{\sqrt 3 } \over 2}$$
D
$${{\sqrt 3 } \over 4}$$

Explanation

Centre at (0, 0)

$${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}}$$ = 1

at point (4, $$-$$ 1)

$${{16} \over {{a^2}}} + {1 \over {{b^2}}}$$ = 1

$$ \Rightarrow $$   16b2 + a2 = a2b2         . . . .(i)

at point ($$-$$ 2, 2)

$${4 \over {{a^2}}} + {4 \over {{b^2}}} = 1$$

$$ \Rightarrow $$   4b2 + 4a2 = a2b2          . . . .(ii)

$$ \Rightarrow $$   16b2 + a2 = 4a2 + 4b2

From equations (i) and (ii)

$$ \Rightarrow $$   3a2 = 12b2

$$ \Rightarrow $$   a2 = 4b2

b2 = a2(1 $$-$$ e2)

$$ \Rightarrow $$   e2 = $${3 \over 4}$$

$$ \Rightarrow $$   e = $${{\sqrt 3 } \over 2}$$
4
MCQ (Single Correct Answer)

JEE Main 2018 (Offline)

Tangents are drawn to the hyperbola 4x2 - y2 = 36 at the points P and Q.

If these tangents intersect at the point T(0, 3) then the area (in sq. units) of $$\Delta $$PTQ is :
A
$$36\sqrt 5 $$
B
$$45\sqrt 5 $$
C
$$54\sqrt 3 $$
D
$$60\sqrt 3 $$

Explanation



Here PQ is the chord of contact.

Equation of PQ is

x.0 $$-$$ y.3 = 36

$$ \Rightarrow \,\,\,\,y = - 12$$

Putting value of y = $$-$$ 12 in the equation

4x2 $$-$$ y2 = 36

we get , 4x2 $$-$$ 144 = 36

$$ \Rightarrow \,\,\,\,4{x^2}\, = \,180$$

$$ \Rightarrow \,\,\,\,\,{x^2}\,\, = \,\,45$$

$$ \Rightarrow \,\,\,\,x = \pm \,3\sqrt 5 $$

$$\therefore\,\,\,$$ Coordinate of $$P = \left( { - 3\sqrt 5 , - 12} \right)$$ and

Coordinate of $$Q = \left( {3\sqrt 5 , - 12} \right)$$

$$\therefore\,\,\,$$ Length of PQ $$ = 3\sqrt 5 + 3\sqrt 5 $$

$$ = 6\sqrt 5 .$$

TM is the height of the triangle Length of TM = 12 + 3 = 15

$$\therefore\,\,\,$$ Area of $$\Delta PQT$$ = $${1 \over 2} \times 6\sqrt 5 \times 15$$

$$ = 45\sqrt 5 $$ sq. units

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

Medical

NEET