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JEE Mains Previous Years Questions with Solutions

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1

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)
A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching $$X$$-axis, the equation of the reflected ray is
A
$$y = x + \sqrt 3 $$
B
$$\sqrt 3 y = x - \sqrt 3 $$
C
$$y = \sqrt 3 x - \sqrt 3 $$
D
$$\sqrt 3 y = x - 1$$

Explanation

$$x + \sqrt 3 y = \sqrt 3 $$ or $$y = - {1 \over {\sqrt 3 }}x + 1$$

Let $$\theta$$ be the angle which the line makes with the positive x-axis.

$$\therefore$$ $$\tan \theta = - {1 \over {\sqrt 3 }} = \tan \left( {\pi - {\pi \over 6}} \right)$$ or $$\theta = \pi - {\pi \over 6}$$

$$\therefore$$ $$\angle ABC = {\pi \over 6}$$; $$\therefore$$ $$\angle DBE = {\pi \over 6}$$

$$\therefore$$ the equation of the line BD is,

$$y = \tan {\pi \over 6}x + c$$ or $$y = {x \over {\sqrt 3 }} + c$$ ..... (1)

The line $$x + \sqrt 3 y = \sqrt 3 $$ intersects the x-axis at $$B(\sqrt 3 ,0)$$ and, the line (1) passes through $$B(\sqrt 3 ,0)$$.

$$\therefore$$ $$0 = {{\sqrt 3 } \over {\sqrt 3 }} + c$$ or, c = $$-$$1

Hence, the equation of the reflected ray is,

$$y = {x \over {\sqrt 3 }} - 1$$ or $$y\sqrt 3 = x - \sqrt 3 $$

2

AIEEE 2012

MCQ (Single Correct Answer)
If the line $$2x + y = k$$ passes through the point which divides the line segment joining the points $$(1, 1)$$ and $$(2, 4)$$ in the ratio $$3 : 2$$, then $$k$$ equals :
A
$${{29 \over 5}}$$
B
$$5$$
C
$$6$$
D
$${{11 \over 5}}$$

Explanation

The point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2 is

$$ = \left( {{{3 \times 2 + 2 \times 1} \over {3 + 2}},{{3 \times 4 + 2 \times 1} \over {3 + 2}}} \right)$$

$$ = \left( {{{6 + 2} \over 5},{{12 + 2} \over 5}} \right) = \left( {{8 \over 5},{{14} \over 5}} \right)$$

Since the line 2x + y = k passes through this point,

$$\therefore$$ $$2 \times {8 \over 5} + {{14} \over 5} = k$$ or $${{30} \over 5} = k$$ or, k = 6

3

AIEEE 2011

MCQ (Single Correct Answer)
The lines $${L_1}:y - x = 0$$ and $${L_2}:2x + y = 0$$ intersect the line $${L_3}:y + 2 = 0$$ at $$P$$ and $$Q$$ respectively. The bisector of the acute angle between $${L_1}$$ and $${L_2}$$ intersects $${L_3}$$ at $$R$$.

Statement-1: The ratio $$PR$$ : $$RQ$$ equals $$2\sqrt 2 :\sqrt 5 $$
Statement-2: In any triangle, bisector of an angle divide the triangle into two similar triangles.

A
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
B
Statement-1 is true, Statement-2 is false.
C
Statement-1 is false, Statement-2 is true.
D
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Explanation



$${L_1}:y - x = 0$$

$${L_2}:2x + y = 0$$

$${L_3}:y + 2 = 0$$

On solving the equation of line $${L_1}$$ and $${L_2}$$ we get their point of

intersection $$(0, 0)$$ i.e., origin $$O.$$

On solving the equation of line $${L_1}$$ and $${L_3},$$

we get $$P=(-2, -2).$$

Similarly, we get $$Q = \left( { - 1, - 2} \right)$$

We know that bisector of an angle of a triangle, divide the opposite side the triangle in the ratio of the sides including the angle [ Angle Bisector Theorem of a Triangle ]

$$\therefore$$ $${{PR} \over {RQ}} = {{OP} \over {OQ}} = {{\sqrt {{{\left( { - 2} \right)}^2} + {{\left( { - 2} \right)}^2}} } \over {\sqrt {{{\left( { - 1} \right)}^2} + {{\left( { - 2} \right)}^2}} }}$$

$$ = {{2\sqrt 2 } \over {\sqrt 5 }}$$
4

AIEEE 2010

MCQ (Single Correct Answer)
The line $$L$$ given by $${x \over 5} + {y \over b} = 1$$ passes through the point $$\left( {13,32} \right)$$. The line K is parrallel to $$L$$ and has the equation $${x \over c} + {y \over 3} = 1.$$ Then the distance between $$L$$ and $$K$$ is
A
$$\sqrt {17} $$
B
$${{17} \over {\sqrt {15} }}$$
C
$${{23} \over {\sqrt {17} }}$$
D
$${{23} \over {\sqrt {15} }}$$

Explanation

Slope of line $$L = - {b \over 5}$$

Slope of line $$K = - {3 \over c}$$

Line $$L$$ is parallel to line $$k.$$

$$ \Rightarrow {b \over 5} = {3 \over c} \Rightarrow bc = 15$$

$$(13,32)$$ is a point on $$L.$$

$$\therefore$$ $${{13} \over 5} + {{32} \over b} = 1 \Rightarrow {{32} \over b} = - {8 \over 5}$$

$$ \Rightarrow b = - 20 \Rightarrow c = - {3 \over 4}$$

Equation of $$K:$$ $$y - 4x = 3$$

$$\,\,\,\,\,\,\,\,\,\,\,$$ $$ \Rightarrow 4x - y + 3 = 0$$

Distance between $$L$$ and $$K$$

$$ = {{\left| {52 - 32 + 3} \right|} \over {\sqrt {17} }} = {{23} \over {\sqrt {17} }}$$

Questions Asked from Straight Lines and Pair of Straight Lines

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

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