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Explore popular questions from Straight Lines for JEE Main. This collection covers Straight Lines previous year JEE Main questions hand picked by experienced teachers.

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Q 1. The number of integral values of {tex} m , {/tex} for which the {tex} x {/tex} -coordinate of the point of intersection of the lines {tex} 3 x + 4 y = 9 {/tex} and {tex} y = m x + 1 {/tex} is also an integer is

2

B

0

C

4

D

1

Explanation

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Q 2. If the coordinates of the middle point of the portion of a line intercepted between coordinate axes {tex} ( 3,2 ) , {/tex} then the equation of the line will be

{tex} 2 x + 3 y = 12 {/tex}

B

{tex} 3 x + 2 y = 12 {/tex}

C

{tex} 4 x - 3 y = 6 {/tex}

D

{tex} 5 x - 2 y = 10 {/tex}

Explanation




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Q 3. A line through point {tex} A ( - 5 , - 4 ) {/tex} meets the lines {tex} x + 3 y + 2 = 0, {/tex} {tex} 2 x + y + 4 = 0 {/tex} and {tex} x - y - 5 = 0 {/tex} at points {tex} B , C {/tex} and {tex} D , {/tex} respectively. If {tex} \left( \frac { 15 } { \mathrm { AB } } \right) ^ { 2 } + \left( \frac { 10 } { \mathrm { AC } } \right) ^ { 2 } = \left( \frac { 6 } { \mathrm { AD } } \right) ^ { 2 } , {/tex} then the equation of the line is

{tex} 2 x + 3 y + 22 = 0 {/tex}

B

{tex} 5 x - 4 y + 7 = 0 {/tex}

C

{tex} 3 x - 2 y + 3 = 0 {/tex}

D

None of these

Explanation





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Q 4. The equation of perpendicular bisectors of sides {tex} A B {/tex} and {tex} A C {/tex} of a triangle {tex} A B C {/tex} are {tex} x - y + 5 = 0 {/tex} and {tex} x + 2 y = 0 {/tex} , respectively. If point {tex} A {/tex} is {tex} ( 1 , - 2 ) , {/tex} then the equation of line {tex} B C {/tex} is

A

{tex} 23 x + 14 y - 40 = 0 {/tex}

B

{tex} 14 x - 23 y + 40 = 0 {/tex}

C

{tex} 23 x - 14 y + 40 = 0 {/tex}

{tex} 14 x + 23 y - 40 = 0 {/tex}

Explanation





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Q 5. The medians {tex} A D {/tex} and {tex} B E {/tex} of a triangle with vertices {tex} A ( 0 , b ) , B ( 0,0 ) {/tex} and {tex} C ( a , 0 ) {/tex} are perpendicular to each other if

A

{tex} a = \sqrt { 2 b } {/tex}

B

{tex} a = - \sqrt { 2 } b {/tex}

Both {tex} ( \mathrm { A } ) {/tex} and {tex} ( \mathrm { B } ) {/tex}

D

None of these

Explanation


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Q 6. Let {tex} P S {/tex} be the median of the triangle with vertices {tex} P ( 2,2 ) , Q ( 6 , - 1 ) {/tex} and {tex} R ( 7,3 ) . {/tex} Then the equation of the line passing through {tex} ( 1 , - 1 ) {/tex} and parallel to {tex} P S {/tex} is

A

{tex} 2 x - 9 y - 7 = 0 {/tex}

B

{tex} 2 x - 9 y - 11 = 0 {/tex}

C

{tex} 2 x + 9 y - 11 = 0 {/tex}

{tex} 2 x + 9 y + 7 = 0 {/tex}

Explanation




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Q 7. The equation of straight line passing through {tex} ( - a , 0 ) {/tex} and making the triangle with axes of area {tex} T {/tex} is

A

{tex} 2 T x + a ^ { 2 } y + 2 a T = 0 {/tex}

{tex} 2 T x - a ^ { 2 } y + 2 a T = 0 {/tex}

C

{tex} 2 T x - a ^ { 2 } y - 2 a T = 0 {/tex}

D

None of these

Explanation



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Q 8. The equations of two equal sides of an isosceles triangle are {tex} 7 x - y + 3 = 0 {/tex} and {tex} x + y - 3 = 0 {/tex} and the third side passes through the point {tex} ( 1 , - 10 ) {/tex} . The equation of the third side is

A

{tex} y = \sqrt { 3 } x + 9 {/tex} but not {tex} x ^ { 2 } - 9 y ^ { 2 } = 0 {/tex}

B

{tex} 3 x + y + 7 = 0 {/tex} but not {tex} x - 3 y - 31 = 0 {/tex}

{tex} 3 x + y + 7 = 0 {/tex} or {tex} x - 3 y - 31 = 0 {/tex}

D

Neither {tex} 3 x + y + 7 {/tex} nor {tex} x - 3 y - 31 = 0 {/tex}

Explanation



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Q 9. If the equation of base of an equilateral triangle is {tex} 2 x - y = 1 {/tex} and the vertex is {tex} ( - 1,2 ) , {/tex} then the length of the side of the triangle is

{tex} \sqrt { \frac { 20 } { 3 } } {/tex}

B

{tex} \frac { 2 } { \sqrt { 15 } } {/tex}

C

{tex} \sqrt { \frac { 8 } { 15 } } {/tex}

D

{tex} \sqrt { \frac { 15 } { 2 } } {/tex}

Explanation




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Q 10. If {tex} x _ { 1 } , x _ { 2 } , x _ { 3 } {/tex} and {tex} y _ { 1 } , y _ { 2 } , y _ { 3 } {/tex} are both in GP, with the same common ratio, then the points {tex} \left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right) {/tex} and {tex} \left( x _ { 3 } , y _ { 3 } \right) {/tex}

Lie on a straight line

B

Lie on an ellipse

C

Lie on a circle

D

Are vertices of a triangle

Explanation

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Q 11. In what direction a line be drawn through the point {tex} ( 1,2 ) {/tex} so that its points of intersection with the line {tex} x + y = 4 {/tex} is at a distance {tex} \sqrt { 6 } / 3 {/tex} from the given point

A

{tex} 30 ^ { \circ } {/tex}

B

{tex} 45 ^ { \circ } {/tex}

C

{tex} 60 ^ { \circ } {/tex}

{tex} 75 ^ { \circ } {/tex}

Explanation





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Q 12. If straight lines {tex} a x + b y + p = 0 {/tex} and {tex} x \cos \alpha + y \sin \alpha - p = 0 {/tex} include an angle {tex} \pi / 4 {/tex} between them and meet the straight line {tex} x \sin \alpha - y \cos \alpha = 0 {/tex} in the same point, then the value of {tex} a ^ { 2 } + b ^ { 2 } {/tex} is equal to

A

1

2

C

3

D

4

Explanation





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Q 13. Given vertices {tex} A ( 1,1 ) , B ( 4 , - 2 ) {/tex} and {tex} C ( 5,5 ) {/tex} of a triangle, then the equation of the perpendicular dropped from {tex} C {/tex} to the the the interior bisector of the angle {tex} A {/tex} is

A

{tex} y - 5 = 0 {/tex}

{tex} x - 5 = 0 {/tex}

C

{tex} y + 5 = 0 {/tex}

D

{tex} x + 5 = 0 {/tex}

Explanation



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Q 14. The equation of the line joining the point {tex} ( 3,5 ) {/tex} to the point of intersection of the lines {tex} 4 x + y - 1 = 0 {/tex} and {tex} 7 x - 3 y - 35 = 0 {/tex} is equidistant from the points {tex} ( 0,0 ) {/tex} and {tex} ( 8,34 ) {/tex}

TRUE

B

FALSE

C

Nothing can be said

D

None of these

Explanation

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Q 15. The line {tex} 3 x + 2 y = 24 {/tex} meets {tex} y {/tex} -axis at point {tex} A {/tex} and {tex} x {/tex} -axis at point {tex} B {/tex} . The perpendicular bisector of {tex} A B {/tex} meets the line through {tex} ( 0 , - 1 ) {/tex} parallel to {tex} x {/tex} -axis at point {tex} C . {/tex} The area of the triangle {tex} A B C {/tex} is

A

182 sq. units

91 sq. units

C

48 sq. units

D

None of these

Explanation




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Q 16. The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point {tex} ( a , b ) {/tex} is

{tex} x ^ { 2 } + y ^ { 2 } - a x - b y = 0 {/tex}

B

{tex} x ^ { 2 } + y ^ { 2 } + a x + b y = 0 {/tex}

C

{tex} x ^ { 2 } + y ^ { 2 } - 2 a x - 2 b y = 0 {/tex}

D

None of these

Explanation




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Q 17. The orthocentre of the triangle formed by the lines {tex} x y = 0 {/tex} and {tex} x + y = 1 {/tex} is

{tex}\mathrm{(0,0)}{/tex}

B

{tex} \left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right) {/tex}

C

{tex} \left( \frac { 1 } { 3 } , \frac { 1 } { 3 } \right) {/tex}

D

{tex} \left( \frac { 1 } { 4 } , \frac { 1 } { 4 } \right) {/tex}

Explanation

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Q 18. The lines joining the origin to the points of intersection of the line {tex} y = m x + c {/tex} and the circle {tex} x ^ { 2 } + y ^ { 2 } = a ^ { 2 } {/tex} will be mutually perpendicular if

A

{tex} a ^ { 2 } \left( m ^ { 2 } + 1 \right) = c ^ { 2 } {/tex}

B

{tex} a ^ { 2 } \left( m ^ { 2 } - 1 \right) = c ^ { 2 } {/tex}

{tex} a ^ { 2 } \left( m ^ { 2 } + 1 \right) = 2 c ^ { 2 } {/tex}

D

{tex} a ^ { 2 } \left( m ^ { 2 } - 1 \right) = 2 c ^ { 2 } {/tex}

Explanation



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Q 19. Two of the lines represented by the equation {tex} a y ^ { 4 } + b x y ^ { 3 } + c x ^ { 2 } {/tex} {tex} y ^ { 2 } + d x ^ { 3 } y + e x ^ { 4 } = 0 {/tex} will be perpendicular when

{tex} ( b + d ) ( a d + b e ) + ( e - a ) ^ { 2 } {/tex}
{tex}( a + c + e ) = 0 {/tex}

B

{tex} ( b + d ) ( a d + b e ) + ( e + a ) ^ { 2 } {/tex}
{tex}( a + c + e ) = 0 {/tex}

C

{tex} ( b - d ) ( a d - b e ) + ( e - a ) ^ { 2 }{/tex}
{tex}( a + c + e ) = 0 {/tex}

D

{tex} ( b - d ) ( a d - b e ) + ( e + a ) ^ { 2 }{/tex}
{tex} ( a + c + e ) = 0 {/tex}

Explanation




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Q 20. The equations of the lines which are parallel to the line common to the pair of the lines given by and and at a distance of 7 units from it are

{tex}3x+4y=12{/tex}

B

{tex}5x-4y=7{/tex}

C

{tex}2x-3y=12{/tex}

D

None of these

Explanation

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Q 21. If and are two fixed points, then the locus of a point which moves in such a way that the angle is a right angle is

A circle

B

An ellipse

C

A parabola

D

None of these

Explanation

Let be two fixed points and let be a variable point such that Then,
Slope of AP Slope of


Hence, the locus of is
which is circle having as diameter

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Q 22. The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at is

A

B

D

Explanation

Let the coordinates of point and are and

and


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Q 23. Two of the lines represented by the equation will be perpendicular, then

B

C

D

Explanation

Let
On comparing the coefficient of similar terms, we get

Now,


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Q 24. The line for different values of p and q passes through the fixed point

A

B

C

Explanation

We have,


Clearly, it represents a family of lines passing through the intersection of the lines and
The coordinates of the point of the intersection these two lines are

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Q 25. If 3, 4 are intercepts of a line then the distance of from the origin is

A

5 units

B

12 units

C

unit

unit

Explanation