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JEE • MATHEMATICS • STRAIGHT LINES

Straight lines practice · Easy

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These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 61-90 of 408 questions

61 Easy

61 of 408

Application +4 | -1

If the lines

x=a+m, y=-2

and

y=m x

are concurrent, the least value of

|a|

is :

View answer and explanation

Correct option: C

2 \sqrt{2}

Option C (

2 \sqrt{2}

) is correct because the condition for concurrency leads to a quadratic equation in 'm' which must have real roots, thus giving the least value of |a| as

2 \sqrt{2}

62 Easy

62 of 408

Application +4 | -1

The line passing through

(1,1)

and parallel to the line

2 x-3 y+5=0

View answer and explanation

Correct option: B

2 x-3 y+1=0

Option B (

2 x-3 y+1=0

) is correct because it has the same slope as the given line and passes through the point (1,1).

63 Easy

63 of 408

Application +4 | -1

The distance of the line

2x - 3y = 4

from the point (1, 1) measured parallel to the line

x + y = 1

, is

View answer and explanation

Correct option: A

\sqrt 2

Option A (

\sqrt 2

) is correct because it represents the distance calculated by finding the intersection point of the two lines and using the given angle.

64 Easy

64 of 408

Application +4 | -1

The set of all values of

\mathrm{k}

for which lines

k x+2 y+2=0,2 x+k y+3=0,3 x+3 y+k=0

are concurrent is

View answer and explanation

Correct option: B

\{2,3,-5\}

Option B ({2,3,-5}) is correct because these are the values of k for which the determinant of the coefficient matrix is zero, indicating concurrency, but k=2 makes the first two lines parallel.

65 Easy

65 of 408

Application +4 | -1

The angle between the lines whose joint equation is

2 x^2-3 x y-6 y^2=0

, is

View answer and explanation

Correct option: B

\theta=\tan ^{-1}\left(-\frac{\sqrt{57}}{4}\right)

Option B (

\theta=\tan ^{-1}\left(-\frac{\sqrt{57}}{4}\right)

) is correct because it is the angle calculated using the formula for the angle between two lines represented by a homogeneous equation.

66 Easy

66 of 408

Application +4 | -1

The equation of the bisector of that angle between the lines

x+y=3

and

2 x-y=2

which contains the point

(1,1)

View answer and explanation

Correct option: A

(\sqrt{5}-2 \sqrt{2}) x+(\sqrt{5}+\sqrt{2}) y-3 \sqrt{5}+2 \sqrt{2}=0

Option A (

\sqrt{5}-2 \sqrt{2}) x+(\sqrt{5}+\sqrt{2}) y-3 \sqrt{5}+2 \sqrt{2}=0

) is correct because it represents the angle bisector that contains the point (1,1) after proper normalization.

67 Easy

67 of 408

Analyzing +4 | -1

Equation of the straight line which belongs to the system of straight lines

a(2 x+y-3)+b(3 x+2 y-5)=0

and is farthest from the point

(4,-3)

View answer and explanation

Correct option: B

3 x-4 y+1=0

Option B (

3x - 4y + 1 = 0

) is correct because it represents the line in the system farthest from the point (4, -3), which is perpendicular to the line joining (1,1) and (4,-3).

68 Easy

68 of 408

Application +4 | -1

The angle between the lines represented by the equation

x^2-2 p x y+y^2=0

, is

View answer and explanation

Correct option: A

\sec ^{-1} p

Option A (

\sec ^{-1} p

) is correct because it is calculated using the formula for the angle between the lines and trigonometric identities.

69 Easy

69 of 408

Application +4 | -1

The line parallel to the

X

-axis and passing through the intersection of the lines

a x+2 b y+3 b=0

and

b x-2 a y-3 a=0,

where

(a, b) \neq(0,0)

View answer and explanation

Correct option: A

Below the

X

-axis at a distance of

\frac{3}{2}

from it

Option A Below the

X

-axis at a distance of

\frac{3}{2}

from it is correct because the line parallel to the X-axis is found to be y = -3/2.

70 Easy

70 of 408

Analyzing +4 | -1

The points

\left(0, \frac{8}{3}\right),(1,3)

and

(82,30)

View answer and explanation

Correct option: C

lie on a straight line.

Option C (lie on a straight line) is correct because the slope between any two pairs of points is the same, indicating collinearity.

71 Easy

71 of 408

Application +4 | -1

The line joining the points

(2, x)

and

(3,1)

is perpendicular to the line joining the points

(x, 4)

and

(7,5)

. The value of

x

View answer and explanation

Correct option: C

Option C (4) is correct because the product of the slopes of two perpendicular lines is -1, which leads to the equation (1-x)/(3-2) * (5-4)/(7-x) = -1, solving for x gives x=4.

72 Easy

72 of 408

Analyzing +4 | -1

Let equation of the side

BC

of a

\Delta \;ABC

x + y + 2 = 0.

If coordinates of its orthocentre and circumcentre are (1, 1) and (2, 0) respectively, then radius of the circumcircle of

\Delta \;ABC

View answer and explanation

Correct option: B

\sqrt {10}

Option B (

\sqrt {10}

) is correct because the radius of the circumcircle is calculated using the distance between the circumcenter and a point on the circumcircle, which is the reflection of the orthocenter in side BC.

73 Easy

73 of 408

Application +4 | -1

The orthocentre of the triangle formed by

\left( {0,0} \right),\left( {8,0} \right),\left( {4,6} \right)

View answer and explanation

Correct option: A

\left( {4,\;8/3} \right)

Option A (

\left( {4,\;8/3} \right)

) is correct because it represents the intersection of the altitudes of the triangle.

74 Easy

74 of 408

Application +4 | -1

The acute angle between the lines joining the origin to the points of intersection of the line

\sqrt 3 x + y = 2

and the circle

{x^2} + {y^2} = 4

View answer and explanation

Correct option: B

\mathrm{\pi }/3

Option B (

\mathrm{\pi }/3

) is correct because the acute angle is calculated by finding the intersection points and their respective angles with the origin.

75 Easy

75 of 408

Application +4 | -1

The range of values of

\theta

in the interval

(0, \pi)

such that the points

(3,2)

and

(\cos \theta, \sin \theta)

lie on the same side of the line

x+y-1=0

, is

View answer and explanation

Correct option: A

\left(0, \frac{\pi}{2}\right)

Option A

\left(0, \frac{\pi}{2}\right)

is correct because the values of

\theta

in this interval ensure that both points lie on the same side of the line x+y-1=0.

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76 Easy

76 of 408

Analyzing +4 | -1

Equation of straight line belonging to families of straight lines

\left( {x + 2y} \right) + \lambda \left( {3x + 2y + 1} \right) = 0

and

\left( {x - 2y} \right) + \mathrm{\mu }\left( {x - y + 1} \right) = 0

View answer and explanation

Correct option: B

5x - 6y + 4 = 0

Option B (

5x - 6y + 4 = 0

) is correct because it represents the equation of the straight line passing through the intersection points of the two families of lines.

77 Easy

77 of 408

Application +4 | -1

{x_1},\;\;{x_2},\;\;{x_3}

and

{y_1},\;\;{y_2},\;\;{y_3}

are both in GP with the same common ratio, then the points

\left( {{x_1},\;{y_1}} \right),\;\left( {{x_2},\;{y_2}} \right),\;\left( {{x_3},\;{y_3}} \right)

View answer and explanation

Correct option: A

Lie on a straight line

Option A (Lie on a straight line) is correct because the area of the triangle formed by the points is zero, indicating collinearity.

78 Easy

78 of 408

Application +4 | -1

The equation of the line equidistant from the lines

2x + 3y + 5 = 0

and

4x + 6y = 11

View answer and explanation

Correct option: C

8x + 12y - 1 = 0

The correct answer is C (8x + 12y - 1 = 0) because it represents a line equidistant from the two given parallel lines, found by averaging their constant terms.

79 Easy

79 of 408

Application +4 | -1

The point

(2,1)

is translated parallel to the line

L: x-y=4

2 \sqrt{3}

units. If the new point

Q

lies in the third quadrant, then the equation of the line passing through

Q

and perpendicular to

L

, is

View answer and explanation

Correct option: D

x+y=3-2 \sqrt{6}

Option D (

x+y=3-2 \sqrt{6}

) is correct because it is the equation of the line passing through the translated point Q in the third quadrant and perpendicular to the given line L.

80 Easy

80 of 408

Application +4 | -1

A(3,-1), B(1,3), C(2,4)

are vertices of

\triangle A B C

. If

D

is the centroid of

\triangle A B C

and

P

is the point of intersection of lines

x+3 y-1=0

and

3 x-y+1=0

, then which of the following points lies on the line joining

D

and

P

View answer and explanation

Correct option: B

(-9,-6)

Option B ((-9,-6)) is correct because the point lies on the line formed by the centroid and the intersection point of the given lines.

81 Easy

81 of 408

Application +4 | -1

The vertices of a triangle are

\left(a b, \frac{1}{a b}\right)

\left(b c, \frac{1}{b c}\right)

and

\left(c a, \frac{1}{c a}\right)

where

a, b, c

are the roots of the equation

x^3-3 x^2+6 x+1=0

. The coordinates of its centroid are

View answer and explanation

Correct option: B

(2,-1)

Option B ((2,-1)) is correct because the centroid coordinates are found by averaging the x and y coordinates of the vertices, and using Vieta's formulas.

82 Easy

82 of 408

Application +4 | -1

The line

(\lambda+1)^2 x+\lambda y-2 \lambda^2-2=0

passes through a point regardless of the value

\lambda

. Which of the following is the line with slope 2 passing through the point?

View answer and explanation

Correct option: A

y=2 x-8

Option A

y=2 x-8

is correct because it is the equation of the line with slope 2 that passes through the fixed point of the given family of lines.

83 Easy

83 of 408

Application +4 | -1

Area of square having two sides

y=x+1

and

y=x+2

View answer and explanation

Correct option: A

\frac{1}{2}

Option A,

\frac{{1}}{{2}}

, is correct because the area of the square is calculated by finding the distance between the parallel lines and squaring it.

84 Easy

84 of 408

Application +4 | -1

The co-ordinates of the foot of perpendicular from the point

(2,3)

on the line

x+y-11=0

are

(x, y)

. Find

x+y

View answer and explanation

Correct option: A

The correct answer is A (11) because it is the sum of the coordinates of the foot of the perpendicular from the point (2,3) on the line x+y-11=0.

85 Easy

85 of 408

Analyzing +4 | -1

Consider three points

P=(-\sin (\beta-\alpha),-\cos \beta)

Q=(\cos (\beta-\alpha), \sin \beta)

and

R(\cos (\beta-\alpha+\theta), \sin (\beta-\theta))

, where

0 < \theta, \alpha, \beta < \frac{\pi}{4}

. Then,

View answer and explanation

Correct option: D

P, Q, R

are non-collinear

Option D (

P, Q, R

are non-collinear) is correct because point R can be expressed as a linear combination of the coordinates of P and Q, but it doesn't lie on the line segment PQ.

86 Easy

86 of 408

Understanding +4 | -1

Consider the following statements.

I. Equation of the line passing through

(0,0)

with slope

{m}

{y}={mx}

II. Equation of the

{x}

-axis is

{x}=0

.
Choose the correct option.

View answer and explanation

Correct option: A

Only I is true

Option A is correct because only statement I is true; statement II incorrectly states the equation of the x-axis.

87 Easy

87 of 408

Analyzing +4 | -1

Given four lines with equations

x + 2y - 3 = 0,\;2x + 3y - 4 = 0,\;3x + 4y - 5 = 0,\;

4x + 5y - 6 = 0

These lines are

View answer and explanation

Correct option: A

Concurrent

Option A (Concurrent) is correct because all four lines intersect at a single point.

88 Easy

88 of 408

Application +4 | -1

A straight line

L

through the point

(3,-2)

is inclined at an angle of

60^{\circ}

to the line

\sqrt{3} x+y=1

. If L also intersects the

x

-axis, then the equation of

L

, is

View answer and explanation

Correct option: B

y-\sqrt{3} x+2+3 \sqrt{3}=0

Option B (

y-\sqrt{3} x+2+3 \sqrt{3}=0

) is correct because it represents a line passing through (3, -2) and inclined at 60 degrees to the given line, and it also intersects the x-axis.

89 Easy

89 of 408

Understanding +4 | -1

u=a_1 x+b_1 y+c_1=0, v=a_2 x+b_2 y+c_2=0

and

\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}

, then

u+k v=0

represents

View answer and explanation

Correct option: B

a family of parallel line

Option B (a family of parallel line) is correct because the condition

\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}

indicates that the lines are parallel, and

u+kv=0

represents a family of lines parallel to them.

90 Easy

90 of 408

Application +4 | -1

Assertion: The distance between the parallel lines

3 x-4 y+9=0 \text { and } 6 x-8 y-15=0 \text { is } \frac{33}{10}

Reason: Distance between the parallel lines

{Ax}+{By}+{C}_1=0

and

{Ax}+{By}+{C}_2=0

, is given by

{d}=\frac{\left|{C}_1-{C}_2\right|}{\sqrt{{A}^2+{B}^2}}

View answer and explanation

Correct option: A

Assertion is correct, reason is correct; reason is a correct
explanation for assertion

Option A is correct because the assertion is true, the reason is true, and the reason correctly explains the assertion, as shown by calculating the distance between the parallel lines.

Revision notes and key takeaways

Review STRAIGHT LINES in your textbook or class notes, then use this set to check your understanding.

Showing 61-90 of 408 questions

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