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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 1-30 of 408 questions

1 Easy

1 of 408

Analyzing +4 | -1

If the three lines

x-3 y=p, a x+2 y=q

and

a x+y=r

form a right-angled triangle then :

View answer and explanation

Correct option: A

a^{2}-9 a+18=0

Option A (

a^{2}-9 a+18=0

) is correct because it represents the condition where the product of the slopes of two lines is -1, indicating a right-angled triangle.

2 Easy

2 of 408

Application +4 | -1

The distance between the parallel lines

y = 2\;x + 4

and

6x = 3y + 5

View answer and explanation

Correct option: D

17\sqrt 5 /15

Option D (

17\sqrt 5 /15

) is correct because it is the distance between the two parallel lines calculated using the formula.

3 Easy

3 of 408

Application +4 | -1

The distance between the pair of lines given by

{x^2} + {y^2} + 2xy - 8ax - 8ay - 9{a^2} = 0

View answer and explanation

Correct option: D

5\sqrt 2 \,a

Option D (

5\sqrt 2 \,a

) is correct because the distance between the parallel lines is calculated by factoring the given equation and applying the distance formula.

4 Easy

4 of 408

Application +4 | -1

Find the image of the point

(3,8)

with respect of the line

x+3 y=7

assuming the line to be plane mirror:

View answer and explanation

Correct option: B

(-1,-4)

Option C ((-1,-4)) is correct because it is the correct image point calculated using the mirror formula.

5 Easy

5 of 408

Application +4 | -1

The centroid of the triangle whose three sides are given by the combined equation

\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0

View answer and explanation

Correct option: C

\left( { - \frac{7}{3},\frac{2}{3}} \right)

Option C ((-7/3, 2/3)) is correct because it is the centroid calculated from the vertices of the triangle formed by the given lines.

6 Easy

6 of 408

Application +4 | -1

A line

L

passes through the points

(1,1)

and

(2,0)

and another line

L^{\prime}

passes through

\left(\frac{1}{2}, 0\right)

and perpendicular to

L

. Then the area of the triangle formed by the lines

L, L^{\prime}

and

y-

axis, is

N

. Find

16 N

View answer and explanation

Correct option: A

The correct answer is A (25) because it is the value of 16N after finding the area of the triangle formed by the lines L, L', and the y-axis.

7 Easy

7 of 408

Application +4 | -1

The orthocenter of the triangle with vertices

\left( { - 2,\; - 6} \right),\;\left( { - 2,\;4} \right)

and (1, 3) is

View answer and explanation

Correct option: C

(1,3)

Option C (1,3) is correct because the orthocenter of a right-angled triangle is the vertex at the right angle.

8 Easy

8 of 408

Application +4 | -1

Points A(1,3) and C(5,1) are opposite vertices of a rectangle ABCD. If the slope of BD is 2, then its equation is

View answer and explanation

Correct option: A

2\;x - y = 4

Option A (

2x - y = 4

) is correct because the equation of BD is found using the midpoint of AC and the given slope of BD.

9 Easy

9 of 408

Application +4 | -1

If the lines

kx - 2y - 1 = 0

and

6x - 4y - m = 2

are identical (coincident ) lines, then the values of

k

and

m

are

View answer and explanation

Correct option: A

k = 3,\;m = 2

Option A (

k = 3,\;m = 2

) is correct because for identical lines, the ratios of the coefficients must be equal.

10 Easy

10 of 408

Application +4 | -1

All points lying inside the triangle formed by the points (1, 3), (5, 0) and

\left( { - 1,\;2} \right)

satisfy

View answer and explanation

Correct option: D

All of these

Option D (All of these) is correct because all the given inequalities hold true for points inside the triangle formed by the given points.

11 Easy

11 of 408

Application +4 | -1

The equation of a straight line which cut off an intercept of 5 units on negative direction of

Y

-axis and make an angle of

120^{\circ}

with positive direction of

X

-axis, is

View answer and explanation

Correct option: B

y+\sqrt{3} x+5=0

Option B (

y+\sqrt{3} x+5=0

) is correct because the equation of a line is

y = mx + c

, where

m

is the slope and

c

is the y-intercept. Given the angle and y-intercept, we can find the equation.

12 Easy

12 of 408

Application +4 | -1

If the line passing through

(3,4)

and

(x, 5)

makes

135^{\circ}

angle with the positive direction of

x

-axis, then

x=

View answer and explanation

Correct option: B

Option B (2) is correct because the slope calculated from the two points must equal the tangent of the angle (135 degrees), leading to x=2.

13 Easy

13 of 408

Application +4 | -1

If the points (1, 2) and (3, 4) were to be on the same side of the line

3x - 5y + a = 0,\;

, then

View answer and explanation

Correct option: D

a < 7\;\mathrm{or\;}a > 11

Option D (

a < 7\;\mathrm{or\;}a > 11

) is correct because the points (1, 2) and (3, 4) must yield the same sign when plugged into the line equation, leading to the inequality

(a - 7)(a - 11) > 0

14 Easy

14 of 408

Application +4 | -1

If the area of the triangle with vertices

\left( {x,0} \right),\left( {1,1} \right)

and (0, 2) is 4 sq unit, then the value of

x

View answer and explanation

Correct option: C

- 6

Option C (-6) is correct because the area of the triangle is given as 4, and solving the determinant equation yields x = -6.

15 Easy

15 of 408

Application +4 | -1

Let

P S

be the median of the triangle with vertices

P(2,2), Q(6,-1)

and

R(7,3)

. The equation of the line passing through

(1,-1)

and parallel to

P S

2 x+b y+c=0.

Find

b+c

View answer and explanation

Correct option: A

The correct answer is B (16) because it is the value of b+c after finding the equation of the line parallel to PS and passing through (1,-1).

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16 Easy

16 of 408

Application +4 | -1

P

and

Q

are the lengths of the perpendiculars from the origin to the lines

x \cos \theta+y \sin \theta=k \cos 2 \theta

and

x \sec \theta-y \operatorname{cosec} \theta=k

respectively then

View answer and explanation

Correct option: B

p^2+4 q^2=k^2

Option B (

p^2+4 q^2=k^2

) is correct because it is derived by substituting the expressions for p and q into the equation and simplifying using trigonometric identities.

17 Easy

17 of 408

Application +4 | -1

The equation of the straight line which is perpendicular to y=x and passes through (3, 2) is

View answer and explanation

Correct option: B

x + y = 5

Option B (

x + y = 5

) is correct because it represents a line perpendicular to y=x and passes through the point (3, 2).

18 Easy

18 of 408

Application +4 | -1

a,\;b,\;c

are in AP, then the straight line

ax + by + c = 0

will always pass through the point

View answer and explanation

Correct option: B

\left( {1,\; - 2} \right)

Option B ((1, -2)) is correct because the line always passes through this point, which satisfies the condition 2b = a + c for a, b, c in AP.

19 Easy

19 of 408

Application +4 | -1

The angle between the line joining the points

\left( {1,\; - 2} \right),\;\left( {3,\;2} \right)

and the line

x + 2y - 7 = 0

View answer and explanation

Correct option: B

\pi /2

Option B (

\pi /2

) is correct because the product of the slopes of the two lines is -1, indicating they are perpendicular.

20 Easy

20 of 408

Application +4 | -1

The equation of straight line through the intersection of the lines

x - 2y = 1

and

x + 3y = 2

and parallel to

3x + 4y = 0

, is

View answer and explanation

Correct option: C

3x + 4y - 5 = 0

Option C (

3x + 4y - 5 = 0

) is correct because it represents the equation of a line parallel to

3x + 4y = 0

and passing through the intersection of the given lines.

21 Easy

21 of 408

Application +4 | -1

If the

x

-intercept of some line

L

is double as that of the line,

3 x+4 y=12

and the

y

-intercept of

L

is half as that of the same line, then the slope of

L

is :

View answer and explanation

Correct option: D

-3 / 16

Option D (

-3 / 16

) is correct because it is derived from finding the intercepts of line L and calculating the slope.

22 Easy

22 of 408

Application +4 | -1

A line passes through (2,2) and is perpendicular to the line

3\;x + y = 3.

Its y-intercept is

View answer and explanation

Correct option: D

04-Mar

Option D (4/3) is correct because the y-intercept is found by substituting x=0 into the equation of the line perpendicular to the given line and passing through (2,2).

23 Easy

23 of 408

Analyzing +4 | -1

A rectangle

A B C D

has its side

A B

parallel to line

y=x

and vertices

A, B

and

D

lie on

y=1, x=2

and

x=-2

respectively. Locus of vertex

C

View answer and explanation

Correct option: C

y=5

The correct answer is C (

y=5

) because the locus of vertex C is found by expressing the coordinates of C in terms of a parameter and eliminating it.

24 Easy

24 of 408

Analyzing +4 | -1

Let

p, q, r

be distinct positive numbers. Three lines

p x+q y+r=0, q x+r y+p=0

and

r x+p y+q=0

are concurrent, if

View answer and explanation

Correct option: C

p^3+q^3+r^3=3 p q r

Option C (

p^3+q^3+r^3=3 p q r

) is correct because the concurrency condition simplifies to this relationship, which is equivalent to

p+q+r=0

p=q=r

. Since p, q, r are distinct,

p+q+r=0

must hold.

25 Easy

25 of 408

Analyzing +4 | -1

If the two lines

x + (a - 1)y = 1\,\mathrm{and}{\kern 1pt} \,2x + {a^2}y = 1,(a \in R - \{ 0,1\} )

are perpendicular, then the distance of their point of intersection from the origin is

View answer and explanation

Correct option: D

\sqrt {\frac{2}{5}}

Option D (

\sqrt{\frac{2}{5}}

) is the correct answer because after finding the value of 'a' using the perpendicularity condition, we solve for the intersection point and calculate its distance from the origin.

26 Easy

26 of 408

Application +4 | -1

p

is the length of the perpendicular from the origin on the line

\frac{x}{a}+\frac{y}{b}=1

and

a^2, p^2, b^2

are in A.P., then

a^4-2 p^2 a^2+2 p^4=

View answer and explanation

Correct option: B

Option B (0) is correct because substituting the expression for p in terms of a and b, and using the A.P. condition, simplifies the given expression to zero.

27 Easy

27 of 408

Application +4 | -1

The area of the figure formed by

a|x|+b|y|+c=0

, is

View answer and explanation

Correct option: B

\frac{2 c^2}{|a b|}

Option B is correct. The figure formed by

a|x|+b|y|+c=0

is a rhombus, and its area is calculated as

\frac{2c^2}{|ab|}

28 Easy

28 of 408

Application +4 | -1

The range of values of

\theta

in the interval

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

such that the points (3,5) and

\left( {\sin \theta ,\cos \theta } \right)

lie on the same side of the line

x + y - 1 = 0

, is

View answer and explanation

Correct option: A

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

The correct answer is A ((0,π/2)) because it's the range of theta values for which both points lie on the same side of the line, determined by the sign of the expression.

29 Easy

29 of 408

Application +4 | -1

The incentre of the triangle with vertices

\left( {1,\;\sqrt 3 } \right),\;\left( {0,\;0} \right)

and (2, 0) is

View answer and explanation

Correct option: D

\left( {1,\frac{1}{{\sqrt 3 }}} \right)

Option D ((

1,\frac{1}{{\sqrt 3 }}}

) is correct because the triangle is equilateral, and the incenter coincides with the centroid, which is easily calculated.

30 Easy

30 of 408

Application +4 | -1

The value of

x

for which the points

(x,-1),(2,1)

and

(4,5)

are collinear, is

View answer and explanation

Correct option: A

Option A (1) is correct because when the points are collinear, the slope between any two pairs of points must be equal, allowing us to solve for x.

Revision notes and key takeaways

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

Key Takeaways

✓ This set contains 408 single-correct-answer MCQs on STRAIGHT LINES.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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