Straight Lines JEE Questions PDF with Solution, Practice Now

Straight Lines JEE Questions: Straight Lines is one of the most important topics of Coordinate Geometry, which is a significant portion in Mathematics for JEE Main and JEE Advanced. It revolves around equations of lines, slopes, intercepts, distance of a point from a line, intersection points, and many other core concepts. 

Straight-line questions challenge the basic conceptual knowledge of a student, along with the analytical approach to problem-solving. In JEE, 1–2 direct questions are asked in JEE Main, and multiple topics are often combined in JEE Advanced straight-line problems. Practicing Straight Lines JEE Questions increases a student’s confidence, speed, and clarifies JEE Main exam patterns.

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Straight Lines JEE Questions

The chapter on straight lines includes topics on the slope of a line, equation of a line (point slope form, slope-intercept form, two-point form), distance, condition of parallelism, perpendicularity, and angle between lines. Straight lines JEE Mains questions are more on the lines of application of formulae and easy calculations, and JEE Advanced straight lines problems are more conceptual in nature. 

They are also used in combination with other coordinate geometry questions. Coordinate geometry PYQs JEE helps students to identify patterns, derive methods to solve difficult problems, and get familiar with the variety and type of questions that can appear in the JEE exam. The chapter on straight lines has good weightage in JEE and can be a scoring chapter if practised well.

Practice Straight Lines JEE Questions

Regular practice ensures that students can approach questions efficiently, avoid common mistakes, and score high marks in both JEE Main and Advanced. Here are some Straight Lines JEE Questions for practice: 

1. If in a triangle ABC, vertex A is (2, 20), circumcenter I is (−1, 2) and the orthocentre H is (1, 4), the coordinates of mid point of side BC are

A. (0, 1/2)
B. (1, 2)
C. (−3/2, −6)
D. (1/3, 8/3)

2. Consider a circle, x² + y² = 1 and point P(1, √3). PAB is a secant drawn from P intersecting circle in A and B (distinct) then range of |PA| + |PB| is

A. [2, 2√2]
B. [2√3, 4]
C. [√3, 4]
D. None of these

3. A rectangle ABCD, A = (0, 0), B = (4, 0), C = (4, 2), D = (0, 2) undergoes the following transformations successively.

(i) f₁(x, y) → (y, x),
(ii) f₂(x, y) → (x + 3y, y),
(iii) f₃(x, y) → ( (x−y)/2 , (x+y)/2 )
The final figure will be
A. a square
B. a rhombus
C. a rectangle
D. a parallelogram

4. The equation of the circle which touches the axis of y at a distance of 4 unit from the origin and cuts the intercept of 6 units from the axis of x.

A. x² + y² + 10x + 8y + 16 = 0
B. x² + y² + 8x + 10y + 61 = 0
C. x² + y² + 20x + 16y + 8 = 0
D. x² + y² + 10x + 8y + 14 = 0

5. If the circumcentre of a triangle lies at the origin and centroid is the middle point of the line joining the points (a² + 1, a² + 1) and (2a, −2a), then the orthocentre lies on the line.

A. y = (a² + 1)x
B. y = 2ax
C. x + y = 0
D. (a − 1)²x − (a + 1)²y = 0

6. The radius of the circle which touches the line x + y = 0 at M(−1, 1) and cuts the circle x² + y² + 6x − 4y + 18 = 0 orthogonally, is

A. 3√2
B. 4√2
C. √2
D. 5√2

7. The area enclosed by 2|x| + |3y| ≤ 6 is

A. 3 sq units
B. 4 sq units
C. 12 sq units
D. 24 sq units

8. A point P lies inside the circles S₁ = x² + y² − 4 = 0 and S₂ = x² + y² − 8x + 7 = 0. The point P moves such that its path encloses the greatest possible area and it is always at a fixed distance from the point (3/2, 0) in its region. The locus of P is:

A. 4x² + 4y² − 12x + 1 = 0
B. 4x² + 4y² + 12x − 1 = 0
C. x² + y² − 3x − 2 = 0
D. x² + y² − 3x + 2 = 0

9. An equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value is

A. y = 2x
B. y = x + 1
C. x + 2y = 5
D. y = 3x − 1

10. If r₁ and r₂ are the radii of smallest and largest circle which passes through (5, 6) and touches the circle (x − 2)² + y² = 4, then r₁r₂ is

A. 4/41
B. 41
C. 5/41
D. 41/6

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Straight Lines JEE Questions PDF with Solution

Download the provided Straight Lines JEE Questions Practice Questions PDF with Answer and Solution. We have also tried to make the preparation of straight lines as easy as possible. The Straight Lines JEE Questions PDF includes easy to hard straight lines JEE Mains questions, JEE Advanced Straight Lines Tough Questions, and all the important coordinate geometry PYQs JEE. All the solutions are given step by step.