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Mathematics - Straight Lines

Practise 109 NTA Abhyas (JEE Main) questions on Straight Lines. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Straight Lines has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 109 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1Let the lengths of the altitudes from the vertices A - 1,1 , B 5,2 , C 3 , - 1 of Δ A B C are p 1 , p 2 , p 3 units respectively, then the v
  2. 2The coordinates of the orthocenter of the triangle that has the coordinates of midpoints of its sides as 0,0 , 1,2 and - 6 ,3 is
  3. 3The maximum value of p for which the lines 3 x - 4 y = 2 , 3 x - 4 y = 12 , 12 x + 5 y = 7 and 12 x + 5 y = p constitute the sides of a rhom
  4. 4Let A x 1 , y 1 , B x 2 , y 2 , C x 3 , y 3 and D x 4 , y 4 are four points which are at equal distance from the lines 3 x - 4 y + 1 = 0 and
  5. 5The maximum negative integral value of b for which the point 2 b + 3 , b 2 lies above the line 3 x - 4 y - a a - 2 = 0 , a R is
  6. 6Let A 2,0 and B - 2,0 are two fixed vertices of ∆ A B C . If the vertex C moves in the first quadrant in such a way that cot ⁡ A + cot ⁡ B =
  7. 7Let the incentre of A B C is I 2 , 5 . If A = 1 , 13 and B = - 4 , 1 , then the sum of the slopes of sides A C and B C is
  8. 8The sum of squares of the abscissas of all the points on the line x + y = 4 that lie at a unit distance from the line 4 x + 3 y - 10 = 0 is
  9. 9If 5 a + 4 b + 20 c = t , then the value of t for which the line a x + b y + c - 1 = 0 always passes through a fixed point is
  10. 10A line passing through the point 2 , 2 encloses an area of 4 s q . u n i t s with coordinate axes. The sum of intercepts made by the line on
  11. 11The distance of the point − 1 , 1 from the line 12 x + 6 = 5 y − 2 is
  12. 12Let in A B C the coordinates of A are 0 , 0 . Internal angle bisector of A B C is x - y + 1 = 0 and mid-point of B C is - 1 , 3 . Then, the
  13. 13Let a + d = c + b and a d = b c , where a , b , c ∈ R + . If the family of lines a 2 x + b 2 y + c 2 + d 2 x = 0 passes through a fixed poin
  14. 14Let the circumcentre of ∆ A B C is S - 1 , 0 and the midpoints of the sides A B and A C are E 1 , - 2 and F - 2 , - 1 respectively, then the
  15. 15The line x = c 2 divides the triangle with vertices 0,0 , 1,1 and 9,1 into two regions. If the area of the two regions is the same, then c i
  16. 16P is a point inside the Δ A B C . Three straight lines parallel to A B , B C and A C are drawn which divides the triangle into six regions.
  17. 17Let 2 a + 2 b + c = 0 , then the equation of the straight line a x + b y + c = 0 which is farthest from the point 1,1 is
  18. 18If the line segment joining P 2,3 and Q 5,7 subtends a right angle at R x , y and the area of P Q R = 2 sq. units, then the maximum number o
  19. 19Let P is a point on the line y + 2 x = 2 and Q and R are two points on the line 3 y + 6 x = 3 . If the triangle P Q R is an equilateral tria
  20. 20The perpendicular bisector of the line segment joining A 1 , 4 and B t , 3 has y -intercept equal to - 4 . Then, the product of all possible
  21. 21If the equal sides A B and A C (each equal to 5 units) of a right-angled isosceles triangle A B C are produced to P and Q such that B P . C
  22. 22Let P a , 0 , Q - 1 , 0 and R 2 , 0 are three given points. If the locus of the point S satisfying the relation S Q 2 + S R 2 = 2 S P 2 is 2
  23. 23If the image of the point M λ , λ 2 on the line x + y = λ 2 is N 0,2 , then the sum of the square of all the possible values of λ is equal t
  24. 24If the point M h , k lie on the line 2 x + 3 y = 5 such that M A - M B is maximum where A 1 , 2 and B 2 , 3 , then the value of h + k is
  25. 25If the vertex opposite to the hypotenuse of a right-angled triangle lies on the straight line 2 x + y - 10 = 0 and the two other vertices ar
  26. 26Let x 2 + y 2 = r 2 and x y = 1 intersect at A and B in the first quadrant. If A B = 14 units, then the square of the distance of A B from t
  27. 27The line through the points m , - 9 and 7 , m has slope m . Then, the x -intercept of this line is
  28. 28If the segment intercepted between the lines x + 6 y - 13 = 0 and x – y + 3 = 0 is bisected at 6,8 , then the square of the length of segmen
  29. 29If the straight lines x + 2 y = 3 , 2 x + 3 y = 5 and k 2 x + ky = - 1 represent a triangle which is right-angled, then the values of k are
  30. 30If the point P 3 a 2 , 1 lies between the two different lines x + y = a and x + y = 2 a , then the least integral value of a is equal to
  31. 31Line L has intercepts a and b on the coordinate axes, when the axes are rotated through a given angle keeping the origin fixed, the same lin
  32. 32The lines represented by the equation x 2 + 2 3 x y + 3 y 2 - 3 x - 3 3 y - 4 = 0 , are
  33. 33The coordinates of the points on the line 3 x + 2 y = 5 which are equidistant from the lines 4 x + 3 y - 7 = 0 and 2 y - 5 = 0 can be
  34. 34Let x 1 , y 1 , x 2 , y 2 , x 3 , y 3 and x 4 , y 4 are four points which are at unit distance from the lines 3 x - 4 y + 1 = 0 and 8 x + 6
  35. 35The point A divides the line segment joining the points ( - 5,1 ) and ( 3,5 ) in the ratio k : 1 internally and the coordinates of points B
  36. 36The line L 1 : x 5 + y b = 1 passes through the point 13 , 32 and is parallel to L 2 : x c + y 3 = 1 . Then, the distance between L 1 and L
  37. 37Let in a ∆ A B C , vertex A , the circumcentre S and the orthocentre H are 1 , 10 , - 1 3 , 2 3 and 11 3 , 4 3 respectively, then mid-point
  38. 38For a ∆ A B C , if B ≡ 3 , 0 , C ≡ - 3 , 0 and the angle B A C is 90 ° , then the locus of the centroid of the triangle is
  39. 39If the area of the rhombus enclosed by the lines x ± y ± n = 0 be 2 square units, then
  40. 40A variable line through the point 6 5 , 6 5 cuts the coordinate axes at the points A and B respectively. If the point P divides A B internal
  41. 41If the locus of the image of the point λ 2 , 2 λ in the line mirror x - y + 1 = 0 (where λ is a parameter) is x - a 2 = b y - c where a , b
  42. 42The lengths of the perpendiculars from the points m 2 , 2 m , m n , m + n and n 2 , 2 n to the line x + 3 y + 3 = 0 are in
  43. 43Let B and C are points of intersection of the parabola y = x 2 and the circle x 2 + y - 2 2 = 8 . The area of the triangle O B C , where O i
  44. 44Let the images of the point A 2,3 about the lines y = x and y = m x are P and Q respectively. If the line P Q passes through the origin, the
  45. 45Let P = 1,0 and Q = - 1,0 are two fixed points and R is a variable point on one side of the line P Q such that R P Q - R Q P = 45 o , then t
  46. 46If the straight line drawn through the point P 3 , 2 and inclined at an angle π 6 with the x - axis meets the line 3 x - 4 y + 8 = 0 at Q, t
  47. 47Let a variable line passing through a fixed point P in the first quadrant cuts the positive coordinate axes at points A and B respectively.
  48. 48The sum of all the values of λ such that the lines x + 2 y - 3 = 0 , 3 x - y - 1 = 0 and 2 λ x + y - 2 = 0 cannot form a triangle is
  49. 49The condition to be imposed on β , so that ( 0 , β ) lies on or insideof the triangle having equation of sides as y + 3 x + 2 = 0 , 3 y - 2
  50. 50The product of all the values of λ , such that the lines x + 2 y - 3 = 0 , 3 x - y - 1 = 0 and λ x + y - 2 = 0 cannot form a triangle, is eq

Frequently Asked Questions

1.How many questions are available for Straight Lines?

This chapter includes 109 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

These are NTA Abhyas (JEE Main) questions specifically for the Straight Lines chapter. Questions from other exams like JEE Main or JEE Advanced are organised separately under their respective exam sections.

3.What is the difficulty level of Straight Lines questions in NTA Abhyas (JEE Main)?

Of the 109 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Straight Lines should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.