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Straight Lines — JEE Main & Advanced IOQM PYQs

24 previous year questions from Straight Lines with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

24 questionsIOQMSolutions on every page

Let A B C be a triangle in the x y plane, where B is at the origin (0,0) . Let B C be produced to D such that B C: C D=1: 1, C A be produced to E such that C A: A E=1: 2 and A B be

Olympiad workbook Solution View → 2

Let A B C D be a unit square. Suppose M and N are points on B C and C D respectively such that the perimeter of triangle M C N is 2 . Let O be the circumcentre of triangle M A N an

Olympiad workbook Solution View → 3

An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a 160^ turn to the right and walks 4 more feet. It then makes another 160^ turn to the right

Olympiad workbook Solution View → 4

A bug travels in the coordinate plane moving only along the lines that are parallel to the x axis or y axis. Let A=(-3,2) and B(3,-2) . Consider all possible paths of the bug from

Olympiad workbook Solution View → 5

In parallelogram A B C D the longer side is twice the shorter side. Let X Y Z W be the quadrilateral formed by the internal bisectors of the angles of A B C D . If the area of X Y

Olympiad workbook Solution View → 6

In a rectangle A B C D, E is the midpoint of A B: F is point on A C such that B F is perpendicular to A C and F E perpendicular to B D . Suppose B C=8 3 . Find A B .

Olympiad workbook Solution View → 7

Consider a square A B C D of side length 16 . Let E, F be points on C D such that C E=E F=F D . Let the line BF and A E meet in M . The area of M A B is:

Olympiad workbook Solution View → 8

Let A B C D be a rectangle in which A B+B C+ C D=20 and A E=9 where E is the mid-point of the side B C . Find the area of the rectangle.

Olympiad workbook Solution View → 9

In the coordinate plane, a point is called a lattice point if both of its coordinates are integers. Let A be the point (12,84) . Find the number of right angled triangles A B C in

Olympiad workbook Solution View → 10

Three parallel lines L₁, L₂, L₃ are drawn in the plane such that the perpendicular distance between L₁ and L₂ is 3 and the perpendicular distance between L₂ and L₃ is also 3 . A sq

Olympiad workbook Solution View → 11

If A B C D is a rectangle and P is a point inside it such that A P=33, B P=16, D P=63 . Find C P .

Olympiad workbook Solution View → 12

A point P in the interior of a regular hexagon is at distance 8,8,16 units from three consecutive vertices of the hexagon, respectively. If r is radius of the circumscribed circle

Olympiad workbook Solution View → 13

If A B C D is a rectangle and P is a point inside it such that A P=33, B P=16, D P=63 . Find C P .

Olympiad workbook Solution View → 14

A bug travels in the coordinate plane moving only along the lines that are parallel to the x axis or y axis. Let A=(-3,2) and B(3,-2) . Consider all possible paths of the bug from

Olympiad workbook Solution View → 15

Let A B C be a triangle in the x y plane, where B is at the origin (0,0) . Let B C be produced to D such that B C: C D=1: 1, C A be produced to E such that C A: A E=1: 2 and A B be

Olympiad workbook Solution View → 16

Three parallel lines L₁, L₂, L₃ are drawn in the plane such that the perpendicular distance between L₁ and L₂ is 3 and the perpendicular distance between L₂ and L₃ is also 3 . A sq

Olympiad workbook Solution View → 17

Let A B C D be a rectangle in which A B+B C+ C D=20 and A E=9 where E is the mid-point of the side B C . Find the area of the rectangle.

Olympiad workbook Solution View → 18

Let A B C D be a unit square. Suppose M and N are points on B C and C D respectively such that the perimeter of triangle M C N is 2 . Let O be the circumcentre of triangle M A N an

Olympiad workbook Solution View → 19

In the coordinate plane, a point is called a lattice point if both of its coordinates are integers. Let A be the point (12,84) . Find the number of right angled triangles A B C in

Olympiad workbook Solution View → 20

Consider a square A B C D of side length 16 . Let E, F be points on C D such that C E=E F=F D . Let the line BF and A E meet in M . The area of M A B is:

Olympiad workbook Solution View → 21

In a rectangle A B C D, E is the midpoint of A B: F is point on A C such that B F is perpendicular to A C and F E perpendicular to B D . Suppose B C=8 3 . Find A B .

Olympiad workbook Solution View → 22

An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a 160^ turn to the right and walks 4 more feet. It then makes another 160^ turn to the right

Olympiad workbook Solution View → 23

A point P in the interior of a regular hexagon is at distance 8,8,16 units from three consecutive vertices of the hexagon, respectively. If r is radius of the circumscribed circle

Olympiad workbook Solution View → 24

In parallelogram A B C D the longer side is twice the shorter side. Let X Y Z W be the quadrilateral formed by the internal bisectors of the angles of A B C D . If the area of X Y

Olympiad workbook Solution View →

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