Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

The lines x+y-1=0,(m-1) x+ (m^2-7 ) y-5=0 and (m-2) x+(2 m-5) y=0 are -

Options

  1. Aconcurrent for three values of m
  2. Bconcurrent for no value of m
  3. Cparallel for one value of m
  4. Dparallel for two values of m

Correct answer

C. parallel for one value of m

Step-by-step solution

For concurrency | array ccc 1 & 1 & -1 m-1 & m^2-7 & -5 m-2 & 2 m-5 & 0 array |=0 aligned & 5(2 ~m -5)-5( ~m -2)-[( m -1)(2 ~m -5) & .-( m -2) ( m ^2-7 ) ]=0 & 10 ~m -25-5 ~m +10-2 ~m ^2+7 ~m -5+ m ^3 & -2 ~m ^2-7 ~m +14=0 & ~m ^3-4 ~m ^2+5 ~m -6=0 & ( ~m -3) ( m ^2- m +2 )=0 aligned m =3 is the only real root But for m =3 the given line becomes parallel. Thus the given lines can only be parallel for m =3 .

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0 , meets the co-ordinate axes at the points P and Q, then the locus of the mid point 2026From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0 . These rays get reflected from the mirror x + 2y = 1 . If the equations of the reflected r 2026In an equilateral triangle PQR , let the vertex P be at (3, 5) and the side QR be along the line x + y = 4 . If the orthocentre of the triangle PQR is ( , ) , then 9( + ) is equal 2026Let P(3 , 2 ) , 0 , be a point on the ellipse x^2 9 + y^2 4 =1 , Q be a point on the circle x^2+y^2-14x-14y+82=0 and R be a point on the line x+y=5 such that the centroid of the tr 2026Let A,B be points on the two half-lines x- 3 |y|= , >0 at a distance of from their point of intersection P . The line segment AB meets the angle bisector of the given half-lines at 2026Let the line L₁ : x + 3 = 0 intersect the lines L₂ : x - y = 0 and L₃ : 3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines L₂ a 2026Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5, -1) . If the centroid of this triangle is (3, 4) and its circumcenter is ( , ) , then 21( + ) 2026Let the mid points of the sides of a triangle ABC be ( 5 2 , 7 ) , ( 5 2 , 3 ) and (4, 5) . If its incentre is (h, k) , then 3h + k is equal to : 2026 Full Straight Lines list All Most Important Selected Qs for JEE Advanced PYQs