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Straight Lines

JEE Main 2024 (Online) 29th January Evening ShiftMCQEasy📈 Topic in 17% papers+4−1
Ques. 1JEE Main 2024, 29 January (Evening Shift)

Let A be the point of intersection of the lines 3x+2y=14, 5x-y=6 and B be the point of intersection of the lines 4x+3y=8, 6x+y=5. The distance of the point P(5,-2) from the line AB is

  1. 132
  2. 8
  3. 52
  4. 6

Answer

(4) 6

Solution

5x-y=6 y=5x-6; put in 3x+2y=14: 13x=26 A(2,4)

6x+y=5 y=5-6x; put in 4x+3y=8: -14x=-7 B ( 12,2 )

Slope of AB = 4-22- 12= 43

AB: y-4= 43(x-2) 4x-3y+4=0

∵ distance = |ax1+by1+c| a2+b2

d= |4(5)-3(-2)+4| 16+9= 305=6

Answer: (4)

Keep practising — Straight Lines

Ques. 2JEE Main 2024, 29 January (Evening Shift)

The distance of the point (2,3) from the line 2x-3y+28=0, measured parallel to the line 3x-y+1=0, is equal to

  1. 3+4 2
  2. 6 3
  3. 4+6 3
  4. 4 2
Ques. 3JEE Main 2024, 27 January (Morning Shift)

The portion of the line 4x+5y=20 in the first quadrant is trisected by the lines L1 and L2 passing through the origin. The tangent of an angle between the lines L1 and L2 is :

  1. 3041
  2. 85
  3. 25
  4. 2541
Ques. 4JEE Main 2024, 27 January (Evening Shift)

Let R be the interior region between the lines 3x-y+1=0 and x+2y-5=0 containing the origin. The set of all values of a, for which the points (a2,a+1 ) lie in R, is :

  1. (-3,0) ( 23,1 )
  2. (-3,0) ( 13,1 )
  3. (-3,-1) ( 13,1 )
  4. (-3,-1) (- 13,1 )
Ques. 5JEE Main 2024, 27 January (Evening Shift)

If the sum of squares of all real values of , for which the lines 2x-y+3=0, 6x+3y+1=0 and x+2y-2=0 do not form a triangle is p, then the greatest integer less than or equal to p is .

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