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Straight Lines

JEE Main 2024 (Online) 29th January Evening ShiftMCQMedium📈 Topic in 16% papers+4−1
Ques. 1JEE 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

Answer

(3) 4+6 3

Solution

[figure]

∵ Slope of 3x-y+1=0 is 3 ⇒ PQ makes 60 with the x-axis.

Parametric form: Q = (2+r 60 , 3+r 60 )

Q = (2+ r2, 3+ 3r2 )

Q lies on 2x-3y+28=0:

4+r-9- 3 32r+28=0 r ( 3 3-22 )=23

r= 463 3-2= 46(3 3+2)27-4=2(3 3+2)

PQ =4+6 3

Answer: (3)

Keep practising — Straight Lines

Ques. 2JEE 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. 3JEE 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. 4JEE 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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