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Straight Lines

JEE Main 2024 (Online) 29th January Morning ShiftMCQEasy📈 Topic in 31% papers+4−1
Ques. 1JEE Main 2024, 29 January (Morning Shift)

Let (5, a4 ) be the circumcenter of a triangle with vertices A(a,-2), B(a, 6) and C ( a4,-2 ). Let denote the circumradius, denote the area and denote the perimeter of the triangle. Then + + is

  1. 60
  2. 62
  3. 53
  4. 30

Answer

(3) 53

Solution

Circumcentre O: OA=OB

(a-5)2+ ( a4+2 )2=(a-5)2+ ( a4-6 )2

a4+2=6- a4 a=8

∴ A(8,-2), B(8,6), C(2,-2), O(5,2)

[figure]

AB=8 (vertical), AC=6 (horizontal) A=90 , BC=10

∵ O is the mid-point of hypotenuse BC: = BC2=5

= 12 8 6=24, =8+6+10=24

+ + =5+24+24=53

Answer: (3)

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

In a ABC, suppose y=x is the equation of the bisector of the angle B and the equation of the side AC is 2x-y=2. If 2AB=BC and the points A and B are respectively (4,6) and ( , ), then +2 is equal to

  1. 42
  2. 39
  3. 48
  4. 45
Ques. 3JEE 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
Ques. 4JEE 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. 5JEE 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. 6JEE 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. 7JEE 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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