Straight Lines

JEE Main 2024 (Online) 27th January Morning ShiftMCQMedium📈 Topic in 7% papers+4−1

Ques. 1JEE 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 :

3041
85
25
2541

Answer

(1) 3041

Solution

The line meets the axes at (5,0) and (0,4); points of trisection (ratios 1 : 2 and 2 : 1):

A ( 53, 83 ), B ( 103, 43 )

[figure]

m1=mOA= 85, m2=mOB= 25

= | m1-m21+m1m2 |= 6/51+16/25= 3041

Answer: (1)

Keep practising — Straight Lines

Ques. 2JEE 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 :

(-3,0) ( 23,1 )
(-3,0) ( 13,1 )
(-3,-1) ( 13,1 )
(-3,-1) (- 13,1 )

Ques. 3JEE 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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