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Match each item in List-I with the correct item in List-II. List-I: (P) Equation of the line parallel to 2x + 3y - 5 = 0 and passing through (0, 0) (Q) Equation of the line perpendicular to 3x + 2y - 1 = 0 and having x-intercept equal to 2 (R) Point P divides segment AB (where A = (1,2) and B = (2,0)) internally in the ratio 1:2. The harmonic conjugate of P with respect to A and B lies on the line: (S) Equation of a line that has equal intercepts on both axes and passes through (1, 1) List-II: (1) x + y = 4 (2) 2x + 3y = 0 (3) 2x - 3y - 4 = 0 (4) x + y = 2
- P->1; Q->3; R->4; S->2
- P->3; Q->2; R->1; S->4
- P->2; Q->3; R->1; S->4
- P->4; Q->3; R->1; S->2
Correct answer: P->2; Q->3; R->1; S->4
Solution
Solve each matching: P->2 (2x+3y=0 passes through origin, parallel to 2x+3y-5=0). Q->3 (perpendicular to 3x+2y=1 has slope 2/3; with x-intercept 2: y = (2/3)(x-2) => 2x-3y-4=0). R: P divides AB in 1:2, P=(4/3, 4/3). Harmonic conjugate divides AB externally in 1:2. Q'=(0,4). Check lines: x+y=4 passes through (0,4). So R->1. S: equal intercepts through (1,1) means x+y=2 (a=b, so x/a+y/a=1 => x+y=a=2). S->4.
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