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Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

Paragraph: A straight line passing through O(0,0) cuts the lines x= , y= and x+y=8 at A, B and C respectively such that O A O B O C=48 2 and f( , ) 0 . Where f(x, y)= | y x - 3 2 |+(3 x-2 y)^6+ e x+2 y-2 e-6 Question: OA + OB + OC equals

Options

  1. A2 2
  2. B4 2
  3. C7 2
  4. D9 2

Correct answer

D. 9 2

Step-by-step solution

Let equation of straight line x = y =r Let O A=r₁, O B=r₂, O C=r₃ then A (r₁ , r₁ ) aligned & B (r₂ , r₂ ) & C (r₃ , r₃ ) aligned A lies on x =2, r ₁ =2 r ₁= 2 .....(1) B lies on y=3, r₂ =3, r₂= 3 ....(2) and C lines on x+y=8r₃ +r₃ =8 r₁ r₂ r₃=48 2 ( 2 ) ( 3 ) ( 8 + )=48 2 2 ( + )=1 2 ( , 4 )=1 Both 2 and ( + 4 ) should be equal to 1 , so - 4 then r₁=2 2 , r₂=3 2 . r₃= 8 2 =4 2 Hence, O A+O B+O C=r₁+r₂+r₃=9 2

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