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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Paragraph Let f( x )= ae ^ 2 x + be ^ x + cx satisfies the condition f(0)=-1, f^ ( 2)=31 and ₀^ 4 (f( x )- cx ) dx = 39 2 . Image of a line x-1 3 = y-3 5 = z-4 2 in the plane (a-3) x+(b+a) y+z+c=0 be a line L=0 whose direction ratios are 1, p , q respectively. Let = a i + b j + c k and m =( p -2) i +2 j +( q +3) k . On the basis of above information, answer the following : Question a+b+c is equal to -

Options

  1. A-2
  2. B2
  3. C1
  4. D0

Correct answer

B. 2

Step-by-step solution

aligned & f(x)=a e^ 2 x +b e^x+c x & f(0)=a+b=-1...(i) & f^ (x)=2 a e^ 2 x +b e^x+c & f^ ( 2)=8 a+2 b+c=31...(ii) aligned ₀^ 4 (a e^ 2 x +b e^x ) d x= (a e^2 x 2 +b e^x )₀^ 4 =8 a+4 b- a 2 -b 15 a 2 +3 b= 39 2 15 a+6 b=39...(iii) Solving (i), (ii) & (iii) we get aligned & a=5, b=-6, c=3 & a+b+c=5-6+3=2 aligned

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