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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Paragraph Two vectors a and b having unit modulus and angle between them is . Now ( )= _ -( a . b )^2 ^ ( a b )^2 f^2( x ) dx and f satisfies the condition f( y )+f( x )= x + y xy for all x , y R - 0 and h ( )=- ( )+ | a b ₁ |^2 | a b ₁ |^2 , where |b₁ |=2|b| . On the basis of above information, answer the following questions : Question If a & b are non collinear vectors, then number of solution of the equation 4 ( )

Options

  1. A2
  2. B4
  3. C6
  4. D8

Correct answer

B. 4

Step-by-step solution

( )= _ - ^2 ^ ^2 (f( x ))^2 dx Also f(x)+f(y)= x+y x y Put y=x aligned & 2 f( x )= 2 x f( x )= 1 x & ( )= _ - ^2 ^ ^2 1 x ^2 dx = [- 1 x ]_ - ^2 ^ ^2 aligned aligned & 4 ( )+ 3 ^ ( )=0 & -16 cosec ^2 2 +16 3 cosec ^2 2 2 =0 & 16 cosec ^2 2 (-1+ 3 2 )=0 aligned 2 = 1 3 ( . as . cosec ^2 2 0 ) 2 = 3 2 = n + 3 = n 2 + 6 , n I So number of solutions in [0,2 ] will be 4 .

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