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Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

Paragraph Consider the function y = f ( x ) f : R - 0 R The functional rule for the function y=f(x) is same as that of the functional rule for hypotenuse ' h ' of the right triangle with area 25 (units) ^2 expressed as a function of its perimeter. On the basis of above information, answer the following : Question The value of [ ⁻¹ f ( (2 ₂ 3 ₃ 4 ₄ 5 . ₃₁ 32 )+10 ) ] , where [ ] denotes the greatest integer function -

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

C. 2

Step-by-step solution

aligned & 1 2 a b=25 a b=50 & a+b+h=x & h=x-(a+b) aligned Now, a ^2+ b ^2= h ^2 aligned & (a+b)^2-2 a b=h^2 & (x-h)^2-100=h^2 & x^2-2 x h+h^2-100=h^2 & h= x^2-100 2 x aligned aligned & 2 ₂ 3 ₃ 4 . ₃₁ 32 &= 2 3 2 4 3 32 31 =2 32 2 &= 2 5=10 & ⁻¹ (f(10)+10)= ⁻¹ 10 &( f (10)=0) & [4 -10]=2 . aligned

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