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Most Important Selected Qs for JEE AdvancedMathematicsFunctions

If f(x)=x^2-p x+q, p, q R such that f(x)=f(6-x) x R and least value of f(x) is -81 4 then:

Options

  1. Athe least value of ⁻¹(22+[f(x)]) is 4
  2. Bthe least value of ⁻¹(22+[f(x)]) is - 4
  3. Clargest integral value of k for which equation sgn (f(x)+k)=0 has a solution is 20 .
  4. Dlargest integral value of k for which equation sgn (f(x)+k)=0 has a solution is 21 . [Note: [y] denotes greate

Correct answer

C. largest integral value of k for which equation sgn (f(x)+k)=0 has a solution is 20 .

Step-by-step solution

Least value of f(x) is -D 4 a = -81 4 Least value of ⁻¹(22+[f(x)]) aligned & ⁻¹ (22+ [- 81 4 ] ) & ⁻¹(22-21)= 4 aligned Largest integral value of k for which equation sgn (f(x)+k)=0 has a solution f(x) has min. value -20.25 If k>20.25 , then sgn (f(x)+k) is always positive. So, largest integral value of k is 20 .

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