Maths-
General
Easy

Question

Consider the following statements S and R: S: Both s i n blankx&cos x are decreasing functions in the interval left parenthesis pi divided by 2 comma pi right parenthesis .
R: If a differentiable function decreases in an interval left parenthesis a comma blank b right parenthesis , then its derivative also decreases in left parenthesis a comma blank b right parenthesis Which of the following is true ?

  1. both S and R are wrong    
  2. both S and R are correct, but R is not the correct explanation for S    
  3. S is correct and R is the correct explanation for S    
  4. S is correct and R is wrong.    

The correct answer is: S is correct and R is wrong.

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A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank The two sides having fence are of same length x The maximum area enclosed by the park is‐

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Let y equals f left parenthesis x right parenthesis be a thrice derivable fu nction such that f left parenthesis a right parenthesis f left parenthesis b right parenthesis less than 0 comma f left parenthesis b right parenthesis f left parenthesis c right parenthesis less than 0 comma f left parenthesis c right parenthesis f left parenthesis d right parenthesis less than 0 where a less than b less than c less than d blankAlso the equations f (x)equalsO& f to the power of ’ ’ end exponent left parenthesis x right parenthesis equals 0 have no common roots.
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Let y equals f left parenthesis x right parenthesis be a thrice derivable fu nction such that f left parenthesis a right parenthesis f left parenthesis b right parenthesis less than 0 comma f left parenthesis b right parenthesis f left parenthesis c right parenthesis less than 0 comma f left parenthesis c right parenthesis f left parenthesis d right parenthesis less than 0 where a less than b less than c less than d blankAlso the equations f (x)equalsO& f to the power of ’ ’ end exponent left parenthesis x right parenthesis equals 0 have no common roots.
Statement‐I:: The equation f left parenthesis x right parenthesis left parenthesis f to the power of ’ ’ end exponent left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent plus f left parenthesis x right parenthesis f to the power of ’ end exponent left parenthesis x right parenthesis f to the power of ’ ’ ’ end exponent left parenthesis x right parenthesis plus left parenthesis f to the power of ’ end exponent left parenthesis x right parenthesis right parenthesis to the power of 2 end exponent f to the power of ’ ’ end exponent left parenthesis x right parenthesis equals 0 has atleast 5 real roots.
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