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integral open parentheses x minus blank to the power of 10 end exponent C subscript 1 end subscript x to the power of 2 end exponent plus blank to the power of 10 end exponent C subscript 2 end subscript x to the power of 3 end exponent minus blank to the power of 10 end exponent C subscript 3 end subscript x to the power of 4 end exponent horizontal ellipsis horizontal ellipsis plus blank to the power of 10 end exponent C subscript 10 end subscript x to the power of 11 end exponent close parentheses d xdx equals:

  1. fraction numerator left parenthesis 1 minus x right parenthesis to the power of 11 over denominator 11 end fraction fraction numerator left parenthesis 1 minus x right parenthesis to the power of 10 over denominator 10 end fraction plus c    
  2. fraction numerator left parenthesis 1 minus x right parenthesis to the power of 12 end exponent over denominator 12 end fractionfraction numerator left parenthesis 1 minus x right parenthesis to the power of 11 end exponent over denominator 11 end fraction+ c    
  3. fraction numerator left parenthesis 1 minus x right parenthesis to the power of 10 end exponent over denominator 10 end fractionfraction numerator left parenthesis 1 minus x right parenthesis to the power of 11 end exponent over denominator 11 end fraction+ c    
  4. None of these    

The correct answer is: None of these


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    The indefinite integral of left parenthesis 12 s i n invisible function application x plus 5 c o s invisible function application x right parenthesis to the power of negative 1 end exponent is, for any arbitrary constant -

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    Statement I : y = f(x) =fraction numerator x to the power of 2 end exponent minus 2 x plus 4 over denominator x to the power of 2 end exponent minus 2 x plus 5 end fraction, xelement ofR Range of f(x) is [3/4, 1)
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    Statement I : y = f(x) =fraction numerator x to the power of 2 end exponent minus 2 x plus 4 over denominator x to the power of 2 end exponent minus 2 x plus 5 end fraction, xelement ofR Range of f(x) is [3/4, 1)
    Statement II : left parenthesis x minus 1 right parenthesis to the power of 2 end exponent equals fraction numerator 4 y minus 3 over denominator 1 minus y end fraction.

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    Statement II : sin x and {x} are both periodic with period 2 pi and 1 respectively.

    Statement I : Function f(x) = sinx + {x} is periodic with period 2 pi
    Statement II : sin x and {x} are both periodic with period 2 pi and 1 respectively.

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    Statement 1 : f : R rightwards arrow R and f left parenthesis x right parenthesis equals e to the power of x end exponent plus e to the power of negative x end exponentis bijective.
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    Statement- 1 colon If f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line Where 2 less than x less than 3 is an identity function.
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    Statement- 1 colon If f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line Where 2 less than x less than 3 is an identity function.
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    Assertion (A) : Graph of open curly brackets left parenthesis x comma y right parenthesis divided by y equals 2 to the power of negative x end exponent text  and  end text x comma y element of R close curly brackets
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    Assertion: The period of f left parenthesis x right parenthesis equals s i n invisible function application 2 x c o s invisible function application left square bracket 2 x right square bracket minus c o s invisible function application 2 x s i n invisible function application left square bracket 2 x right square bracket is 1/2.
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    Assertion: The period of f left parenthesis x right parenthesis equals s i n invisible function application 2 x c o s invisible function application left square bracket 2 x right square bracket minus c o s invisible function application 2 x s i n invisible function application left square bracket 2 x right square bracket is 1/2.
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    Assertion : Fundamental period of c o s invisible function application x plus c o t invisible function application x text  is  end text 2 pi.
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    Assertion: The function defined by f left parenthesis x right parenthesis equals x to the power of 3 end exponent plus a x to the power of 2 end exponent plus b x plus c is invertible if and only if a to the power of 2 end exponent less or equal than 3 b.
    Reason: A function is invertible if and only if it is one-to-one and onto function.

    Assertion: The function defined by f left parenthesis x right parenthesis equals x to the power of 3 end exponent plus a x to the power of 2 end exponent plus b x plus c is invertible if and only if a to the power of 2 end exponent less or equal than 3 b.
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    Assertion : f left parenthesis x right parenthesis equals s g n left parenthesis x minus vertical line x vertical line right parenthesiscan never become positive.
    Reason : f(x) = sgn x is always a positive function.

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    If f (x) = open curly brackets table row cell e to the power of cos invisible function application x end exponent end cell cell sin invisible function application x text for  end text vertical line x vertical line less or equal than 2 end cell row cell text 2, end text end cell cell text otherwise end text end cell end table comma text then  end text not stretchy integral subscript text -2 end text end subscript superscript 3 end superscript f ​ left parenthesis x right parenthesis d x equals close

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