Maths-
General
Easy

Question

straight f left parenthesis straight x right parenthesis equals straight x cubed minus 2 straight x squared plus 3 straight x minus 5 not stretchy rightwards double arrow straight f open square brackets sin space open parentheses fraction numerator 5 straight pi over denominator 2 end fraction close parentheses close square brackets plus straight f open square brackets sin space open parentheses fraction numerator 3 straight pi over denominator 2 end fraction close parentheses close square brackets equals

  1. 10
  2. -10
  3. 14
  4. -14

The correct answer is: -14


    Step by step solution:
    Given, straight f left parenthesis straight x right parenthesis equals straight x cubed minus 2 straight x squared plus 3 straight x minus 5
    sin open parentheses fraction numerator 5 straight pi over denominator 2 end fraction close parentheses equals 1
    sin open parentheses fraction numerator 3 straight pi over denominator 2 end fraction close parentheses equals negative 1
    Now, f open square brackets sin open parentheses fraction numerator 5 straight pi over denominator 2 end fraction close parentheses close square bracketsplus f open square brackets sin open parentheses fraction numerator 3 straight pi over denominator 2 end fraction close parentheses close square brackets
    equals f left parenthesis 1 right parenthesis plus f left parenthesis negative 1 right parenthesis
    equals left parenthesis 1 right parenthesis cubed minus 2 open parentheses 1 close parentheses squared plus 3 left parenthesis 1 right parenthesis minus 5plus left parenthesis negative 1 right parenthesis cubed minus 2left parenthesis negative 1 right parenthesis squared plus 3 left parenthesis negative 1 right parenthesis minus 5
    =1 minus 2 plus 3 minus 5negative 1 minus 2 minus 3 minus 5
    =negative 14
    Hence, option(d) is the correct option.

    Related Questions to study

    General
    Maths-

    If cos theta equals 3 over 5 and theta is not in the first quadrant, then fraction numerator 5 tan space left parenthesis pi plus theta right parenthesis plus 4 cos space left parenthesis pi plus theta right parenthesis over denominator secc space left parenthesis 2 pi minus theta right parenthesis minus 4 cot space left parenthesis 2 pi plus theta right parenthesis end fraction equals

    If cos theta equals 3 over 5 and theta is not in the first quadrant, then fraction numerator 5 tan space left parenthesis pi plus theta right parenthesis plus 4 cos space left parenthesis pi plus theta right parenthesis over denominator secc space left parenthesis 2 pi minus theta right parenthesis minus 4 cot space left parenthesis 2 pi plus theta right parenthesis end fraction equals

    Maths-General
    General
    Maths-

    text  If  end text a sin space theta plus b cos comma theta equals c text  then  end text fraction numerator a minus b tan space theta over denominator b plus a tan space theta end fraction equals

    text  If  end text a sin space theta plus b cos comma theta equals c text  then  end text fraction numerator a minus b tan space theta over denominator b plus a tan space theta end fraction equals

    Maths-General
    General
    Maths-

    cosec squared space alpha equals fraction numerator 4 x y over denominator left parenthesis x plus y right parenthesis squared end fraction left square bracket left parenthesis x comma y right parenthesis not equal to left parenthesis 0 comma 0 right parenthesis right square bracket text  is  end text

    cosec squared space alpha equals fraction numerator 4 x y over denominator left parenthesis x plus y right parenthesis squared end fraction left square bracket left parenthesis x comma y right parenthesis not equal to left parenthesis 0 comma 0 right parenthesis right square bracket text  is  end text

    Maths-General
    parallel
    General
    Maths-

    text  If  end text 0 less or equal than x less or equal than pi comma 81 to the power of sin squared space x end exponent plus 81 to the power of cos squared space x end exponent equals 30 text  then  end text x equals

    text  If  end text 0 less or equal than x less or equal than pi comma 81 to the power of sin squared space x end exponent plus 81 to the power of cos squared space x end exponent equals 30 text  then  end text x equals

    Maths-General
    General
    Maths-

    if sin space theta plus cos space theta equals p and sin cubed space theta plus cos cubed space theta equals q then straight p open parentheses straight p squared minus 3 close parentheses equals

    if sin space theta plus cos space theta equals p and sin cubed space theta plus cos cubed space theta equals q then straight p open parentheses straight p squared minus 3 close parentheses equals

    Maths-General
    General
    Chemistry-

    In the reaction

    the structure of the product Tis:

    In the reaction

    the structure of the product Tis:

    Chemistry-General
    parallel
    General
    Chemistry-

    In the reaction for denigration,

    the major dinitrated product (X) is:

    In the reaction for denigration,

    the major dinitrated product (X) is:

    Chemistry-General
    General
    Chemistry-

    The major product of the following reaction,
    ? is:

    The major product of the following reaction,
    ? is:

    Chemistry-General
    General
    Maths-

    if square root of fraction numerator 1 minus sin space A over denominator 1 plus sin space A end fraction end root equalssec A-tan A then  lies in the quadrants

    if square root of fraction numerator 1 minus sin space A over denominator 1 plus sin space A end fraction end root equalssec A-tan A then  lies in the quadrants

    Maths-General
    parallel
    General
    Maths-

    If t a n invisible function application A plus t a n invisible function application B equals p and c o t invisible function application A plus c o t invisible function application B equals q then c o t invisible function application left parenthesis A plus B right parenthesis equals

    If t a n invisible function application A plus t a n invisible function application B equals p and c o t invisible function application A plus c o t invisible function application B equals q then c o t invisible function application left parenthesis A plus B right parenthesis equals

    Maths-General
    General
    Chemistry-

    In the following reaction sequence,

    The compounds (X) and (Y) respectively are:

    In the following reaction sequence,

    The compounds (X) and (Y) respectively are:

    Chemistry-General
    General
    Chemistry-

    The correct order of increasing basic nature of the following bases is:
    1)
    2)
    3)
    4)
    5)

    The correct order of increasing basic nature of the following bases is:
    1)
    2)
    3)
    4)
    5)

    Chemistry-General
    parallel
    General
    Chemistry-

    In a reaction of aniline, a colored product' C' was obtained.

    The structure of 'C' would be:

    In a reaction of aniline, a colored product' C' was obtained.

    The structure of 'C' would be:

    Chemistry-General
    General
    Chemistry-

    In the following reaction,
    The structure of major product 'X' is:

    In the following reaction,
    The structure of major product 'X' is:

    Chemistry-General
    General
    Chemistry-

    ?

    ?

    Chemistry-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.