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    Maths-
    General
    Easy

    Question

    Number of ordered pairopen parentheses s close parentheses open parentheses a comma blank b close parentheses for each of which the equality a open parentheses cos invisible function application x minus 1 close parentheses plus b to the power of 2 end exponent equals cos invisible function application open parentheses a x plus b to the power of 2 end exponent close parentheses minus 1 holds true for all x element of R are

    1. 1  
    2. 2  
    3. 3  
    4. 4  

    The correct answer is: 2

      Putting x equals 0 blank rightwards double arrow b to the power of 2 end exponent equals cos invisible function application b to the power of 2 end exponent minus 1 rightwards double arrow cos invisible function application b to the power of 2 end exponent equals 1 plus b to the power of 2 end exponent rightwards double arrow b equals 0
      Forblank b equals 0 comma we haveblank a open parentheses cos invisible function application x minus 1 close parentheses equals cos invisible function application a x minus 1
      rightwards double arrow 2 a sin to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction equals 2 sin to the power of 2 end exponent invisible function application fraction numerator a x over denominator 2 end fraction
      rightwards double arrow a equals 0 orblank a equals 1
      Hence, ordered pairs are open parentheses a comma blank b close parentheses identical to open parentheses 0 comma blank 0 close parentheses orblank open parentheses 1 comma blank 0 close parentheses

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