MathematicsState true/ false:Three rational numbers between −2   and −3  are −11 4 , −10 4 , −9 4  .

State true/ false:


Three rational numbers between 2   and 3  are 11 4 , 10 4 , 9 4  .


  1. A
    True
  2. B
    False 

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    Solution:

    Here, we have to find three rational numbers between 2   and 3  .
    We know that,
    In order to find n   rational numbers between two rational numbers a   and b   (where, b>a   )  we can use the relation: (a+d),(a+2d),(a+3d),,(a+nd)   where,
    d= ba n+1   n   = Number of rational numbers between the two rational numbers.
    Comparing the two numbers,
    Clearly, 2>3   Therefore, a=3,b=2,n=3  .
    Then,
    d= ba n+1  
    Substituting the values of a=3,b=2,n=3  ,
    d= 2(3) 3+1 = 1 4  
    Three rational numbers between 2   and 3   using the relation: (a+d),(a+2d),(a+3d),,(a+nd)   are,
    (a+d)= 3+(1) 1 4 = 11 4 (a+2d)= 3+(2) 1 4 = 10 4 (a+3d)= 3+(3) 1 4 = 9 4   Hence, three rational numbers between 2   and 3   are 11 4 , 10 4 , 9 4  .
    Thus, the given statement is true.
    Therefore, option 1 is correct.
     
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