Numbers



  2. Question:17. Simplify :
    (i) `896 xx 896 - 204 xx 204 =?`
    
   (ii) `57 xx 57 + 43 xx 43 + 2 xx 57 xx 43 =?`
    
   (iii) `81 xx 81 + 68 xx 68 - 2 xx 81 xx 68=?` 
    Answer
    Sol. (i) Given Exp.=`(896)^2-(204)^2`
                          
                          =`(896+204)^2(896-204)`
                           
                          =`1100 xx 692`
                           
                          =761200.
       
 (ii) Gieven Exp. =`(57)^2+(43)^2+2 xx 57 xx 43`
                              
                        =`a^2+b^2+2ab`,where a = 57b=43
                              
                        =`(a+b)^2`=`(57+43)^2 = (100)^2`
                              
                        =10000.
      
 (iii)Given exp.=`(81)^2+(68)^2-2xx81xx68`
                          
                     =`a^2+b^2-2ab`,where a=81&b=68
                          
                     =`(a-b)^2`=`(81-68)^2`=`(13)^2`=169.






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  3. Question:18.Evaluate :`(313 xx 313 + 287 xx 287).` 
    Answer
    `(a^2+b^2)=``1/2``[(a+b)^2`+`(a^2-b)^2`]
   
  :. `(313)^2+(287)^2`
         
   =`1/2``[(313+287)^2`+`(313-287)^2`]
         
   =`1/2``[(600)^2`+`(26)^2]`
          
   =`1/2``(360000+676)`
           
   =180338






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  4. Question:2o.What least number must be subtracted from 2000 to get a number exactly divisible by 17? 
    Answer
    On dividing 2000 by 17,we get 11 as remainder.
:.Required number to be subtracted =11






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  5. Question:21.What least number be added to 3000 to obtain a number exactly divisible by 19? 
    Answer
    On dividing 3000 by 19, we get 17 remainder.
:. Number to be added =(19-17)=2.






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  6. Question:22.Find the number which is nearest to 3105 and exactly divisible by 21. 
    Answer
    On dividing 3105 by 21,we get 18 as remainder.
:. number to added to 3105 is (21-18)=3
:. 3108 the required number.






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