General Mathematics

Question:15.Evaluate :
 (i)`(527 xx 527 xx 527 + 183 xx 183 xx 183)/(527 xx 527 - 527 xx 183 xx 183 xx 183)`

 (ii)`(458 xx 458 xx 458 - 239 xx 239 xx 239)/(458 xx 458 + 458 xx 239 + 239 xx 239)`

 (iii)`((614 +168)^2-(614-168)^2/614 xx 168)`

 (iv)`((832+278)^2+(832-278)^2/832 xx 832 + 278 xx 278)` 
AnswerSol.(i) Given Expression =`(527)^3 + (183)^3/(527)^2 - 527 xx 183 + (183)^2`
                                  
                                   =`a^3 + b^3/a^2 - ab + b^2`
                                  
                                   = (a+b) = (527 + 183) =710

      (ii) Given Expression =`(458)^3 - (239)^3/(458)^2+458 xx 239 + (239)^2`
                                    
                                    =`(a^3-b^3)/(a^2+ab+b^2)`
                                    
                                   = (a-b) = (458-239) = 219.
    
      (iii) Given Expression =`(a+b)^2-(a-b)^2)/ab`
    
      (iv) Given Expression =`((a+b)^2+(a-b)^2)/(a^2+b^2)`
                                    
                                     =`(2(a^2+b^2)/(a^2+b^2))`=2

Report

Question:16.Simplify :

   (i) `1605 xx 160 =?`

`(ii) 1398 xx 1398 =?` 
AnswerSol. (i)`1605 xx 1605 = (1605)^2`
                            =`(1600+5)^2`
                             =`(1600)^2+5^2+2x1600x5`
                              =2560000+25+16000
                              =2576025

     (ii)1398x1398=`(1398)^2`
                         =`(1400-2)^2`
                         =`(1400)^2+2^2-2x1400x2`
                         =1960000+4-5600
                          =1954404.

Report

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=?` 
AnswerSol. (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.

Report

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

Report

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

Report

First Prev 20 21 22 23 24 Next Last

Question:15.Evaluate : (i)`(527 xx 527 xx 527 + 183 xx 183 xx 183)/(527 xx 527 - 527 xx 183 xx 183 xx 183)` (ii)`(458 xx 458 xx 458 - 239 xx 239 xx 239)/(458 xx 458 + 458 xx 239 + 239 xx 239)` (iii)`((614 +168)^2-(614-168)^2/614 xx 168)` (iv)`((832+278)^2+(832-278)^2/832 xx 832 + 278 xx 278)`

Question:16.Simplify : (i) `1605 xx 160 =?` `(ii) 1398 xx 1398 =?`

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=?`

Question:18.Evaluate :`(313 xx 313 + 287 xx 287).`

Question:2o.What least number must be subtracted from 2000 to get a number exactly divisible by 17?