1. Question:`5358 xx 51` 

    Answer
    `5358 xx (50 + 1)`
    `=(5358 xx 50) + (5358 xx 1)`
      =267900 + 5358=273258.






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  2. Question:`1307 xx 1307` 

    Answer
    `=(1307)^2`=`(1300 + 7)^2`
    `=(1300)^2 + (7)^2 + 2 xx 1300 xx 7`
    =1690000 + 49 + 18200
    =1708249.






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  3. Question:Requred digit 

    Answer
    =unit digit in the product `(4 xx 8 xx 7 xx 3)`=2






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  4. Question:`9 xx 6 xx 4`216. 

    Answer
    In order to obtain 2 at the unit place it must be multiplied by a number whose unit digit is 7.
    So,*must be replace by 7.






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  5. Question:Unit digit in `7^4`is 1.` 

    Answer
    :.Unit digit in `7^68`is 1.
    
     :.Unit digit in `7^71`is 3. `[1 xx 7 xx 7 xx 7` gives unit digit 3]
    
     Again,every power of 6 will give unit digit 6.
    
     :. Unit digit in `6^59` is 6.
    
     Clearly,unit digit in `3^4` is 1.
    
     So,unit digit in `3^64` is 1
    
     :.Unit digit in `3^65` is 3.
    
     :. Unit digit in `(7^71 xx 6^59 xx 3^65)` is 4. `[3 xx 6 xx 3`gives unit digit 4]`






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