1. Question:Unit digit in the given product=unit digit in `7^153 xx 1^72`. 

    Answer
    Now `7^4`gives unit digit 1.
    :.`7^152` gives unit digit 1.
    :.`7^152` gives unit digit `(1 xx 7)=7`
    Also `1^72`gives digit 1.
    :.Unit digit in the product =`(7 xx 1)=7`.






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

    Answer
    So,unit digit in `7^92` is 1.
    :.Unit digit in `7^95` is 3.   [:. Unit digit in `1 xx 7 xx 7 xx `is 3 ]
    Unit digit in `3^4`is 1
    :. Unit digit in `3^56` is 1.
    :. Unit digit in `3^58` is 9. [:.Unit digit in `1 xx 3 xx 3 xx` is 9]
    :. Unit digit in `(7^95 - 3^58)` is 4.[Subtracting  unit digit 9 from unit digit]






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  3. Question:`4^11 xx 7^5 xx 11^2` 

    Answer
    =`(2 xx 2)^11 xx 7^5 xx 11^2`
    =`2^11 xx 2^11 xx 7^5 xx 11^2`
    =`2^22 xx 7^5 xx 11^2`.
    :.The number of prime factors is (22 + 5 + 2)=29






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  4. Question:Convert the following into vulgar fractions : (i)0.75 (ii) 3.004 (iii) .0056 

    Answer
    (i) `.075=75/100=3/4`.
    
     (ii) `3.004=3004/100=751/250`.
    
     (iii) `.0056/1000=7/1250`.






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  5. Question:Simplily : (i) `1.84/2.99` (ii) `.365/.584` 

    Answer
    (i) `1.84/2.99=184/299=8/13`.
    (ii) `.365/.584=365/584=5/8`.






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