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  1. Answer
    Product of unit's digits in given numbers `= ( 6 xx 7 xx 9 xx 2) = 756`
    `:.` Unit digit in the given product is `6`.

    Explanation: Not available 


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  2. Answer
    Clearly, unit digit in `3^4` is 1.
    ∴ Unit digit in `3^64` is 1.
    ∴ Unit digit in `3^67` is 7. [Because Unit digit in `1 xx 3 xx 3 xx 3` is `7` ]
    Clearly, unit digit in every power of 6 is 6
    ∴ Unit digit in `6^39` is 6.
    Clearly, unit digit in `7^4` is 1.
    ∴ Unit digit in `7^52` is 1.
    ∴ Unit digit in `7^53` is 7. [Because Unit digit in `1 xx 7` is 7 ]
    ∴ Unit digit in given product = Unit digit in `( 7 xx 6 xx 7 ) = 4`.

    Explanation: Not available 


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  3. Answer
    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
    
    Test : Let p be a given number. Find a whole number nearly greater than the square root of p.
    Let `k > sqrt p` .
    Test whether p is divisible by any prime number less than k. If yes, then p is not prime. Otherwise, p is prime.

    Explanation: Not available 


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  4. Answer
    Clearly, the unit's digit of `9130525` is `5`, which is not divisible by `2`. 
    So, `9130525` is not divisible by `2`.
    Each one of the other numbers has a unit divisible by `2`.
    So, each one other than `9130525` is divisible by `2`.

    Explanation: Divisibility By `2` : A number divisible by `2`, if its unit digit is any of `0, 2, 4, 6, 8`. 


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  5. Answer
    1) Sum of digits in 541326 is 21, which is divisible by 3.
    
     So, 541326 is divisible by 3
    
     2) Sum of digits in 5967013 is 31, which is not divisible by 3.
     
     Hence, 5967013 is not divisible by 3.

    Explanation: Not available 


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