1. Question: The difference between the local value and the face value of `7` in the numeral `657903` is

    A
    `0`

    B
    `7896`

    C
    `6993`

    D
    `903`

    Note: Required difference `= (7000-7)=6993`
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  2. Question: The difference between the place values of `7` in the numeral `574873` is

    A
    `69930`

    B
    `59930`

    C
    `96390`

    D
    `69305`

    Note: Required difference `= (70000 - 70) = 69930`
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  3. Question: Solve the following equation `6581-(38+286+1593+3074)=(...?...)`

    A
    `1391`

    B
    `1590`

    C
    `2070`

    D
    `1940`

    Note: Required Number `= (6581-4991) = 1590`
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  4. Question: `(3500731) - (...?...) = 1735618`

    A
    `1865113`

    B
    `1775123`

    C
    `1765113`

    D
    `1765123`

    Note: Let `3500731-x=1735618`. Then, `x=(3500731-1735618)=1765113`.
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  5. Question: `(...?...) - (1936248) = (1635773)`

    A
    3572021

    B
    3561231

    C
    3562121

    D
    3536021

    Note: Let `x-1936248 = 1635773` or `x=(1635773 + 1936248)` `x=3572021`
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  6. Question: The unit's digit in the product `(274 xx 318 xx 577 xx 313)` is :

    A
    2

    B
    3

    C
    4

    D
    5

    Note: Required digit = unit digit in the product `(4 xx 8 xx 7 xx 3)` `= 2`
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  7. Question: The digit in the unit place of the number represented by `(7^95 - 3^58)` is :

    A
    7

    B
    0

    C
    6

    D
    4

    Note: Unit digit in `7^4` is 1. So, unit digit in `7^92` is 1.`:.` Unit digit in `7^95` is 3. [`:.` Unit digit in `1xx7xx7xx7` 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 `1xx3xx3` is 9] `:.` Unit digit in `(7^95 - 3^58)` is 4. [Subtracting unit digit 9 from unit digit 3 ]
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  8. Question: The total number of prime factor in the expression `(4)^11 xx (7)^5 xx (11)^2` is :

    A
    7

    B
    18

    C
    29

    D
    110

    Note: `4^7 xx 7^5 xx 11^2 = (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`.
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  9. Question: If `a/b = 4/3`, Then `(3a + 2b) / (3a - 2b)`= ?

    A
    -1

    B
    3

    C
    5

    D
    6

    Note: `(3a + 2b) / (3a - 2b)` = `(3 a/b + 2)/ (3 a/b - 2)` = `(3 xx 4/3 + 2) / (3 xx 4/3 - 2)` = `6/2` = 3. [Dividing Nr & Dr by b ]
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  10. Question: If `a^3b` = abc = 180 and a, b, c are positive integers, then the value of c is :

    A
    110

    B
    25

    C
    15

    D
    None

    Note: Since a , b, c are positive integer and 180 is not divisible by any of `2^3 , 3^3, 4^5` and `5^3`. So , `a^3b ` = 180 is possible only when `a^3` = 1 and b = 180. `:.`a = 1 and b = 180. Now `a^3b ` = abc =>c = `a^2` = 1.
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