Number System


  1. The simplified value of
    1 −
    1
    1 −
    1
    1 −
    1
    ........ 1 −
    1
    1 −
    1
    34599100









  1. View Hint View Answer Discuss in Forum

    2
    ×
    3
    ×
    4
    ×......×
    98
    ×
    98
    34599100


    =
    2
    =
    1
    10050

    Correct Option: C

    2
    ×
    3
    ×
    4
    ×......×
    98
    ×
    98
    34599100


    =
    2
    =
    1
    10050


  1. The sum of the squares of two positive numbers is 100 and difference of their squares is 28. Find the sum of the numbers :









  1. View Hint View Answer Discuss in Forum

    According to question
    x2 + y2 = 100 ...(i)
    x2 − y2 = 28 ...(ii)
    Adding both the equations
    x2 + y2
    x2 − y2
    -----------
    2x2    128
    ⇒  x2 = 64    ∴  x = 8
    From the equation (i)
    y2 = 100 − 64    ∴  y = 6
    So, x + y = 8 + 6 = 14

    Correct Option: C

    According to question
    x2 + y2 = 100 ...(i)
    x2 − y2 = 28 ...(ii)
    Adding both the equations
    x2 + y2
    x2 − y2
    -----------
    2x2    128
    ⇒  x2 = 64    ∴  x = 8
    From the equation (i)
    y2 = 100 − 64    ∴  y = 6
    So, x + y = 8 + 6 = 14



  1. The numbers 1, 3, 5,7 .., 99 and128 are multiplied together. The number of zeros at the end of the product must be :









  1. View Hint View Answer Discuss in Forum

    In 2m × 5n, the number of zeros
    = n when m ≥ n
    = m when m < n
    Here, 128 = 27
    In 1 × 3 × 5 × 7 × ... × 99 multiples of 5 are 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 (= 510)
    Clearly, 7 zeros will be found in the product.

    Correct Option: C

    In 2m × 5n, the number of zeros
    = n when m ≥ n
    = m when m < n
    Here, 128 = 27
    In 1 × 3 × 5 × 7 × ... × 99 multiples of 5 are 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 (= 510)
    Clearly, 7 zeros will be found in the product.


  1. A number of friends decided to go on a picnic and planned to spend ₹108 on eatables. Three of them however did not turn up. As a consequence each one of the remaining had to contribute ₹3 extra. The number of them who attended the picnic was :









  1. View Hint View Answer Discuss in Forum

    Let the original number of friends be x.


    ∴ 
    108
    +
    108
    = 3
    x − 3x

    ⇒  108
    x − x + 3
    = 3
    x(x − 3)

    ⇒  x (x – 3) = 108
    ⇒  x2 – 3x – 108 = 0
    ⇒  x2 –12 x + 9x –108 = 0
    ⇒  (x– 12) + 9 (x – 12) = 0
    ⇒  (x – 12) (x + 9) = 0
    ⇒  x = 12 as x ≠ – 9
    ∴  The number of friends who attended the picnic
    = 12 – 3 = 9

    Correct Option: C

    Let the original number of friends be x.


    ∴ 
    108
    +
    108
    = 3
    x − 3x

    ⇒  108
    x − x + 3
    = 3
    x(x − 3)

    ⇒  x (x – 3) = 108
    ⇒  x2 – 3x – 108 = 0
    ⇒  x2 –12 x + 9x –108 = 0
    ⇒  (x– 12) + 9 (x – 12) = 0
    ⇒  (x – 12) (x + 9) = 0
    ⇒  x = 12 as x ≠ – 9
    ∴  The number of friends who attended the picnic
    = 12 – 3 = 9



  1. If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is :









  1. View Hint View Answer Discuss in Forum

    Let the number be x.
    ∴  According to question,
    2x + 20 = 8x – 4
    or 8x – 2x = 20 + 4
    or 6x = 24
    ∴  x = 4

    Correct Option: C

    Let the number be x.
    ∴  According to question,
    2x + 20 = 8x – 4
    or 8x – 2x = 20 + 4
    or 6x = 24
    ∴  x = 4