Numbers and Sequences Book Back Questions

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    6 x 1 = 6
  1. Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

    (a)

    1 < r < b

    (b)

    0 < r < b

    (c)

    \(\le\) r < b

    (d)

    0 < r \(\le\) b

  2. Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

    (a)

    0, 1, 8

    (b)

    1, 4, 8

    (c)

    0, 1, 3

    (d)

    0, 1, 3

  3. If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

    (a)

    4

    (b)

    2

    (c)

    1

    (d)

    3

  4. Given F1 = 1, F2 = 3 and Fn = Fn-1+Fn-2 then F5 is

    (a)

    3

    (b)

    5

    (c)

    8

    (d)

    11

  5. If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is

    (a)

    0

    (b)

    6

    (c)

    7

    (d)

    13

  6. In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

    (a)

    6

    (b)

    7

    (c)

    8

    (d)

    9

  7. 3 x 2 = 6
  8. Find the greatest number that will divide 445 and 572 leaving remainders 4 and 5 respectively.

  9. Find the remainders when 70004 and 778 is divided by 7

  10. Find the number of integer solutions of 3x \(\equiv \) 1 (mod 15).

  11. 2 x 5 = 10
  12. In the given factor tree, find the numbers m and n.

  13. Find the sum of all natural numbers between 300 and 600 which are divisible by 7.

  14. 1 x 8 = 8
  15. A positive integer when divided by 88 gives the remainder 61. What will be the remainder when the same number is divided by 11?

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