Numbers and Sequences Important Questions

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  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. The sum of the exponents of the prime factors in the prime factorization of 1729 is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  5. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

    (a)

    2025

    (b)

    5220

    (c)

    5025

    (d)

    2520

  6. 7 x 2 = 14
  7. Show that the square of an odd integer is of the form 4q + 1, for some integer q.

  8. If the Highest Common Factor of 210 and 55 is expressible in the form 55x - 325, find x 

  9. Find the greatest number that will divide 445 and 572 leaving remainders 4 and 5 respectively.

  10. Find the HCF of 396, 504, 636.

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

  12. Find the LCM and HCF of 6 and 20 by the prime factorisation method.

  13. Prove that \(\sqrt { 3 } \) is irrational

  14. 7 x 3 = 21
  15. In the given factor tree, find the numbers m and n.

  16. Can the number 6n, n being a natural number end with the digit 5? Give reason for your answer.

  17. Is 7 x 5 x 3 x 2 + 3 a composite number? Justify your answer 

  18. Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
    4,10,16,22, ...

  19. Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
    -2, 2, -2, 2, -2

  20. Determine the AP whose 3rd term is 5 and the 7th term is 9.

  21. In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 is the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

  22. 2 x 5 = 10
  23. Find all positive integers, when divided by 3 leaves remainder 2.

  24. How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?

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