#### 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?