Assignment - Real Number, Class 10 Mathematics PDF Download

VERY SHORT ANSWER TYPE QUESTIONS

1. Show that the product of two numbers 60 and 84 is equal to the product of their HCF and LCM.
2. The product of two numbers is 396 × 576 and their LCM is 6336. Find their HCF.
3. Without actually performing the long division, state whether the following rational numbers have a terminating decimal expansion or a non-terminating repeating decimal expansion :

1. 1/7
2. 1/11
3. 22/7
4. 3/5
5. 7/20
6. 2/13
7. 27/40
8. 13/125
9. 23/7
10. 42/100

4. Write down the decimal expansions of the following rational numbers :

1. 
2. 19/256
3. 25/1600
4. 9/30
5. 

5. Show that 5309 and 3072 are prime to each other.
6. The HCF of two numbers is 119 and their LCM is 11781. If one of the numbers is 1071, find the other.
7. The LCM of two numbers is 2079 and their HCF is 27. If one of the numbers is 189, find the other.
8. Find the prime factorization of the following numbers :

(i) 10000 (ii) 2160 (iii) 396 (iv) 4725 (v) 1188

9. Find the missing numbers in the following factorisation :

10. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion :

1. 11/125
2. 19/128
3. 32/405
4. 15/3200
5. 29/2401

11. Write down the decimal expansions of the following rational numbers :

1. 5/8
2. 12/125
3. 13/625
4. 7/64
5. 7/8

SHORT ANSWER TYPE QUESTIONS

12. Use Euclid's algorithm to find the HCF of 4052 and 12576.
13. Find the HCF 84 and 105, using Euclid's algorithm.
14. Find the HCF of 595 and 107, using Euclid's algorithm.
15. Find the HCF of 861 and 1353, using Euclid's algorithm.
16. Find the HCF of 616 and 1300, using Euclid's algorithm.
17. Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.
18. Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.
19. Show that one and only one out of n, n + 2 or n + 4 is divisible by 3, where n is any positive integer.
20. Find the greatest length which can be contained exactly in 10 m 5 dm 2 cm 4 mm and 12m 7dm 5cm  2mm.
21. Find the greatest measure which is exactly contained in 10 litres 857 millilitres and 15 litres 87 millilitres.
22. Consider the number 4n, where n is a natural number. Check whether there is any value of n ∈  N for  which 4ⁿ ends with the digit zero.
23. Find the LCM and HCF of 6 and 20 by the prime factorisation method.
24. Find the HCF of 12576 and 4052 by using the prime factorisation method.
25. Find the HCF and LCM of 6, 72 and 120 using the prime factorisation method.
26. Find the prime factors of the following numbers :
(i) 1300 (ii) 1365 (iii) 3456

27. Find the LCM and HCF of 18, 24, 60, 150.
28. Find the HCF and LCM of 60, 32, 45, 80, 36, 120.
29. Split 4536 and 18711 into their prime factors and hence find their LCM and HCF.
30. Prove that √5 is irrational.
31. Prove that √7 is irrational.
32. Prove that  s irrational.
33. Prove that 3√5 is irrational.
34. Prove that 3-√3is irrational.
35. Prove that 7+√2 is irrational.
36. Prove that 5-√5 is irrational.
37. Prove that 3√2 is irrational.

38. Use Euclid's division lemma to find the HCF of
(i) 13281 and 15844 (ii) 1128 and 1464 (iii) 4059 and 2190
(iv) 10524 and 12752 (v) 10025 and 14035

39. What is the greatest number by which 1037 and 1159 can both be divided exactly?
40. Find the greatest number which both 2458090 and 867090 will contain an exact number of times.
41. Find the greatest weight which can be contained exactly in 3 kg 7 hg 8 dag 1 g and 9kg 1hg 5dag 4g.
42. Find the LCM of the following using prime factorization method. :
(i) 72, 90, 120 (ii) 24, 63, 70 (iii) 455, 117, 338 (iv) 225, 240, 208
(v) 2184, 2730, 3360

43. Prove that √13 is irrational.
44. Prove that 2√2 is irrational.
45. Prove that 1/√5 is irrational.
46. Prove that 7+√3 is irrational.
47. Prove that 8-√2 is irrational.

PREVIOUS YEARS BOARD (CBSE) QUESTIONS

QUESTIONS CARRYING 1 MARK

1. If p/q is a rational number (q 0), what is condition of q so that the decimal representation of p/q is terminating?

[Delhi-2008]

2. Write a rational number between √2 and √3.

[AI-2008]

3. Complete the missing entries in the following factor tree :

[Foreign-2008]

4. The decimal expansion of the rational number  will terminate after how many places of decimals?

[Delhi-2009]

5. Find the [HCF × LCM] for the numbers 100 and 190.

[AI-2009]

6. Find the [HCF × LCM] for the numbers 105 and 120.

[AI-2009]

7. Write whether the rational number 51/1500 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

[Foreign-2009]

8. The HCF and LCM of two numbers are 9 and 360 respectively. If one number is 45, write the other number.

[Foreign-2009]

ANSWER KEY

VERY SHORT ANSWER TYPE QUESTIONS
2. 36.
3. (i) Non-terminating repeating ; (ii) Non-terminating repeating ; (iii) Non-terminating repeating
 (iv) Terminating ; (v) Terminating ; (vi) Non-terminating repeating ; (vii) Terminating ; (viii) Terminating
 (ix) Non-terminating repeating ; (x) Terminating
4. (i) 1.205 ; (ii) 0.07421875 ; (iii) 0.015625 ; (iv) 0.3 ; (v) 0.0266 6. 1309 7. 297
8. (i) 2⁴ × 5⁴ ; (ii) 2⁴ × 3³ × 5 ; (iii) 2² × 3² × 11 ; (iv) 3³ × 5² × 7 ; (v) 2² × 3³ × 11
9. (a) 4800 ; (b) 2400 ; (c) 1200 ; (d) 600 ; (e) 300 ; (f) 150 ; (g) 75 ; (h) 25
10. (i) Terminating ; (ii) Terminating ; (iii) Non-terminating repeating ; (iv) Terminating ; (v) Non-terminating
repeating
11. (i) 0.625 ; (ii) 0.96 ; (iii) 0.0208 ; (iv) 0.109375 ; (v) 0.875

SHORT ANSWER TYPE QUESTIONS

12. 4

13. 21

14. 119

15. 123

16. 4

20. 4 mm

21. 141 millilitres

22. No

23. 60, 2
24. 4

25. 6, 360

26. (i) 2² × 5² × 13 ; (ii) 3 × 5 × 7 × 13 ; (iii) 27 × 33

27. 1800, 6

28. 1, 1440
29. 149688, 567

38. (i) 233 ; (ii) 24 ; (iii) 3 ; (iv) 4 ; (v) 2005.

39. 61 40. 10 41. 1 hg 9 dag 9 g