CBSE Class 10 Mathematics Real Numbers Worksheet Set F

Question. The sum of exponents of prime factors in the prime-factorisation of 196 is:
(a) 3
(b) 4
(c) 5
(d) 6
Answer : B

Question. The HCF and the LCM of 12, 21, 15 respectively are
(a) 3, 140
(b) 12, 420
(c) 3, 420
(d) 420, 3
Answer : C

Question. 7 × 11 × 13 × 15 + 15 is a:
(a) Composite number
(b) Whole number
(c) Prime number
(d) (a) and (b) both
Answer : D

Question. LCM of (2³ × 3 × 5) and (2⁴ × 5 × 7) is
(a) 40
(b) 560
(c) 1120
(d) 1680
Answer : D

Question. If two positive integers a and b are written as a = x³y² and b = xy³, where x and y are prime numbers, then the HCF (a, b) is:
(a) xy
(b) xy²
(c) x³y³
(d) x²y²
Answer : B

Question. If two positive integers p and q can be expressed as p = ab² and q = a³b where a and b are prime numbers, then the LCM (p, q) is:
(a) ab
(b) a²b²
(c) a³b²
(d) a³b³
Answer : C

Question. The decimal representation of 11/2³ × 5 will:
(a) terminate after 1 decimal place
(b) terminate after 2 decimal places
(c) terminate after 3 decimal places
(d) not terminate
Answer : C

Question. The total number of factors of a prime number is
(a) 1
(b) 0
(c) 2
(d) 3
Answer : C

Question. The LCM of smallest two digit composite number and smallest composite number is:
(a) 12
(b) 4
(c) 20
(d) 44
Answer : C

Question. The cube of any positive integer is not of the form:
(a) 9q
(b) 9q + 1
(c) 9q + 3
(d) 9q + 8
Answer : C

Question. If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a =
(a) 1
(b) 2
(c) 3
(d) 4
Answer : D

Question. The product of a non–zero rational and an irrational number is:
(a) always irrational
(b) always rational
(c) rational or irrational
(d) one
Answer : A

Question. 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75, what is the HCF of (525, 3000)?
(a) 25
(b) 125
(c) 75
(d) 15
Answer : C

Question. The decimal expansion of the rational number 14587/1250 will terminate after:
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) four decimal places
Answer : D

Question. 1.23451326... is
(a) an integer
(b) an irrational number
(c) a rational number
(d) none of these
Answer : B

Question. The number of decimal places after which the decimal expansion of the rational number 9/2⁴ × 5 will terminate, is:
(a) 1
(b) 2
(c) 3
(d) 4
Answer : D

Question. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is:
(a) 10
(b) 100
(c) 504
(d) 2520
Answer : D

Question. If HCF (a, b) = 45 and a × b = 30375, then LCM (a, b) is:
(a) 1875
(b) 1350
(c) 625
(d) 675
Answer : D

Question. If HCF of two numbers is 1, the numbers are called relatively ......... or ......... .
(a) Prime, co-prime
(b) Composite, prime
(c) Both (a) and (b)
(d) None of the above
Answer : A

Case Study Based Questions

I. The Army Day is celebrated on 15th January every year in India. The day is celebrated in the form of parades and other military shows in the national capital New Delhi as well as in all headquarters of army.

Parade I: An Army contingent of 616 members is to march behind an army band of 32 members in parade. The two groups are to march in the same number of columns.
Parade II: An Army contingent of 1000 members is to march behind an army band of 56 members in parade. The two groups are to march in the same number of columns.

Refer to Parade I

Question. Number 616 can be expressed as a product of its prime factors as
(a) 2¹ × 14¹ × 22¹
(b) 2² × 11¹ × 14¹
(c) 2³ × 7¹ × 11¹
(d) 2⁴ × 7² × 11¹
Answer : C

Question. The HCF of 32 and 616 is
(a) 8
(b) 16
(c) 18
(d) 12
Answer : A

Refer to Parade II

Question. The LCM of 56 and 1000 is
(a) 6000
(b) 7000
(c) 8000
(d) 9000
Answer : B

Question. Number 1000 can be expressed as a product of its prime factors as
(a) 2³ × 5³
(b) 2² × 5⁴
(c) 2⁴ × 5²
(d) 2³ × 5⁴
Answer : A

Question. The maximum number of columns in which army can march is
(a) 6
(b) 10
(c) 12
(d) 8
Answer : D

II. Traffic Lights are used to control movement of traffics. They are installed at crossings and intersections of roads. Usually three different colours of lights (Red, Yellow and Green) are used to tell commuters what to do.
The traffic lights at different road crossings change after every 48 seconds, 72 seconds and 120 seconds respectively.

Question. 120 can be expressed as a product of its prime factors as
(a) 2³ × 3¹ × 5¹
(b) 2² × 3² × 5¹
(c) 2² × 3¹ × 5²
(d) 2³ × 3² × 5¹
Answer : A

Question. The HCF of 48, 72 and 120 is
(a) 12
(b) 16
(c) 18
(d) 24
Answer : D

Question. The LCM of 48, 72 and 120 is
(a) 432
(b) 420
(c) 720
(d) 840
Answer : C

Question. If all the traffic lights change simultaneously at 7 : 30 : 00 hours, they will change again simultaneously at
(a) 7 : 42 : 00 hrs
(b) 7 : 52 : 00 hrs
(c) 7 : 36 : 00 hrs
(d) 7 : 46 : 00 hrs
Answer : A

Question. The [HCF × LCM] for the numbers 48, 72 and 120 is
(a) 17480
(b) 17280
(c) 12280
(d) 18280
Answer : B

1. If 7x5x3x2 + 3 is composite number? Justify your answer

2. Show that any positive odd integer is of the form 4q + 1 or 4q +3 where q is a positive integer

3. Prove that √2 + √5 is irrational

4. Prove that 5 - 2√3 is an irrational number

5. Prove that √2 is irrational

6. Use Euclid’s Division Algorithms to find the H.C.F of a) 135 and 225 (45)

b) 4052 and 12576 (4)

c) 270, 405 and 315 (45)

7. Find the HCF and LCM of 26 and 91 and verify that LCM X HCF = Product of two numbers (13,182) 8. Explain why 29 is a terminating decimal expansion 23 x 53 

9. 163 will have a terminating decimal expansion. State true or false .Justify your answer. 150

10. Find HCF of 96 and 404 by prime factorization method. Hence, find their LCM. (4, 9696)

11. Using prime factorization method find the HCF and LCM of 72, 126 and 168 (6, 504)

12. If HCF (6, a) = 2 and LCM (6, a) = 60 then find a (20)

13. given that LCM (77, 99) = 693, find the HCF (77, 99) (11)

14. Find the greatest number which exactly divides 280 and 1245 leaving remainder 4 and 3 (138)

15. The LCM of two numbers is 64699, their HCF is 97 and one of the numbers is 2231. Find the other (2813)

16. Two numbers are in the ratio 15: 11. If their HCF is 13 and LCM is 2145 then find the numbers (195,143)

17. Express 0.363636………… in the form a/b (4/11)

18. Write the HCF of smallest composite number and smallest prime number

19. Write whether 2√45 + 3√20 on simplification give a rational or an irrational number 2√5

20. State whether 10.064 is rational or not. If rational, express in p/q form

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

22. State the fundamental theorem of arithmetic PREPARED BY: MAHABOOB PASHA IX – X BOYS

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