Real Numbers Class 10 Extra Questions

Table of Contents

The product of a non-zero rational number and an irrational number is

a) Always irrational b) always rational c) rational or irrational d) none

2. The ratio of HCF to LCM of the least composite number and the least prime number is :

a) 1:2 b) 2:1 c) 1:1 d)1:3

3. If ‘p’ and ‘q’ are natural numbers and ‘p’ is a multiple of ‘q’, then what is the HCF of ‘p’ and ‘q’?

a) pq b) p c) q d) p + q

4. If a and b are two coprime numbers, then a³ and b³ are

a) Coprime b) not coprime c) even d) odd

5. The exponent of 5 in the prime factorization of 3750 is

a) 3 b) 4 c) 5 d) 6

6. What is the greatest possible speed at which a girl can walk 95 m and 171m in an exact number of minutes?

a) 17 m/min b) 19 m/min c) 23 m/min d) 13 m/min

7. If two positive integers a and b are written as a = x³y² and b = xy³, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a,b) is

a) xy b) xy² c) x³y³ d) x²y²

8. If n is any natural number, then 6ⁿ– 5ⁿ always ends with which digits?

a) 0 b) 1 c) 2 d) 3

SUBJECTIVE TYPE QUESTIONS

9. Find the sum of exponents of prime factors in the prime factorization of 196.

10. If HCF of 144 and 180 is expressed in the form 13m – 16. Find the value of m.

11. What is the remainder when the square of any prime number greater than 3 is divided by 6. ?

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

13. If a and b are prime numbers, then what is their L.C.M?

14. If n=2³x 3⁴ x 5⁴ x 7. Then what are the number of consecutive zeros in n, where n is a natural number?

15. If the LCM of a and 18 is 36 and the HCF of a and 18 is 2 then find a .

16. If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then what is the least prime factor of a+b?

17. Show that (12)ⁿ cannot end with digit 0 or 5 for any natural number n.

18. Can 2 numbers have 16 as their HCF and 380 as their LCM? Give reason.

19. Explain whether 3 x 12 x 101 + 4 is a prime number or a composite number.

20. If three pieces of planks 63m, 42m and 49 m long have to be divided into planks of same length, then what will be the least possible number of planks?

21. Three bells toll at intervals of 9, 12, 15 mins respectively. If they start tolling together, after what time will they next toll together

22. Check whether 4ⁿ can end with the digit 0 for any natural number n.

23. The L.C.M of two numbers is 14 times their H.C.F. The sum of L.C.M and H.C.F is 600. If one number is 280, then find the other number.

24. Find HCF of 96 and 404 by prime factorization method. Hence find their L.C.M

25. Find the largest positive integer that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively.

26. Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of a container which can measure the petrol of either tanker in exact number of times.

27. The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change together next?

28. Prove that √8 is irrational.

29. Prove that √2 + √5 is irrational.

30. Prove that is (3+ 2√5)² irrational. Given that √5 is irrational.

31. 2002 cartons of Lassi bottles and 2618 cartons of Frooti are to be stacked in a storeroom. If each stack is of the same height and is to contain cartons of the same type of bottles, what would be the greatest number of cartons each stack would have ?

32. Find the 4 digits largest number which is divisible by 12,15 and 24 .

33. If two numbers are in 5:3 and their LCM is 90. Find their HCF.

34. Given that HCF (2520,6600)=120 and LCM(2520,6600)=252k, then what is value of k ?

35. Find the smallest number which when increased by 17 is exactly divisible by both 520 and 468.

36. What is the smallest number that,when divided by 35,56 and 91 leaves remainder of 7 in each case.

37. A rectangular courtyard is 18m 72cm long and 13m 20cm broad. It is to be paved with square tiles of the same size . Find the least possible number of such tiles.

38. Assertion (A): If HCF (336, 54) = 6, then LCM (336, 54) = 3000.

Reason (R): The sum of exponents of prime factors in the prime factorization of 196 is 4

39. Assertion (A): HCF of two or more numbers = Product of the smallest power of each common prime factors, involved in the numbers.

Reason (R): The HCF of 12, 21 and 15 is 3.

40. Assertion (A): 6ⁿ ends with the digit 0, where n is a natural number.

Reason(R): Any number ends with the digit zero, if its prime factors are of the form 2^m x 5ⁿ ,where m ,n are natural numbers.

CASE STUDY

41. To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

1. What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?

2. Express 36 as a product of its primes

3. 7 is a ________ number

4. If p and q are positive integers such that p = a and q= b, where a , b are prime numbers, then find the LCM (p, q)

Trigonometry Class 10 Extra Questions https://www.youtube.com/@SharmaTutorial

https://sharmatutorial.in/important-questions-class-10-maths-with-solutions-pdf/

Real Numbers Class 10 Extra Questions

Real Numbers Class 10 Extra Questions | Real Numbers