# CHAPTER 1 – REAL NUMBERS – Class 10 – MATHS ASSIGNMENT

- Express each number as product of its prime factors:

1). 140 2). 156 3). 3825 4). 5005 6). 742

**2.** Given that HCF (306, 657) = 9, find LCM (306, 657).

**3**. [ 7×11×13×15+15 ] is a

(a) Composite number (b) Whole number (c) Prime number (d) none of these.

**4.** For what least value of ‘n’ a natural number, (24)^{n} is divisible by 8?

(a) 0 (b) -1 (c) 1 (d) No value of ‘n’ is possible

**5**. The sum of a rational and an irrational number is

(a) Rational (b) Irrational (c) Both (a) & (c) (d) Either (a) or (b)

**6**. HCF of two numbers is 113, their LCM is 56952. If one number is 904, then other number is:

(a) 7719 (b) 7119 (c) 7791 (d) 7911

**7**. If H C F of two numbers is 1, the two numbers are called relatively

(a) prime, co-prime (b) composite, prime (c) Both (a) and (b) (d) None of these.

**8.** 2.35 is

(a) a terminating decimal number (b) a rational number

(c) an irrational number (d) Both (a) and (b)

**9**. 2.13113111311113……is :

(a) a rational number (b) a non-terminating decimal number

(c) an irrational number (d) Both (a) & (c)

**10. **The smallest composite number is:

(a) 1 (b) 2 (c) 3 (d) 4

**11.** 1.2348 is

(a) an integer (b) an irrational number (c) a rational number (d) None of these

**12. **Π is

(a) a rational number (b) an irrational number (c) both (a) & (b) (d) neither rational nor irrational.

**13**. (2+√5) is

(a) a rational number (b) an irrational number (c) an integer (d) not real number

**14**. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

**15**. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

1). 26 and 91 2). 510 and 92 3). 336 and 54

**16**. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

**17**. Prove that √5 is irrational.

**18**. Prove that (3+2√5) is irrational.

**19**. Prove that the difference and quotient of (3 +2√3) and (3-2√3) are irrational.

**20**. Check whether 6*n *can end with the digit 0 for any natural number *n*.

**21**. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where *q *is some integer.

**22**. Show that every positive even integer is of the form 2q and that every positive odd integer is of the form 2q + 1 for some integer q.

**23**. Show that any number of the form 4n, n Є N can never end with the digit 0.

**24**. Show that any number of the form 6x, x Є N can never end with the digit 0.Show that every positive odd integer is of the form (4q + 1) or (4q + 3) for some integer q.

**25**. Prove that if x and y are odd positive integers, then x2 + y2 is even but not divisible by 4.

**26**. Show that (n2 – 1) is divisible by 8, if n is an odd positive integer.

**27**. Show that one and only one out of n, (n + 2) or (n + 4) is divisible by 3, where n Є N.

**28**. Given that HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, find the other.

**29**. Find HCF and LCM of 18 and 24 by the prime factorization method.

**30.** The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, find the other.

**31**. Find the largest number which divides 245 and 1029 leaving remainder 5 in each case.

**32**. A shopkeeper has 120 liters of petrol, 180 liters of diesel and 240 liters of kerosene. He wants to sell oil by filling the three kinds of oils in tins of equal capacity. What should be the greatest capacity of such a tin?

**33**. Find the greatest number of 6 digits exactly divisible by 24, 15 and 36.

**34.** 144 cartons of coke can and 90 cartons of Pepsi can are to be stacked in a canteen. If each stack is of the same height and is to contain cartons of the same drink. What would be the greater number of cartons each stack would have?

**35**. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?