**CBSE Class 10 Question Bank mathematics Euclid’s Division Lemma**

Questions on Euclid’s Division Lemma

Objective Questions:

**1.Euclid’s division lemma, states that for any two positive integers ‘a’ and ‘b’ we can find two whole numbers ‘q’ and ‘r’ such that a = b × q + r**

**what are permissible values of r?**

a.0 or more but less than b

b. 0 or more but less than a

c b or more but less than a

d. Between 0 and infinity

**2.Euclid’s division lemma can be used to find the .............. of any two positive integers**

a. HCF

b. Multiples

c Both

d. None

**3.Euclid’s division lemma is not applicable for which value of b ?**

a. Positive integer

b. Zero

c Negative integer

d. All of these

**4.Any positive integer can be expressed as ?**

a. 6q +1

b. 6q +3

c 6q+5

d. All of these

**5.Product of 3 consecutive positive integers is always divisible by ?**

a. 4

b. 5

c 6

d. 7

**6.Using Euclid’s division lemma HCF of 455 and 42 can be expressed as**

a. 455 = 42*9+77

b. 455 = 42*10+35

c 455 = 42*11 -7

d. 455 = 42*12 -49

**7.Any positive integer is of the form............for some integer q.**

a. 3q

b.3q + 1

c 3q + 2

d. all of these

**8.One out of any four consecutive integers is always divisible by 5.**

a. FALSE

b.TRUE

c None of these

d. all of these

**9. For any value of n,last digit of**6

^{n}

**always ends with**

a. 4

b 8

c either 4 or 8

d.None of these

**10. 4q+1 or 4q+3 , a positive integer is always**

a. ODD

b EVEN

c None of these

d. all of these

**Hot And Tough Questions:**

1.Prove that the product of two consecutive positive integers is always divisible by 2

2.Show that n

^{2}- 1 is divisible by 8, if n is an odd positive integer.

3.Show that one and only one out of n,n+2,n+4 is divisible by 3, where n is any positive integer.

4.prove that for any value of n,12

^{n }cant have 5 as last digit5. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

6.Prove that the product of three consecutive positive integers is divisible by 6.

7.Prove that one of every three consecutive integers is divisible by 3.

8.Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m +1 for some integer m.

9.Prove that sum of any three consecutive integers is divisible by 3.

Answer

1:a

2.a

3.b

4.d

5. c

6. b

7 d

8. a

9. d

10. a

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