MULTIPLE CHOICE QUESTIONS (MCQ’s )
1. Euclid’s division algorithm can be applied to ____
(a) Only positive integers
(b) Only negative integers
(c) All integers
(d) All rational numbers.
2. Find the HCF of 12, 18.
(a) 6
(b) 2
(c) 3
(d) 4
3. For some integer m, every even integer is of the form _____
(a) m
(b) m + 1
(c) 2m
(d) 2m + 1
4. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ______
(a) 1
(b) 2
(c) 3
(d) 4
5. If two positive integers p and q can be expressed as p = ab2 and q = a3b,
a; b being prime numbers, then LCM (p, q) is _____
(a) ab
(b) a2 b2
(c) a3 b2
(d) a3 b3
6. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) will be _____
(a) 10
(b) 100
(c) 504
(d) 2520
7. The product of two numbers is 192. The HCF is 8 ∴ The LCM = ____
(a) 14
(b) 24
(c) 34
(d) 44
8. 7 × 11 × 13 × 15 + 15 is _____
(a) Composite number
(b) Prime number
(c) Neither composite nor prime
(d) None of these
9. The number 1.23 is _____
(a) An integer
(b) An irrational number
(c) A rational number
(d) None of these
10. Euclid’s division lemma states that for two positive integers a and b, there
exist unique integers q and r such that a = bq + r, where ____
(a) 0 < r ≤ b
(b) 1 < r < b
(c) 0 < r < b
(d) 0 ≤ r < b
11. 3.24636363 . . . is ____
(a) A terminating decimal number
(b) A non-terminating repeating decimal number
(c) A rational number
(d) Both (b) and (c)
12. Find HCF if the LCM of 90, 210 is 630
(a) 14
(b) 24
(c) 30
(d) 40
13.(n + 1)2 – 1 is divisible by 8, if n is ____
(a) An odd integer
(b) An even integer
(c) A natural number
(d) An integer
14. A ______ is a proven statement used for proving another statement.
(a) Theorem
(b) Lemma
(c) Axiom
(d) Postulate
15. A number is said to be an _________number , if it cannot be expressed
in the form \frac { p }{ q } where “p” and “q” are integers and q ≠ 0
(a) Irrational
(b) Rational
(c) Perfect
(d) Square
16. If HCF of x and 54 is 27 and their is LCM is 162 what is the value of x ?
(a) 81
(b) 36
(c) 80
(d) 54
17. If a\times b = 1600 and LCM of a and b is 320 ,then what is the HCF of a and b?
(a) 7
(b) 4
(c) 5
(d) 9
18. Which of the following has a terminating decimal expression?
(a) \frac { 25 }{ 61 }
(b) \frac { 13 }{ 43 }
(c)\frac { 19 }{ 80 }
(d) \frac { 3 }{ 7 }
19. For what least value n, is (24)n divisible by 8?
(a) n = 1
(b) n = 2
(c) n = 3
(d) n = 4
20. Product of two numbers is 864.If HCF is 12 .Then LCM + ___
(a) 72
(b) 42
(c) 54
(d) 96
21. The sum of a rational and an irrational number is
(a) Rational
(b) Irrational
(c) Both (a) & (c)
(d) Either (a) or (c)
22. HCF of two number is 113 and their LCM is 56952.
If one number is 904 , then the other number is :
(a) 7719
(b) 7119
(c) 7791
(d) 7911
23. A lemma is an axiom used for proving:
(a) Other statement
(b) No statement
(c) Contradictory statement
(d) None of the above
24. Find HCF of 81, 135
(a) 32
(b) 42
(c) 54
(d) 27
25. 2.13113111311113….. is:
(a) A rational number
(b) A non-terminating repeating decimal number
(c) An irrational number
(d) Both (a) & (b)
26. The smallest composite number is:
(a) 1
(b) 2
(c) 3
(d) 4
27. HCF is 36 The numbers are 360,252 .Then the LCM is ___
(a) 1540
(b) 2554
(c) 2520
(d) 412
28. 1.2348 is _______
(a) An integers
(b) An irrational number
(c) A rational number
(d) None of these
29. The product of two numbers is 1815. The LCM is 55. Then the HCF is ____
(a) 15
(b) 33
(c) 25
(d) 41
30. π is ___
(a) A rational number
(b) An irrational number
(c) Both (a) & (b)
(d) Neither rational nor irrational
31. (2 + √5) is ____
(a) A rational number
(b) An irrational number
(c) An integer
(d) Not a real number
32. The product of two numbers is 1640 and their HCF is 5. Find their LCM.
(a) 430
(b) 330
(c) 350
(d) 552
33. The prime factors of 1356 are ____-
(a) 2 x 3 x 3 x 7 x 11
(b) 2 x 3 x 3 x 7 x 13
(c) 2 x 3 x 7 x 7 x 11
(d) 2 x 5 x 3 x 7 x 11
34. The LCM of 12, 15, 21 is ___
(a) 156
(b) 332
(c) 420
(d) 410
35. Express 315 as the product of it’s factors.
(a) 3 x 3 x 5 x 11
(b) 3 x 7 x 5 x 7
(c) 3 x 3 x 5 x 7
(d) 3 x 5 x 5 x 7
Answers + Clues:
1.(a) ⇒ Read Euclid’s Algorithm
2.(a) ⇒ Find the factors and common factors multiplied will be HCF
3.(c) ⇒ It has to be multiple of 2 (even)
4.(b) ⇒ HCF of 65, 117 is 13. So 13 = 65m − 117 ∴ m = 2
5.(c) ⇒ ab2 = a x b x b and a3 b = a x a x a x b then find LCM by factor method.
6.(d) ⇒ Find the factors e.g. 1 = 1 x 1 , 2 = 2 x 2 , 3 = 3 x 1 , 4 = 2 x 2 and so on. Then find LCM
7. (b) ⇒ HCF x LCM = Product of numbers
8.(a) ⇒ 7\times 11\times 13\times 15+15=15(7\times 11\times 13)+1 ∴ it is composite number
9.(c) ⇒ 1.23 = \frac { 123 }{ 150 }
10.(d) ⇒ Read Euclid’s Division Lemma
11.(b) ⇒ Since 636363…… is repeated and not terminating
12.(c) ⇒ HCF x LCM = Product of numbers
13.(b) ⇒ (n + 2)2 −1 divisible by 8
{ 2 + 1 }^{ 2 }−1 = 9−1 = 8\div 8
{ (4 + 1) }^{ 2 }−1 = 25−1 = 24\div 8
{ (6 + 1) }^{ 2 }−1 = 49−1 = 48\div 8
14.(b) ⇒ Lemma definition
15.(a) ⇒ Irrational number definition
16.(a) ⇒ HCF x LCM = product of numbers
17.(c) ⇒ a x b = 1600. LCM = 320 ∴ HCF x LCM = Product of numbers
18.(c) ⇒ Any expression with denominator an odd number, cannot have a terminating decimal
19. (a) ⇒ (24)n (24)1 = \frac { 8\times 3 }{ 8 } = { (3) }^{ 1 } least value is 1
20. (a) ⇒ HCF x LCM = Product of numbers
21. (b) ⇒ Text book statement
22. (b) ⇒ HCF x LCM = Product of numbers
23.(a) ⇒ Property of Lemma
24. (d) ⇒ Find the factors and common factors multiplied by remaining factors will be LCM
25.(c) ⇒ Examples of irrational numbers in text book
26.(d) ⇒ Definition of composite number.
27. (c) ⇒ HCF x LCM = Product of numbers
28.(c) ⇒ 1.2348 = \frac { 12348 }{ 1000 }
29. (b) ⇒ HCF x LCM = Product of numbers
30.(b) ⇒ Since π = \frac { 22}{ 7} which is a rational number.
31.(b) ⇒ (2+\sqrt { 5 } ) = sum of rational number + irrational number is irrational
32.(b) ⇒ HCF x LCM = Product of numbers
33. (a)⇒ Find the factors
34. (c) ⇒ Find the factors and common factors multiplied by remaining factors will be LCM
35. (c) ⇒ Find the factors