1.The decimal form of 12.9225775 is
(a) terminating
(b) non-termining
(c) non-terminating non-repeating
(d) none of the above
2. HCF of 8, 9, 25 is
(a) 8
(b) 9
(c) 25
(d) 1
3. Which of the following is not irrational?
(a) (2 – √3)^2
(b) (√2 + √3)^2
(c) (√2 -√3)(√2 + √3)
(d)27√7
4. The product of a rational and irrational number is
(a) rational
(b) irrational
(c) both of above
(d) none of above
5. The sum of a rational and irrational number is
(a) rational
(b) irrational
(c) both of above
(d) none of above
6. The product of two different irrational numbers is always
(a) rational
(b) irrational
(c) both of above
(d) none of above
7. The sum of two irrational numbers is always
(a) irrational
(b) rational
(c) rational or irrational
(d) one
8. If b = 3, then any integer can be expressed as a =
(a) 3q, 3q+ 1, 3q + 2
(b) 3q
(c) none of the above
(d) 3q+ 1
9. The product of three consecutive positive integers is divisible by
(a) 4
(b) 6
(c) no common factor
(d) only 1
10. The set A = {0,1, 2, 3, 4, …} represents the set of
(a) whole numbers
(b) integers
(c) natural numbers
(d) even numbers
11. Which number is divisible by 11?
(a) 1516
(b) 1452
(c) 1011
(d) 1121
12. LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
(a) x
(b) y
(c) xy
(d) xy
13. The largest number that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively is
(a) 17
(b) 11
(c) 34
(d) 45
14. There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students
(a) 52
(b) 56
(c) 48
(d) 63
15. There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. 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 ?
(a) 36 minutes
(b) 18 minutes
(c) 6 minutes
(d) They will not meet
16. Express 98 as a product of its primes
(a) 2² × 7
(b) 2² × 7²
(c) 2 × 7²
(d) 23 × 7
17. Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.
(a) 98 kg
(b) 290 kg
(c) 200 kg
(d) 350 kg
18. For some integer p, every even integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p
19. For some integer p, every odd integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p
20. m² – 1 is divisible by 8, if m is
(a) an even integer
(b) an odd integer
(c) a natural number
(d) a whole number
21. If two positive integers A and B can be ex-pressed as A = xy3 and B = xiy2z; x, y being prime numbers, the LCM (A, B) is
(a) xy²
(b) x4y²z
(c) x4y3
(d) x4y3z
22. The product of a non-zero rational and an irrational number is
(a) always rational
(b) rational or irrational
(c) always irrational
(d) zero
23. If two positive integers A and B can be expressed as A = xy3 and B = x4y2z; x, y being prime numbers then HCF (A, B) is
(a) xy²
(b) x4y²z
(c) x4y3
(d) x4y3z
24. The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is
(a) 260
(b) 75
(c) 65
(d) 13
25. The least number that is divisible by all the numbers from 1 to 5 (both inclusive) is
(a) 5
(b) 60
(c) 20
(d) 100
26. The least number that is divisible by all the numbers from 1 to 8 (both inclusive) is
(a) 840
(b) 2520
(c) 8
(d) 420
27. The decimal expansion of the rational number 14587/250 will terminate after:
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) four decimal places
28. The decimal expansion of the rational number 97/2 ×5^4will terminate after:
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) four decimal place
29. The product of two consecutive natural numbers is always:
(a) prime number
(b) even number
(c) odd number
(d) even or odd
30. If the HCF of 408 and 1032 is expressible in the form 1032 x 2 + 408 × p, then the value of p is
(a) 5
(b) -5
(c) 4
(d) -4
31. The number in the form of 4p + 3, where p is a whole number, will always be
(a) even
(b) odd
(c) even or odd
(d) multiple of 3
32. When a number is divided by 7, its remainder is always:
(a) greater than 7
(b) at least 7
(c) less than 7
(d) at most 7
33. (6 + 5 √3) – (4 – 3 √3) is
(a) a rational number
(b) an irrational number
(c) a natural number
(d) an integer
34. If HCF (16, y) = 8 and LCM (16, y) = 48, then the value of y is
(a) 24
(b) 16
(c) 8
(d) 48
35. According to the fundamental theorem of arith-metic, if T (a prime number) divides b2, b > 0, then
(a) T divides b
(b) b divides T
(c) T2 divides b2
(d) b2 divides T2
36. The number ‘π’ is
(a) natural number
(b) rational number
(c) irrational number
(d) rational or irrational
37. If LCM (77, 99) = 693, then HCF (77, 99) is
(a) 11
(b) 7
(c) 9
(d) 22
38. Euclid’s division lemma states that for two positive integers a and b, there exist unique integer q and r such that a = bq + r, where r must satisfy
(a) a < r < b
(b) 0 < r ≤ b
(c) 1 < r < b
(d) 0 ≤ r < b
39. For some integer m, every odd integer is of the form
(A) m
(B) m + 1
(C) 2m
(D) 2m + 1
40. If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is:
(A) pq
(B) pq2
(C) p3q3
(D) p2q2
41. The product of a non-zero number and an irrational number is:
(A) always irrational
(B) always rational
(C) rational or irrational
(D) one
42. If the HCF of 65 and 117 is expressible in the form 65 m – 117, then the value of m is
(A) 4
(B) 2
(C) 1
43. The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is
(A) 13
(B) 65
(C) 875
(D) 1750
44. 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) a2b2
(C) a3b2
(D)
45. The values of the remainder r, when a positive integer a is divided by 3 are:
(A) 0, 1, 2, 3
(B) 0, 1
(C) 0, 1, 2
(D) 2, 3, 4
45.irratoonal number means
(A) Terminating decimal expansion
(B) Non-Terminating Non repeating decimal expansion
(C) Non-Terminating repeating decimal expansion
(D) None of these
46. A rational number in its decimal expansion is 327.7081. What would be the prime factors of q when the number is expressed in the p/q form?
(A) 2 and 3
(B) 3 and 5
(C) 2, 3 and 5
(D) 2 and 5
47. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
(A) 10
(B) 100
(C)2060
(D) 2520
48. n2 – 1 is divisible by 8, if n is
(A) an integer
49.
987/10500 will have
(B) a natural number
(C) an odd integer greater than 1
(D) an even integer
Answer: C
Explanation: n can be
49. If n is a rational number, then 52n − 22n is divisible by
(A) 3 (B) 7
(C) Both 3 and 7
(D) None of these
50. The H.C.F of 441, 567 and 693 is
(A) 1 (B) 441
(C)126
(D)
51. On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
(A) 2520cm
(B) 2525cm
(C)2555cm
(D) 2528cm
52. The decimal expansion of 22/7 is
(a) Terminating
(b) Non-terminating and repeating
(c) Non-terminating and Non-repeating
(d) None of the
53. For some integer n, the odd integer is represented in the form of:
(a) n
(b) n + 1
(c) 2n + 1
(d) 2n
54. HCF of 26 and 91 is:
(a) 15
(b) 13
(c) 19
55. Which of the following is not irrational?
(a) (3 + √7)
(b) (3 – √7)
(c) (3 + √7) (3 – √7)
(d) 3√7
Answer: (c) (3 + √7) (3 – √7)
56. The addition of a rational number and an irrational number is equal to:
(a) rational number
(b) Irrational number
(c) Both
(d) None of the above
57. The multiplication of two irrational numbers is:
(a) irrational number
(b) rational number
(c) Maybe rational or irrational
(d) None
58. If set A = {1, 2, 3, 4, 5,…} is given, then it represents:
(a) Whole numbers
(b) Rational Numbers
(c) Natural numbers
(d) Complex numbers
59. If p and q are integers and is represented in the form of p/q, then it is a:
(a) Whole number
(b) Rational number
(c) Natural number
(d) Even number
60. The largest number that divides 70 and 125, which leaves the remainders 5 and 8, is:
(a) 65
(b) 15
(c) 13
(d)
61. The least number that is divisible by all the numbers from 1 to 5 is:
(a) 70
(b) 60
(c) 80
(d) 90
62. The sum or difference of of two irrational numbers is always
(a) rational
(b) irrational
(c) rational or irrational
(d) not
63. The decimal expansion of the rational number 23/(22 . 5) will terminate after
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) more than 3 decimal places
64. 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 r must satisfy
(a) 1 < r < b
(b) 0 < r ≤ b
(c) 0 ≤ r < b
(d) 0 < r < b
65. For some integer m, every even integer is of the form
(a) m
(b) m + 1
(c) 2m
(d) 2m + 1
66. Using Euclid’s division algorithm, the HCF of 231 and 396 is
(a) 32
(b) 21
(c) 13
(d) 33
67. If the HCF of 65 and 117 is expressible in the form of 5m – 117, then the value of m is
(a) 4
(b) 2
(c) 1
(d)
68. The prime factorisation of 96 is
(a) 25 × 3
(b) 26
(c) 24 × 3
(d) 24 × 32
69. n² – 1 is divisible by 8, if n is
(a) an integer
(b) a natural number
(c) an odd integer
(d) an even integer
Answer: (c) an odd integer
Explanation:
We know that an odd number in the form (2Q + 1) where Q is a natural number ,
so, n² -1 = (2Q + 1)² -1
= 4Q² + 4Q + 1 -1
= 4Q² + 4Q
Substituting Q = 1, 2,…
When Q = 1,
4Q² + 4Q = 4(1)² + 4(1) = 4 + 4 = 8 , it is divisible by 8.
When Q = 2,
4Q² + 4Q = 4(2)² + 4(2) =16 + 8 = 24, it is also divisible by 8 .
When Q = 3,
4Q² + 4Q = 4(3)² + 4(3) = 36 + 12 = 48 , divisible by 8
It is concluded that 4Q² + 4Q is divisible by 8 for all natural numbers.
Hence, n² -1 is divisible by 8 for all odd values of n.
70. For any two positive integers a and b, HCF (a, b) × LCM (a, b) =
(a) 1
(b) (a × b)/2
(c) a/b
(d) a × b
71. The values of the remainder r, when a positive integer a is divided by 3 are
(a) 0, 1, 2
(b) Only 1
(c) Only 0 or 1
(d) 1, 2
72.The decimal form of 12.9225775 is
(a) terminating
(b) non-termining
(c) non-terminating non-repeating
(d) none of the above
73. HCF of 8, 9, 25 is
(a) 8
(b) 9
(c) 25
(d) 1
74. Which of the following is not irrational?
(a) (2 – √3)^2
(b) (√2 + √3)^2
(c) (√2 -√3)(√2 + √3)
(d)27√7
75. The product of a rational and irrational number is
(a) rational
(b) irrational
(c) both of above
(d) none of above
5. The sum of a rational and irrational number is
(a) rational
(b) irrational
(c) both of above
(d) none of above
6. The product of two different irrational numbers is always
(a) rational
(b) irrational
(c) both of above
(d) none of above
7. The sum of two irrational numbers is always
(a) irrational
(b) rational
(c) rational or irrational
(d) one
8. If b = 3, then any integer can be expressed as a =
(a) 3q, 3q+ 1, 3q + 2
(b) 3q
(c) none of the above
(d) 3q+ 1
9. The product of three consecutive positive integers is divisible by
(a) 4
(b) 6
(c) no common factor
(d) only 1
10. The set A = {0,1, 2, 3, 4, …} represents the set of
(a) whole numbers
(b) integers
(c) natural numbers
(d) even numbers
11. Which number is divisible by 11?
(a) 1516
(b) 1452
(c) 1011
(d) 1121
12. LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
(a) x
(b) y
(c) xy
(d) xy
13. The largest number that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively is
(a) 17
(b) 11
(c) 34
(d) 45
14. There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students
(a) 52
(b) 56
(c) 48
(d) 63
15. There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. 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 ?
(a) 36 minutes
(b) 18 minutes
(c) 6 minutes
(d) They will not meet
16. Express 98 as a product of its primes
(a) 2² × 7
(b) 2² × 7²
(c) 2 × 7²
(d) 23 × 7
17. Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.
(a) 98 kg
(b) 290 kg
(c) 200 kg
(d) 350 kg
18. For some integer p, every even integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p
19. For some integer p, every odd integer is of the form
(a) 2p + 1
(b) 2p
(c) p + 1
(d) p
20. m² – 1 is divisible by 8, if m is
(a) an even integer
(b) an odd integer
(c) a natural number
(d) a whole number
21. If two positive integers A and B can be ex-pressed as A = xy3 and B = xiy2z; x, y being prime numbers, the LCM (A, B) is
(a) xy²
(b) x4y²z
(c) x4y3
(d) x4y3z
22. The product of a non-zero rational and an irrational number is
(a) always rational
(b) rational or irrational
(c) always irrational
(d) zero
23. If two positive integers A and B can be expressed as A = xy3 and B = x4y2z; x, y being prime numbers then HCF (A, B) is
(a) xy²
(b) x4y²z
(c) x4y3
(d) x4y3z
24. The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is
(a) 260
(b) 75
(c) 65
(d) 13
25. The least number that is divisible by all the numbers from 1 to 5 (both inclusive) is
(a) 5
(b) 60
(c) 20
(d) 100
26. The least number that is divisible by all the numbers from 1 to 8 (both inclusive) is
(a) 840
(b) 2520
(c) 8
(d) 420
27. The decimal expansion of the rational number 14587250 will terminate after:
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) four decimal places
28. The decimal expansion of the rational number 972×54 will terminate after:
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) four decimal place
29. The product of two consecutive natural numbers is always:
(a) prime number
(b) even number
(c) odd number
(d) even or odd
30. If the HCF of 408 and 1032 is expressible in the form 1032 x 2 + 408 × p, then the value of p is
(a) 5
(b) -5
(c) 4
(d) -4
31. The number in the form of 4p + 3, where p is a whole number, will always be
(a) even
(b) odd
(c) even or odd
(d) multiple of 3
32. When a number is divided by 7, its remainder is always:
(a) greater than 7
(b) at least 7
(c) less than 7
(d) at most 7
33. (6 + 5 √3) – (4 – 3 √3) is
(a) a rational number
(b) an irrational number
(c) a natural number
(d) an integer
34. If HCF (16, y) = 8 and LCM (16, y) = 48, then the value of y is
(a) 24
(b) 16
(c) 8
(d) 48
35. According to the fundamental theorem of arith-metic, if T (a prime number) divides b2, b > 0, then
(a) T divides b
(b) b divides T
(c) T2 divides b2
(d) b2 divides T2
36. The number ‘π’ is
(a) natural number
(b) rational number
(c) irrational number
(d) rational or irrational
37. If LCM (77, 99) = 693, then HCF (77, 99) is
(a) 11
(b) 7
(c) 9
(d) 22
38. Euclid’s division lemma states that for two positive integers a and b, there exist unique integer q and r such that a = bq + r, where r must satisfy
(a) a < r < b
(b) 0 < r ≤ b
(c) 1 < r < b
(d) 0 ≤ r < b
39. For some integer m, every odd integer is of the form
(A) m
(B) m + 1
(C) 2m
(D) 2m + 1
40. If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is:
(A) pq
(B) pq2
(C) p3q3
(D) p2q2
41. The product of a non-zero number and an irrational number is:
(A) always irrational
(B) always rational
(C) rational or irrational
(D) one
42. If the HCF of 65 and 117 is expressible in the form 65 m – 117, then the value of m is
(A) 4
(B) 2
(C) 1
43. The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is
(A) 13
(B) 65
(C) 875
(D) 1750
44. 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) a2b2
(C) a3b2
(D)
45. The values of the remainder r, when a positive integer a is divided by 3 are:
(A) 0, 1, 2, 3
(B) 0, 1
(C) 0, 1, 2
(D) 2, 3, 4
45.irratoonal number means
(A) Terminating decimal expansion
(B) Non-Terminating Non repeating decimal expansion
(C) Non-Terminating repeating decimal expansion
(D) None of these
46. A rational number in its decimal expansion is 327.7081. What would be the prime factors of q when the number is expressed in the p/q form?
(A) 2 and 3
(B) 3 and 5
(C) 2, 3 and 5
(D) 2 and 5
47. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
(A) 10
(B) 100
(C)2060
(D) 2520
48. n2 – 1 is divisible by 8, if n is
(A) an integer
49.
987/10500 will have
(B) a natural number
(C) an odd integer greater than 1
(D) an even integer
Answer: C
Explanation: n can be
49. If n is a rational number, then 52n − 22n is divisible by
(A) 3 (B) 7
(C) Both 3 and 7
(D) None of these
50. The H.C.F of 441, 567 and 693 is
(A) 1 (B) 441
(C)126
(D)
51. On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
(A) 2520cm
(B) 2525cm
(C)2555cm
(D) 2528cm
52. The decimal expansion of 22/7 is
(a) Terminating
(b) Non-terminating and repeating
(c) Non-terminating and Non-repeating
(d) None of the
53. For some integer n, the odd integer is represented in the form of:
(a) n
(b) n + 1
(c) 2n + 1
(d) 2n
54. HCF of 26 and 91 is:
(a) 15
(b) 13
(c) 19
55. Which of the following is not irrational?
(a) (3 + √7)
(b) (3 – √7)
(c) (3 + √7) (3 – √7)
(d) 3√7
Answer: (c) (3 + √7) (3 – √7)
56. The addition of a rational number and an irrational number is equal to:
(a) rational number
(b) Irrational number
(c) Both
(d) None of the above
57. The multiplication of two irrational numbers is:
(a) irrational number
(b) rational number
(c) Maybe rational or irrational
(d) None
58. If set A = {1, 2, 3, 4, 5,…} is given, then it represents:
(a) Whole numbers
(b) Rational Numbers
(c) Natural numbers
(d) Complex numbers
59. If p and q are integers and is represented in the form of p/q, then it is a:
(a) Whole number
(b) Rational number
(c) Natural number
(d) Even number
60. The largest number that divides 70 and 125, which leaves the remainders 5 and 8, is:
(a) 65
(b) 15
(c) 13
(d)
61. The least number that is divisible by all the numbers from 1 to 5 is:
(a) 70
(b) 60
(c) 80
(d) 90
62. The sum or difference of of two irrational numbers is always
(a) rational
(b) irrational
(c) rational or irrational
(d) not
63. The decimal expansion of the rational number 23/(22 . 5) will terminate after
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) more than 3 decimal places
64. 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 r must satisfy
(a) 1 < r < b
(b) 0 < r ≤ b
(c) 0 ≤ r < b
(d) 0 < r < b
65. For some integer m, every even integer is of the form
(a) m
(b) m + 1
(c) 2m
(d) 2m + 1
66. Using Euclid’s division algorithm, the HCF of 231 and 396 is
(a) 32
(b) 21
(c) 13
(d) 33
67. If the HCF of 65 and 117 is expressible in the form of 5m – 117, then the value of m is
(a) 4
(b) 2
(c) 1
(d)
68. The prime factorisation of 96 is
(a) 25 × 3
(b) 26
(c) 24 × 3
(d) 24 × 32
69. n² – 1 is divisible by 8, if n is
(a) an integer
(b) a natural number
(c) an odd integer
(d) an even integer
Answer: (c) an odd integer
Explanation:
We know that an odd number in the form (2Q + 1) where Q is a natural number ,
so, n² -1 = (2Q + 1)² -1
= 4Q² + 4Q + 1 -1
= 4Q² + 4Q
Substituting Q = 1, 2,…
When Q = 1,
4Q² + 4Q = 4(1)² + 4(1) = 4 + 4 = 8 , it is divisible by 8.
When Q = 2,
4Q² + 4Q = 4(2)² + 4(2) =16 + 8 = 24, it is also divisible by 8 .
When Q = 3,
4Q² + 4Q = 4(3)² + 4(3) = 36 + 12 = 48 , divisible by 8
It is concluded that 4Q² + 4Q is divisible by 8 for all natural numbers.
Hence, n² -1 is divisible by 8 for all odd values of n.
70. For any two positive integers a and b, HCF (a, b) × LCM (a, b) =
(a) 1
(b) (a × b)/2
(c) a/b
(d) a × b
71. The values of the remainder r, when a positive integer a is divided by 3 are
(a) 0, 1, 2
(b) Only 1
(c) Only 0 or 1
(d) 1, 2values of n.
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