Subject: Mathematics (Real Numbers)Max Marks: 100Time: 60 Mins
Name:
Date:
Section A: Multiple Choice Questions (Basic Concepts)40 x 1 = 40 Marks
1. Which of the following is not a Rational Number?
(a) $\sqrt{4}$
(b) $3.14$
(c) $\frac{22}{7}$
(d) $\pi$
2. The Fundamental Theorem of Arithmetic deals with the factorization of which type of
numbers?
(a) Prime Numbers
(b) Composite Numbers
(c) Odd Numbers
(d) Even Numbers
3. If $p$ is a prime number, then $\sqrt{p}$ is always:
(a) Rational
(b) Irrational
(c) Integer
(d) None of these
4. The HCF of two prime numbers is always:
(a) 0
(b) 1
(c) Their Product
(d) Their Sum
5. The LCM of two prime numbers $a$ and $b$ is:
(a) 1
(b) $a+b$
(c) $ab$
(d) $a-b$
6. For any two positive integers $a$ and $b$, which formula is correct?
(a) $HCF \times LCM = a + b$
(b) $HCF \times LCM = a \times b$
(c) $HCF + LCM = a \times b$
(d) $HCF / LCM = a / b$
7. Which of the following numbers has a terminating decimal expansion?
(a) $\frac{1}{7}$
(b) $\frac{1}{3}$
(c) $\frac{3}{8}$
(d) $\frac{1}{6}$
8. The prime factorization of 12 is:
(a) $2^2 \times 3$
(b) $2 \times 3^2$
(c) $4 \times 3$
(d) $6 \times 2$
9. If a number ends with 0, its prime factorization must contain:
(a) Only 2
(b) Only 5
(c) Both 2 and 5
(d) Neither
10. Euclid's Division Lemma states that for any 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) $0 < r \le b$
(c) $0 \le r < b$
(d) $0 \le r \le
b$
11. A composite number is a number that has:
(a) Exactly 2 factors
(b) More than 2 factors
(c) Only 1 factor
(d) No factors
12. Smallest composite number is:
(a) 1
(b) 2
(c) 3
(d) 4
13. Smallest prime number is:
(a) 0
(b) 1
(c) 2
(d) 3
14. Is 1 a prime or composite number?
(a) Prime
(b) Composite
(c) Neither Prime nor Composite
(d) Both
15. The product of a non-zero rational and an irrational number is:
(a) Always Rational
(b) Always Irrational
(c) Sometimes Rational
(d) 1
16. The decimal expansion of $\frac{17}{8}$ will terminate after how many decimal
places?
(a) 1
(b) 2
(c) 3
(d) 4
17. $2.\overline{35}$ is:
(a) An Integer
(b) A Rational Number
(c) An Irrational Number
(d) A Natural Number
18. HCF of 96 and 404 is:
(a) 2
(b) 3
(c) 4
(d) 8
19. If $a = 2^3 \times 3$ and $b = 2 \times 3 \times 5$, then LCM(a, b) is:
(a) $2^3 \times 3 \times 5$
(b) $2 \times 3$
(c) $2 \times 3 \times 5$
(d) $2^4 \times 3^2 \times 5$
20. Which of the following is an irrational number?
(a) $\sqrt{9}$
(b) $\sqrt{16}$
(c) $\sqrt{11}$
(d) $\sqrt{25}$
21. The relationship between HCF and LCM of three numbers $a, b, c$ is:
(a) $HCF \times LCM = a \times b \times
c$
(b) $HCF(a,b,c) \times LCM(a,b,c) \neq a
\times b \times c$
(c) $HCF + LCM = a + b + c$
(d) None
22. $\pi$ is:
(a) Rational
(b) Irrational
(c) Integer
(d) Whole Number
23. Sum of two irrational numbers is:
(a) Always Rational
(b) Always Irrational
(c) Rational or Irrational
(d) Always Integer
24. $n^2 - 1$ is divisible by 8, if $n$ is:
(a) An Integer
(b) A Natural Number
(c) An Odd Integer
(d) An Even Integer
25. If two positive integers $p$ and $q$ can be expressed as $p = ab^2$ and $q = a^3b$,
$a, b$ being prime numbers, then LCM(p, q) is:
(a) $ab$
(b) $a^2b^2$
(c) $a^3b^2$
(d) $a^3b^3$
26. HCF of co-prime numbers is always:
(a) 0
(b) 1
(c) Product
(d) Sum
27. Euclid's Division Algorithm is a technique to compute:
(a) HCF
(b) LCM
(c) Remainder
(d) Quotient
28. The decimal form of $\frac{129}{2^2 \cdot 5^7 \cdot 7^5}$ is:
(a) Terminating
(b) Non-terminating
(c) Non-terminating repeating
(d) None of the above
29. Which of these is a pair of co-primes?
(a) (14, 35)
(b) (18, 25)
(c) (31, 93)
(d) (32, 62)
30. Any positive odd integer is of the form:
(a) $2q$
(b) $2q+1$
(c) $3q$
(d) $4q$
31. LCM of 12, 15 and 21 is:
(a) 420
(b) 240
(c) 120
(d) 480
32. HCF of 12, 15 and 21 is:
(a) 3
(b) 4
(c) 12
(d) 1
33. If $n$ is a natural number, then $6^n$ always ends with:
(a) 0
(b) 5
(c) 6
(d) 2
34. A rational number $p/q$ has a terminating decimal expansion if prime factorization
of $q$ is of the form:
(a) $2^n 5^m$
(b) $2^n 3^m$
(c) $3^n 5^m$
(d) $7^n 5^m$
35. The largest number which divides 70 and 125, leaving remainders 5 and 8,
respectively, is:
(a) 13
(b) 65
(c) 875
(d) 1750
36. If two integers $a$ and $b$ are written as $a = x^3y^2$ and $b = xy^3$, where $x,y$
are prime numbers, then HCF(a, b) is:
(a) $xy$
(b) $xy^2$
(c) $x^3y^3$
(d) $x^2y^2$
37. Total number of factors of a prime number is:
(a) 1
(b) 0
(c) 2
(d) 3
38. Every composite number can be expressed as a product of primes, and this
decomposition is unique, apart from the order. This is statement of:
(a) Euclid's Division Lemma
(b) Fundamental Theorem of Arithmetic
(c) Pythagoras Theorem
(d) Thales Theorem
39. The number of decimal places after which the decimal expansion of the rational
number $\frac{23}{2^2 5}$ will terminate is:
(a) 1
(b) 2
(c) 3
(d) 4
40. $\frac{6}{15}$ decimal expansion is:
(a) 0.4
(b) 0.3
(c) 0.6
(d) Non-terminating
Section B: Fill in the Blanks20 x 1 = 20 Marks
41. The fundamental theorem of arithmetic states that every composite number can be
expressed as a product of .
42. HCF(a, b) $\times$ LCM(a, b) = .
43. If a number has a non-terminating non-recurring decimal expansion, it is .
44. $\sqrt{3}$ is an number.
45. A rational number $p/q$ terminates if the prime factorization of $q$ is of the form
.
46. The HCF of two consecutive even numbers is .
47. The smallest prime number which is even is .
48. $7 \times 11 \times 13 + 13$ is a
number.
49. The HCF of 52 and 130 is .
50. If $n$ is a natural number, $4^n$ can never end with the digit .
51. The exponent of 2 in the prime factorization of 144 is .
52. LCM of 5 and 7 is .
53. The number of irrational numbers between 2 and 3 is .
54. $3 + \sqrt{5}$ is an number.
55. Standard form of $0.125$ is .
56. Prime factorization of 5005 is .
57. The smallest number divisible by both 306 and 657 is .
58. Any positive integer ending with digit 5 is divisible by .
59. Euclid's Division Lemma is basically a restatement of the long process.
60. Two numbers having only 1 as a common factor are called .
Section C: True or False20 x 1 = 20 Marks
61. Every natural number is a whole number.
True
False
62. Every integer is a rational number.
True
False
63. There are infinitely many rational numbers between any two rational numbers.
True
False
64. The sum of two irrational numbers is always irrational.
True
False
65. $\pi$ is a rational number.
True
False
66. The product of two prime numbers is always a prime number.
True
False
67. $\sqrt{4}$ is an irrational number.
True
False
68. HCF is always a factor of LCM.
True
False
69. Every composite number can be expressed as product of primes in a unique
way.
True
False
70. The decimal expansion of $13/125$ is non-terminating repeating.
True
False
71. 3 is a factor of 10.
True
False
72. All prime numbers are odd.
True
False
73. HCF of $(a, 1) = 1$.
True
False
74. LCM of $(a, 1) = a$.
True
False
75. The number $1.232323...$ is rational.
True
False
76. The product of three consecutive positive integers is divisible by 6.
True
False
77. $\sqrt{p} + \sqrt{q}$ is always irrational if p, q are prime.
True
False
78. Terminating decimal numbers are always Rational.
True
False
79. $17/6$ is a terminating decimal.
True
False
80. Every real number is either rational or irrational.
True
False
Section D: One Word / Formula Recall20 x 1 = 20 Marks
81. Write the formula for HCF and LCM of two numbers a and b.
82. Define Prime Number.
83. Define Composite Number.
84. What is the value of $\sqrt{225}$?
85. Give an example of two irrational numbers whose product is rational.
86. Write the prime factorization of 100.
87. What is the HCF of two prime numbers $x$ and $y$?
88. What is the LCM of two prime numbers $x$ and $y$?
89. Check if $13/3125$ is terminating. (Yes/No)
90. Is zero a rational number? (Yes/No)
91. Write the condition for a rational number to be terminating decimal.
92. Find HCF(10, 100).
93. Find LCM(4, 5).
94. What is the HCF of smallest prime and smallest composite number?
95. If $p$ is a prime, then $p^2$ has how many factors?
96. Name the mathematician associated with the Division Lemma.
97. Is $22/7$ rational or irrational?
98. Write 0.375 in p/q form.
99. Express 140 as product of primes.
100. Can two numbers have 18 as their HCF and 380 as their LCM? (Yes/No)
