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VARDAAN LEARNING INSTITUTE

Level 0: Solution Sheet

Subject: Mathematics (Real Numbers) Max Marks: 100 Time: 60 Mins
Section A: Multiple Choice Questions ANSWERS
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 $a = bq + r$, 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 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. Product of non-zero rational and irrational:
(a) Always Rational
(b) Always Irrational
(c) Sometimes Rational
(d) 1
16. Decimal expansion of $\frac{17}{8}$ terminates after:
(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. LCM of $2^3 \times 3$ and $2 \times 3 \times 5$:
(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 is irrational?
(a) $\sqrt{9}$
(b) $\sqrt{16}$
(c) $\sqrt{11}$
(d) $\sqrt{25}$
21. Relation HCF/LCM for 3 numbers $a, b, c$:
(a) $HCF \times LCM = abc$
(b) $HCF \times LCM \neq abc$
(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. $n^2 - 1$ divisible by 8 if $n$ is:
(a) An Integer
(b) A Natural Number
(c) An Odd Integer
(d) An Even Integer
25. LCM of $p = ab^2$ and $q = a^3b$:
(a) $ab$
(b) $a^2b^2$
(c) $a^3b^2$
(d) $a^3b^3$
26. HCF of co-prime numbers is:
(a) 0
(b) 1
(c) Product
(d) Sum
27. Euclid's Division Algorithm computes:
(a) HCF
(b) LCM
(c) Remainder
(d) Quotient
28. Decimal form of $\frac{129}{2^2 \cdot 5^7 \cdot 7^5}$:
(a) Terminating
(b) Non-terminating
(c) Non-terminating repeating
(d) None of the above
29. Pair of co-primes:
(a) (14, 35)
(b) (18, 25)
(c) (31, 93)
(d) (32, 62)
30. Any positive odd integer is of form:
(a) $2q$
(b) $2q+1$
(c) $3q$
(d) $4q$
31. LCM of 12, 15 and 21:
(a) 420
(b) 240
(c) 120
(d) 480
32. HCF of 12, 15 and 21:
(a) 3
(b) 4
(c) 12
(d) 1
33. If $n$ is natural, $6^n$ ends with:
(a) 0
(b) 5
(c) 6
(d) 2
34. Terminating decimal condition for $q$:
(a) $2^n 5^m$
(b) $2^n 3^m$
(c) $3^n 5^m$
(d) $7^n 5^m$
35. Largest number dividing 70 and 125 remainder 5 and 8:
(a) 13
(b) 65
(c) 875
(d) 1750
36. HCF of $a=x^3y^2$ and $b=xy^3$:
(a) $xy$
(b) $xy^2$
(c) $x^3y^3$
(d) $x^2y^2$
37. Total factors of a prime number:
(a) 1
(b) 0
(c) 2
(d) 3
38. Fundamental Theorem of Arithmetic Statement:
(a) Euclid Relation
(b) Fundamental Theorem
(c) Pythagoras
(d) Thales
39. Decimal of $\frac{23}{2^2 5}$ terminates after:
(a) 1
(b) 2
(c) 3
(d) 4
40. $\frac{6}{15}$ decimal expansion:
(a) 0.4
(b) 0.3
(c) 0.6
(d) Non-terminating
Section B: Fill in the Blanks (ANSWERS)
41. Primes
42. Product of numbers ($a \times b$)
43. Irrational
44. Irrational
45. $2^n \times 5^m$
46. 2
47. 2
48. Composite
49. 26
50. 0
51. 4
52. 35
53. Infinite
54. Irrational
55. $\frac{1}{8}$
56. $5 \times 7 \times 11 \times 13$
57. 22338
58. 5
59. Division
60. Co-prime
Section C: True or False (ANSWERS)
61. False
62. True
63. True
64. False
65. False
66. False
67. False
68. True
69. True
70. False
71. False
72. False
73. True
74. True
75. True
76. True
77. True
78. True
79. False
80. True
Section D: One Word / Formula Recall (ANSWERS)
81. $HCF \times LCM = Product$
82. Number with exactly 2 factors
83. Number with > 2 factors
84. 15
85. $\sqrt{2}, \sqrt{8}$
86. $2^2 \times 5^2$
87. 1
88. $xy$
89. Yes
90. Yes (0/1)
91. Denominator in $2^n 5^m$ form
92. 10
93. 20
94. 2
95. 3
96. Euclid
97. Rational
98. $3/8$
99. $2^2 \times 5 \times 7$
100. No