Real Numbers

Euclid’s division algorithm helps in determining:
a) LCM
b) HCF
c) Square root
d) Cube root
Answer: b

Which of the following is not a property of real numbers:
a) Associative
b) Commutative
c) Distributive
d) Imaginary
Answer: d

Fundamental Theorem of Arithmetic states:
a) Every number is a rational number
b) Every composite number can be expressed uniquely as a product of primes
c) Prime numbers are finite
d) Every number is divisible by 1
Answer: b

The prime factorization of 32760 is:
a)

b)

c)

d)

Answer: b

The product of HCF and LCM of two numbers is equal to:
a) The sum of the two numbers
b) The difference of the two numbers
c) The product of the two numbers
d) None of these
Answer: c

The HCF of 96 and 404 is:
a) 2
b) 4
c) 6
d) 8
Answer: b

The LCM of 96 and 404 is:
a) 9696
b) 9604
c) 4852
d) 8008
Answer: a

Which of the following numbers is irrational:
a) 4\sqrt{4}
b) 9\sqrt{9}
c) 2\sqrt{2}
d) 55
Answer: c

If ppp is a prime number and divides a2a^2, then ppp:
a) Divides aa
b) Divides a3a^3
c) Divides a4a^4
d) Does not divide aa
Answer: a

The LCM of 6, 72, and 120 is:
a) 120
b) 240
c) 360
d) 720
Answer: c

The HCF of 6, 72, and 120 is:
a) 2
b) 3
c) 6
d) 12
Answer: c

The decimal expansion of 78\frac{7}{8} is:
a) Terminating
b) Non-terminating
c) Recurring
d) Both b and c
Answer: a

Which of the following is a composite number:
a) 13
b) 17
c) 23
d) 42
Answer: d

Which number among these has a terminating decimal expansion:
a) 23\frac{2}{3}
b) 712\frac{7}{12}
c) 18\frac{1}{8}
d) 27\frac{2}{7}
Answer: c

The Fundamental Theorem of Arithmetic is also known as:
a) Euclid’s Lemma
b) Unique Factorization Theorem
c) Composite Factorization Theorem
d) Gauss’ Law
Answer: b

3\sqrt{3} is:
a) Rational
b) Irrational
c) Integer
d) Whole number
Answer: b

The product of smallest power of each common factor in two numbers is called:
a) HCF
b) LCM
c) Both HCF and LCM
d) None of these
Answer: a

A number that has only two factors is called:
a) Composite
b) Prime
c) Rational
d) Irrational
Answer: b

The HCF and LCM of two numbers are 6 and 120. If one of the numbers is 24, the other is:
a) 20
b) 30
c) 15
d) 10
Answer: a

Which of the following is a prime factorization of 156:
a) 2×2×3×132 × 2 × 3 × 13
b) 2×3×132 × 3 × 13
c) 22×3×132^2 × 3 × 13
d) 22×3×112^2 × 3 × 11
Answer: c

The value of 16\sqrt{16} is:
a) 3
b) 4
c) 5
d) 6
Answer: b

If 2\sqrt{2} is multiplied by a rational number, the result is:
a) Rational
b) Irrational
c) Integer
d) Whole number
Answer: b

The HCF of 21 and 14 is:
a) 3
b) 7
c) 14
d) 21
Answer: b

Which number is divisible by 5:
a) 32
b) 50
c) 63
d) 77
Answer: b

How many prime numbers are there less than 20:
a) 6
b) 7
c) 8
d) 9
Answer: b

Which of the following is a rational number:
a) 7\sqrt{7}
b) π\pi
c) 3.53.5
d) 5\sqrt{5}
Answer: c

The LCM of 9 and 12 is:
a) 36
b) 18
c) 9
d) 24
Answer: a

49\sqrt{49} is equal to:
a) 5
b) 6
c) 7
d) 8
Answer: c

Which of the following numbers is irrational:
a) 1.5
b) 34\frac{3}{4}
c) 2
d) 11\sqrt{11}
Answer: d

Which of the following numbers is divisible by both 2 and 3:
a) 10
b) 15
c) 18
d) 20
Answer: c

The product of 2×2\sqrt{2} \times \sqrt{2} is:
a) 1
b) 2
c) 2\sqrt{2}
d) 4
Answer: b

The HCF of 45 and 75 is:
a) 5
b) 15
c) 25
d) 35
Answer: b

Which of the following is not a prime number:
a) 19
b) 23
c) 25
d) 29
Answer: c

A number is divisible by 9 if:
a) The number ends in 9
b) The sum of its digits is divisible by 9
c) The number is even
d) None of these
Answer: b

The square root of which number is irrational:
a) 16
b) 36
c) 25
d) 20
Answer: d

The smallest prime number is:
a) 1
b) 2
c) 3
d) 5
Answer: b

The decimal expansion of 13\frac{1}{3} is:
a) Terminating
b) Recurring
c) Non-terminating, non-recurring
d) None of these
Answer: b

Which of the following is a composite number:
a) 31
b) 37
c) 49
d) 53
Answer: c

The HCF of 8 and 12 is:
a) 4
b) 6
c) 8
d) 12
Answer: a

121\sqrt{121} is equal to:
a) 10
b) 11
c) 12
d) 13
Answer: b

The sum of a rational and an irrational number is:
a) Rational
b) Irrational
c) Integer
d) Whole number
Answer: b

If a2=4a^2 = 4, then aaa is:
a) 1
b) 2
c) ±2
d) ±1
Answer: c

Which number is divisible by 6:
a) 22
b) 36
c) 45
d) 57
Answer: b

25+9\sqrt{25} + \sqrt{9} is equal to:
a) 5
b) 6
c) 10
d) 12
Answer: c

The Fundamental Theorem of Arithmetic applies to:
a) All real numbers
b) Only composite numbers
c) Only prime numbers
d) Integers only
Answer: b

The HCF of 81 and 27 is:
a) 3
b) 9
c) 27
d) 81
Answer: c

The LCM of 7 and 14 is:
a) 7
b) 14
c) 21
d) 28
Answer: b

Which of the following is an example of a rational number:
a) 3\sqrt{3}
b) π\pi
c) 58\frac{5}{8}
d) 5\sqrt{5}
Answer: c

The smallest positive integer is:
a) 0
b) 1
c) 2
d) 3
Answer: b

The decimal expansion of 17\frac{1}{7} is:
a) Terminating
b) Non-terminating recurring
c) Non-terminating, non-recurring
d) None of these
Answer: b