REAL NUMBERS - MCQs

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Maths — REAL NUMBERS

50 Questions Class 10 MCQs
1
The least positive integer that is divisible by 12, 18, and 21 is:
2
The HCF of 65 and 117 is:
3
The largest number which divides 245 and 1029 exactly is:
4
Which of the following is irrational?
5
Euclid’s division lemma applies to:
6
The decimal form of a rational number is:
7
The product of a rational and an irrational number is:
8
“Every composite number can be expressed (factorised) as a product of primes,” is called:
9
The LCM and HCF of two numbers are 180 and 6 respectively. If one number is 30, the other number is:
10
The number 0.101001000100001...0.101001000100001...0.101001000100001... is:
11
If p and q are coprime numbers, HCF(pq, p + q) is:
12
If the HCF of 65 and 117 can be written as 65x + 117y, then the value of x is:
13
The decimal expansion of \(\frac{23}{16}\) is:
14
The number \(\sqrt{2}\) is:
15
The LCM of 1 and any number aaa is:
16
If a whole number has a non-terminating, non-repeating decimal expansion, then it is:
17
The smallest prime number is:
18
Every rational number can be written as:
19
Which of the following has a terminating decimal expansion?
20
The Fundamental Theorem of Arithmetic is related to:
21
The square root of a non-perfect square natural number is:
22
The decimal expansion of \(\frac{77}{600}\) will terminate after:
23
If \(n=pq \) where \(p,~q\) are prime, then how many factors does \(n \)have?
24
The sum of two irrational numbers is always:
25
The decimal expansion of \(\frac{17}{40}\) is:
26
The sum of a rational and an irrational number is:
27
HCF(84, 90) = ?
28
There are infinitely many primes divisible by:
29
The number \(\frac{2}{3}\) is:
30
If a number's decimal representation terminates, then its denominator in lowest form is:
31
Euclid’s algorithm is used to find:
32
\(\frac{13}{50}\) in decimal form is:
33
Which of the following is not rational?
34
The decimal expansion of \(\frac{4}{11}\) is:
35
The HCF of 15, 25, and 30 is:
36
LCM (16, 24) is:
37
Product of two non-zero rational numbers is:
38
The number \(\sqrt{49}\) is:
39
The largest 2-digit prime number is:
40
If a number is not rational, it is:
41
The HCF of two consecutive even numbers is always:
42
The number 17 is:
43
An irrational number between 2 and 3 is:
44
For any two positive integers a and b, a = bq + r. 0 ? r < b. Here, r is:
45
Which of the following is a non-terminating non-repeating decimal?
46
LCM of 9 and 15 is:
47
The denominator of a rational number with terminating decimal expansion has the form:
48
The sum of two rational numbers is:
49
Which of these is not a real number?
50
The set of real numbers consists of:
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Frequently Asked Questions

Real numbers include all rational and irrational numbers, representing all points on the number line.

Rational numbers can be expressed asp/qp/qp/qwherepppandqqqare integers andq?0q \neq 0q?=0.

Irrational numbers cannot be expressed asp/qp/qp/q; their decimal expansion is non-terminating and non-repeating.

Euclid, an ancient Greek mathematician, proposed the division lemma used for finding HCF.

For any two positive integersaaaandbbb, there exist unique integersqqqandrrrsuch thata=bq+ra = bq + ra=bq+r, where0=r<b0 \leq r < b0=r<b.

It helps find the Highest Common Factor (HCF) of two numbers using repeated division.

It is the process of applying Euclid’s Lemma repeatedly to find the HCF of two numbers.

HCF (Highest Common Factor) is the greatest number that divides two or more numbers exactly.

LCM (Least Common Multiple) is the smallest number divisible by the given numbers.

HCF×LCM=Product of the two numbers\text{HCF} \times \text{LCM} = \text{Product of the two numbers}HCF×LCM=Product of the two numbers.

Prime numbers are natural numbers greater than 1 that have only two factors: 1 and itself.

Composite numbers have more than two factors. Examples: 4, 6, 8, 9.

Every composite number can be expressed as a product of primes in a unique way, except for order of factors.

Expressing a number as a product of prime numbers.

List prime factors of each number and multiply common factors with least power.

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