Class 10 Exam > Class 10 Notes > Real Numbers - MCQ with Solution, Class 10 Mathematics
Real Numbers - MCQ with Solution, Class 10 Mathematics PDF Download
1. Euclid’s division algorithm can be applied to :
(a) only positive integers
(b) only negative integers
(c) all integers
(d) all integers except 0.
2. For some integer m, every even integer is of the form :
(a) m
(b) m + 1
(c) 2m
(d) 2m + 1
3. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is :
(a) 1
(b) 2
(c) 3
(d) 4
4. 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
(b) a3b3
5. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :
(a) 10
(b) 100
(c) 504
(d) 2520
6. 7 × 11 × 13 × 15 + 15 is :
(a) composite number
(b) prime number
(c) neither composite nor prime
(d) none of these
7. 1.23 is :
(a) an integer
(b) an irrational number
(c) a rational number
(d) none of these
8. If two positive integers p and q can be expressed as p = ab2 and q = a2b; a, b being prime numbers, then LCM (p, q) is :
(a) a2b2
(b) ab
(c) ac3b3
(d) a3b2
9. 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 :
(a) 0 < r ≤ b
(b) 1 < r < b
(c) 0 < r < b
(d) 0 ≤ r < b
10. 3.24636363... is :
(a) a terminating decimal number
(b) a non-terminating repeating decimal number
(c) a rational number
(d) both (b) and (c)
11.(n + 1)2 – 1 is divisible by 8, if n is :
(a) an odd integer
(b) an even integer
(c) a natural number
(d) an integer
12. The largest number which divides 71 and 126, leaving remainders 6 and 9 respectively is :
(a) 1750
(b) 13
(c) 65
(d) 875
13. For some integer q, every odd integer is of the form :
(a) 2q
(b) 2q + 1
(c) q
(d) q + 1
14. If the HCF of 85 and 153 is expressible in the form 85 m – 153, then the value of m is :
(a) 1
(b) 4
(c) 3
(d) 2
15. According to Euclid’s division algorithm, HCF of any two positive integers a and b with a > b is obtained by applying Euclid’s division lemma to a and b to find 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
FAQs on Real Numbers - MCQ with Solution, Class 10 Mathematics
| 1. What are real numbers? |  |
Ans. Real numbers are the set of all rational and irrational numbers, which include positive, negative, and zero numbers. They are represented on the number line, and they can be expressed in decimal form or as fractions.
| 2. What is the difference between rational and irrational numbers? | |
Ans. Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Irrational numbers cannot be expressed as a fraction and are non-repeating, non-terminating decimals. Examples of irrational numbers include √2, π, and e.
| 3. How are real numbers used in daily life? | |
Ans. Real numbers are used in many aspects of daily life, including measurements, money, and time. For example, when measuring a room's dimensions, we use real numbers to represent the length, width, and height in feet or meters. When buying groceries, we use real numbers to represent the cost of each item. When calculating time, we use real numbers to represent hours, minutes, and seconds.
| 4. How do real numbers help in solving mathematical problems? | |
Ans. Real numbers are essential in solving mathematical problems because they allow us to perform operations such as addition, subtraction, multiplication, and division. They also allow us to compare and order numbers. Real numbers are used in algebra, geometry, calculus, and other branches of mathematics.
| 5. What is the importance of understanding real numbers in Class 10 Mathematics? | |
Ans. Understanding real numbers is crucial in Class 10 Mathematics because it forms the foundation for many topics covered in higher classes, such as algebra, trigonometry, and calculus. Real numbers are used extensively in solving equations and inequalities. It is essential to have a clear understanding of real numbers to succeed in mathematics and other related fields.
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