Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Unit Test: Real Numbers
Unit Test: Real Numbers | Mathematics (Maths) Class 10 PDF Download
Time: 1 hour
M.M. 30
Attempt all questions.
- Question numbers 1 to 5 carry 1 mark each.
- Question numbers 6 to 8 carry 2 marks each.
- Question numbers 9 to 11 carry 3 marks each.
- Question number 12 & 13 carry 5 marks each.
Q1: Which of the following numbers is irrational? (1 Mark)
(a) √25
(b) 3.14
(c) 0.333...
(d) -7
Q2: What is the value of (5² + 12²)? (1 Mark)
(a) 169
(b) 144
(c) 25
(d) 169√2
Q3: Which one is not a prime number? (1 Mark)
(a) 1
(b) 2
(c) 3
(d) 5
Q4: State whether "√16" is a rational number or not. (1 Mark)
Q5: Without performing the actual division, state whether "1089" is divisible by "9" or not. (1 Mark)
Q6: Write a rational number between √5 and √6. (2 Marks)
Q7: Express 0.37 as a fraction in its simplest form. (2 Marks)
Q8: Find the LCM (Least Common Multiple) of 15 and 20. (2 Marks)
Q9: Prove that the square of any positive integer of the form (5k + 1) is one more than a multiple of 8, where "k" is an integer. (3 Marks)
Q10: Find the HCF (Highest Common Factor) of 72 and 96 using the prime factorization method. (3 Marks)
Q11: Given that p is a rational number and q is an irrational number, prove that their sum (p + q) is an irrational number. (3 Marks)
Q12: A circular garden has a circumference of 44 meters. Find the area of the garden (in square meters) using the formula for the area of a circle. (Take π = 3.14). (5 Marks)
Q13: Prove that 5√3 - 3√75 is an irrational number. (5 Marks)
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FAQs on Unit Test: Real Numbers - Mathematics (Maths) Class 10
| 1. What are real numbers and how are they classified? |  |
Ans. Real numbers are the set of numbers that include all the rational and irrational numbers. They can be classified into several categories: natural numbers (1, 2, 3,...), whole numbers (0, 1, 2, 3,...), integers (...,-2, -1, 0, 1, 2,...), rational numbers (numbers that can be expressed as a fraction of two integers, such as 1/2, -3/4), and irrational numbers (numbers that cannot be expressed as a simple fraction, such as √2, π).
| 2. How do you perform operations with real numbers? | |
Ans. Operations with real numbers include addition, subtraction, multiplication, and division. To perform these operations, you need to follow the standard arithmetic rules. For instance, when adding or subtracting real numbers, you align them based on their decimal points. For multiplication, you multiply the numbers directly, and for division, you divide the numerator by the denominator. When dealing with irrational numbers, it is important to leave them in their radical form unless specified.
| 3. What is the difference between rational and irrational numbers? | |
Ans. Rational numbers are numbers that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero (e.g., 1/3, -2). Irrational numbers, on the other hand, cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions (e.g., √3, π). The key difference is that rational numbers can be written as a fraction, while irrational numbers cannot.
| 4. How can real numbers be represented on a number line? | |
Ans. Real numbers can be represented on a number line by marking specific points that correspond to each number. The number line is a straight horizontal line where each point represents a real number. Positive numbers are located to the right of zero, while negative numbers are to the left. Rational numbers can be plotted as exact points, while irrational numbers are also represented, though they may not correspond to exact locations. The distance between points reflects the value of the numbers.
| 5. What are some common properties of real numbers? | |
Ans. Real numbers exhibit several important properties, including the commutative property (a + b = b + a and ab = ba), associative property ((a + b) + c = a + (b + c) and (ab)c = a(bc)), distributive property (a(b + c) = ab + ac), identity property (a + 0 = a and a × 1 = a), and inverse property (a + (-a) = 0 and a × (1/a) = 1 for a ≠ 0). These properties are essential for simplifying expressions and solving equations involving real numbers.
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