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CBSE Class 9  >  Class 9 Test  >  Mathematics (Maths)   >  Test: Number Systems - 1 - Class 9 MCQ

Test: Number Systems - 1 - Class 9 MCQ


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25 Questions MCQ Test Mathematics (Maths) Class 9 - Test: Number Systems - 1

Test: Number Systems - 1 for Class 9 2026 is part of Mathematics (Maths) Class 9 preparation. The Test: Number Systems - 1 questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Number Systems - 1 MCQs are made for Class 9 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Number Systems - 1 below.
Solutions of Test: Number Systems - 1 questions in English are available as part of our Mathematics (Maths) Class 9 for Class 9 & Test: Number Systems - 1 solutions in Hindi for Mathematics (Maths) Class 9 course. Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free. Attempt Test: Number Systems - 1 | 25 questions in 50 minutes | Mock test for Class 9 preparation | Free important questions MCQ to study Mathematics (Maths) Class 9 for Class 9 Exam | Download free PDF with solutions
Test: Number Systems - 1 - Question 1
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If x = 2+√3, then Find  

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Test: Number Systems - 1 - Question 2
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The value of  is 

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Test: Number Systems - 1 - Question 3
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The value of  is 

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Test: Number Systems - 1 - Question 4
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Which of the following is an rational number?

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- A rational number is a number that can be expressed as a fraction where both the numerator and denominator are integers.
- √196 is a rational number because it simplifies to 14/1, which is a fraction where both the numerator and denominator are integers.
- Options B and C are irrational numbers because they cannot be expressed as fractions.
- Option A is a repeating decimal, which can be rational if it eventually settles into a repeating pattern, but without further information, it is not clear if this is the case.

Test: Number Systems - 1 - Question 5
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Test: Number Systems - 1 - Question 6
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(5+√8)+(3−√2)(√2−6) is

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And we know that the value of 11√2 is greater than 15 so it's value will be positive, And also sum or differences of rational and irrational is irrational

Test: Number Systems - 1 - Question 7
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√8+2√32−5√2 is equal to

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√8 = 2√2.

√32 = 4√2.

Substitute these into the expression to get: 2√2 + 2×4√2 - 5√2

Combine like terms: (2 + 8 - 5)√2 = 5√2

Therefore the value of the expression is 5√2,
So, option A is correct.

Test: Number Systems - 1 - Question 8
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Every rational number is

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Every rational number is a real number. Real Number is a set of numbers formed by both Rational and Irrational numbers are combined.

Test: Number Systems - 1 - Question 9
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The simplest form of   is

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Test: Number Systems - 1 - Question 10
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(125/216) -1/3 =

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Test: Number Systems - 1 - Question 11
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8√15 ÷ 2√3

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Test: Number Systems - 1 - Question 12
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Ifn x = 3+2√2, then the value of 

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Test: Number Systems - 1 - Question 13
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Decimal representation of a rational number cannot be 

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A rational number is a number that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0 

Its decimal representation is either terminating (like 0.75 = ¾)
or non-terminating but repeating (like 0.333... = ⅓).

It cannot be non-terminating and non-repeating, because that form represents an irrational number (like π or √2).

 Therefore, the decimal representation of a rational number cannot be non-terminating and non-repeating.

Test: Number Systems - 1 - Question 14
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The simplest form of  is

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Test: Number Systems - 1 - Question 15
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If 3x + 64 = 26 + (√3)8, then the value of ‘x’ is 

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Test: Number Systems - 1 - Question 16
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If x1/12 = 491/24, then the value of ‘x’ is

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Test: Number Systems - 1 - Question 17
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The value of (0.00032)-2/5 is

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Test: Number Systems - 1 - Question 18
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The decimal representation of an irrational number is

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An irrational number is a type of number that cannot be expressed as a simple fraction. Its decimal representation has unique characteristics:

Non-terminating: The decimal goes on forever without ending.
Non-repeating: There are no repeating patterns in the digits.

Examples of irrational numbers include:

Pi (π): Approximately 3.14159, it continues infinitely without repetition.
The square root of 2: Approximately 1.41421, also non-terminating and non-repeating.

In summary, the decimal representation of an irrational number is neither terminating nor repeating.

Test: Number Systems - 1 - Question 19
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A number which can neither be expressed as a terminating decimal nor as a repeating decimal is called

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A number that cannot be expressed as a terminating or repeating decimal is classified as an irrational number. Here are some key points to understand this concept:

Rational numbers can be written as fractions, which either terminate (like 0.5) or repeat (like 0.333...).
Irrational numbers, on the other hand, cannot be written as simple fractions. Their decimal representations are non-terminating and non-repeating.
Examples of irrational numbers include π (pi) and √2 (the square root of 2).
Irrational numbers are essential in mathematics, particularly in geometry and calculus.

In summary, a number that cannot be expressed as either a terminating or a repeating decimal is indeed called an irrational number.

Test: Number Systems - 1 - Question 20
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The value of  is 

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Test: Number Systems - 1 - Question 21
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Which of the following is a rational number?

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Zero (0) is an integer, and all integers are rational numbers because they can be expressed as a fraction where the denominator is 1 (e.g., 0/1).

The other options involve irrational numbers that cannot be expressed as simple fractions. Thus, 0 is the only rational number among the given choices.

Test: Number Systems - 1 - Question 22
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The value of  is 

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Test: Number Systems - 1 - Question 23
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The number (3 − √3)(3 + √3) is:

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The given expression is in the form of (a - b)(a + b), which is a standard identity:

(a - b)(a + b) = a² - b²

Here,
a = 3
b = √3

Now apply the identity:

(3 - √3)(3 + √3) = 3² - (√3)² = 9 - 3 = 6

So, the result is 6, which is a rational number.

Test: Number Systems - 1 - Question 24
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On simplifying (√5 + √7)², we get

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We use the identity
(a + b)² = a² + 2ab + b²

Here,
a = √5
b = √7

Now apply the identity:

(√5 + √7)² = (√5)² + 2 × √5 × √7 + (√7)²
= 5 + 2√35 + 7
= 12 + 2√35

Test: Number Systems - 1 - Question 25
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Express 0.375 as a fraction in its simplest form.

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0.375 = 375/1000 because there are three digits after the decimal point, so the denominator is 1000

Find the highest common factor of 375 and 1000
HCF (375,1000) = 125
Divide both numerator and denominator by 125
So, 375 ÷ 125 = 3 and 1000 ÷ 125 = 8

Therefore the fraction in simplest form is 3/8
So, option A is correct.

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