1.
A number line consists of ___________________ number.
Correct Answer
C. Integer
Explanation
A number line consists of integer numbers because it includes all the whole numbers, both positive and negative, as well as zero. Natural numbers only include positive whole numbers starting from 1, while whole numbers include natural numbers and zero. Therefore, the correct answer is integer.
2.
Numbers which include Zero Are called____________________
Correct Answer
C. Whole numbers
Explanation
Whole numbers include zero. They are a set of numbers that includes all the natural numbers (positive integers) and zero. Natural numbers are only the positive integers, irrational numbers are numbers that cannot be expressed as a fraction, and odd numbers are integers that are not divisible by 2. Therefore, the correct answer is whole numbers.
3.
Integers are denoted by________________________
Correct Answer
C. Z
Explanation
Integers are denoted by the letter Z. This is a standard mathematical notation used to represent the set of whole numbers, including both positive and negative numbers, as well as zero. The letter Z comes from the German word "Zahlen," which means numbers.
4.
The number which is in the form of P/q,q≠0, Such numbers are called as____
numbers
Correct Answer
A. Rational
Explanation
The correct answer is "Rational". Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. These numbers can be written in the form of P/q, where P and q are integers and q is not equal to zero.
5.
Every whole number is a natural number
Correct Answer
A. True
Explanation
Every whole number is a natural number because the set of natural numbers includes all positive integers starting from 1, and whole numbers include both positive integers and zero. Since every whole number is a positive integer or zero, it is also a natural number. Therefore, the statement is true.
6.
Zero is a rational number
Correct Answer
A. True
Explanation
Zero is considered a rational number because it can be expressed as a fraction, where the numerator is 0 and the denominator is any non-zero number. In this case, the fraction would be 0/1. Since the definition of a rational number is any number that can be expressed as a fraction, including integers, zero fits this definition and is therefore a rational number.
7.
Fraction form of 3.142678 is____________________
Correct Answer
3142678/1000000
Explanation
The given fraction form, 3142678/1000000, is the correct representation of the decimal number 3.142678. To convert a decimal to a fraction, the decimal is written as the numerator and the denominator is determined by the number of decimal places. In this case, there are six decimal places, so the denominator is 10^6, which equals 1000000. Therefore, the fraction form of 3.142678 is 3142678/1000000.
8.
The decimal form of 382/1000 is ________________
Correct Answer
0.382
Explanation
To find the decimal form of a fraction, we divide the numerator by the denominator. In this case, 382 divided by 1000 equals 0.382. Therefore, the decimal form of 382/1000 is 0.382.
9.
The product of 6√5 and 2 √5 is _________________
Correct Answer
60
Explanation
The product of two square roots can be found by multiplying the numbers inside the square roots and then simplifying if possible. In this case, the numbers inside the square roots are both 5. Multiplying 6 and 2 gives us 12. Therefore, the product of 6√5 and 2√5 is 12√5. However, since the square root of 5 cannot be simplified further, the final answer is 12 multiplied by the square root of 5, which is 12√5.
10.
The division of 8√7 by 4√7 is __________________
Correct Answer
2
Explanation
When dividing two numbers with the same radical, we can simplify the expression by canceling out the common radical. In this case, both numbers have the radical √7. By dividing the coefficients (numbers outside the radical), which are 8 and 4, we get 8/4 = 2. Therefore, the division of 8√7 by 4√7 is 2.
11.
The numbers which are not rational are called ___________
Correct Answer
Irrational Numbers
Explanation
The numbers which are not rational are called irrational numbers. Irrational numbers cannot be expressed as a fraction or ratio of two integers and their decimal representation goes on infinitely without repeating. Examples of irrational numbers include the square root of 2 (√2), pi (π), and the golden ratio (φ). These numbers are important in mathematics and have unique properties that distinguish them from rational numbers.
12.
Every rational number is __________________number
Correct Answer
Real
Explanation
Every rational number is a real number. This is because rational numbers can be expressed as a quotient of two integers, and real numbers include both rational and irrational numbers. Therefore, every rational number is a subset of the set of real numbers.
13.
2√7/7√7 is _________________ (rational or irrational)
Correct Answer
Rational
Explanation
The given expression can be simplified as √7/√7, which is equal to 1. Since 1 is a rational number (it can be expressed as a fraction of two integers), the given expression is also rational.
14.
There are _____________________ laws of components.
Correct Answer
5
Explanation
The sentence states that there are laws of components. The number given after the sentence indicates the number of laws, which is 5. Therefore, the correct answer is 5.
15.
The value of (16) to the power 1/4 is _______________
Correct Answer
2
Explanation
The value of (16) to the power 1/4 is 2 because when a number is raised to the power of 1/4, it means finding the fourth root of that number. The fourth root of 16 is 2, as 2 multiplied by itself four times equals 16.
16.
The simplest form of (125) to the power o 1/3 is _________
Correct Answer
5
Explanation
The question asks for the simplest form of the cube root of 125. The cube root of 125 is 5, because 5 multiplied by itself three times equals 125. Therefore, the simplest form of (125) to the power of 1/3 is 5.
17.
In decimal expansion if there is no end then it is called
Correct Answer
non terminating
Explanation
In decimal expansion, if a number does not have an end or does not repeat a pattern, it is called a non-terminating decimal. This means that the digits after the decimal point continue indefinitely without a pattern or end point.
18.
In decimal expansion if numbers are repeated then it is
Correct Answer
recurring
Explanation
If numbers in a decimal expansion are repeated, it means that there is a recurring pattern in the digits after the decimal point. This pattern can continue indefinitely. Therefore, the correct answer is "recurring".
19.
the value of (23 to the power 5 )*(23 to the power 7) is 23 to the power 17
Correct Answer
B. False
Explanation
The given statement is false. When multiplying two numbers with the same base, you add the exponents. In this case, (23^5) * (23^7) would be equal to 23^(5+7) which simplifies to 23^12, not 23^17.
20.
the value of 318/10000 is 0.318
Correct Answer
B. False
Explanation
The given statement is false because the value of 318/10000 is actually 0.0318, not 0.318.