Simplify 3√3+10√3
Question : Simplify 3√3+10√3 $13 \sqrt{3}$ $10 \sqrt{3}$ $12 \sqrt{3}$ $11 \sqrt{3}$ Solution: Correct option is 1. $13 \sqrt{3}$ $3 \sqrt{3}+10 \sqrt{3}=13 \sqrt{3}$...
Read More →5√3+2√3 = 7√6 enter 1 for true and 0 for false
Question : 5√3+2√3 = 7√6 enter 1 for true and 0 for false Solution : Correct answer is 0 $5 \sqrt{3}+2 \sqrt{3}=7 \sqrt{3}$ Therefore: False....
Read More →Find the nine rational numbers between 0 and 1
Question : Find the nine rational numbers between 0 and 1. $0.1,0.2,0.3, \ldots, 0.9$ $1.1,0.2,10.3, \ldots, 0.9$ $0.1,0.2,0.3, \ldots, 20.9$ $0.1,0.2,10.3, \ldots, 0.9$ Solution : Correct option is 1. $0.1,0.2,10.3, \ldots, 0.9$ $0(0+0.1)=0.1(0.1+0.1)=0.2(0.2+0.1)$ $=0.3\ldots(0.8+1)=0.9(0.9+0.1)=1$ $00.10.20.3\ldots0.91$ $\therefore$ The nine rational numbers between 0 and 1 are $0.1,0.2,0.3, \ldots, 0.9$...
Read More →Which of the following numbers are rational ?
Question : Which of the following numbers are rational ? $1$ $-6$ $3 \frac{1}{2}$ All above are rational Solution : The correct option is 4. All above are rational None of the number is irrational as every number can be expressed in the form of $\frac{\mathrm{p}}{\mathrm{q}}$, where $\mathrm{q} \neq 0$....
Read More →What are two rational numbers between $\frac{1}{5}$ and $\frac{4}{5}$ ?
Question : Two rational numbers between $\frac{1}{5}$ and $\frac{4}{5}$ are : 1 and $\frac{3}{5}$ $\frac{2}{5}$ and $\frac{3}{5}$ $\frac{1}{2}$ and $\frac{2}{1}$ $\frac{3}{5}$ and $\frac{6}{5}$ Solution : The correct option is 2. $\frac{2}{5}$ and $\frac{3}{5}$ Since the denominator of both rational numbers are same. So, for getting the rational numbers between the given rational numbers, we only have to consider the numerators of the rational numbers. Two numbers between 1 4 are 2 and 3. So, tw...
Read More →A rational number can always be written in a fraction $\frac{a}{b}$, where a and $b$ are not integers $(b \neq 0)$
Question : State True or False. A rational number can always be written in a fraction $\frac{\mathrm{a}}{\mathrm{b}}$, where a and $\mathrm{b}$ are not integers $(b \neq 0)$. True False Solution : The correct option is 2. False A number that can always be written in the form of $\mathrm{p} / \mathrm{q}$, where $\mathrm{p}$ is any integer and $\mathrm{q}$ is a non-zero integer, is a rational number. The given statement is false....
Read More →1/0 is not rational
Question : Say true or false. $\frac{1}{0}$ is not rational. True False Solution : The correct option is 1. True A rational number is a number that can be defined in the form of $\frac{p}{q}$, where $q$ is nonzero. Now, if $\mathrm{q}$ is 0 , although an integer, the solution will not be a rational number. It will give an undefined result, so the statement is true....
Read More →Prove that root 5 is irrational number
Question : $\sqrt{5}$ is an irrational number. True False Solution : The correct option is 1. True An irrational number is any real number that cannot be expressed as a ratio $\mathrm{a} / \mathrm{b}$, where a and $\mathrm{b}$ are integers and $\mathrm{b}$ is non-zero. $\sqrt{5}$ is irrational as it can never be expressed in the form $\mathrm{a} / \mathrm{b}$...
Read More →What is the value of (6+√27)−(3+√3)+(1−2√3) when simplified ?
Quetion : The value of $(6+\sqrt{27})-(3+\sqrt{3})+(1-2 \sqrt{3})$ when simplified is : positive and irrational negative and rational positive and rational negative and irrational Solution : The correct option is 3. positive and rational $6+\sqrt{27}-(3+\sqrt{3})+(1-2 \sqrt{3})=6+3 \sqrt{3}-3-\sqrt{3}+1-2 \sqrt{3} = 4$ 4 is a positive rational number. Hence, correct answer is option 3....
Read More →Find the value of $\left(3^{1}+4^{1}+5^{1}\right)^{0}$
Question : Find the value of $\left(3^{1}+4^{1}+5^{1}\right)^{0}$. Solution : The correct answer is 1 Any number with a power of zero is equal to one....
Read More →What is the rationalizing factor of (a+√b)
Question : The rationalizing factor of $(\mathrm{a}+\sqrt{\mathrm{b}})$ is $a-\sqrt{b}$ $\sqrt{a}-b$ $\sqrt{a}-\sqrt{b}$ None of these Solution : Correct option is 1. $a-\sqrt{b}$ The rationalizing factor of $a + \sqrt{b}$ is $a - \sqrt{b}$ as the product of these two expressions give a rational number....
Read More →The decimal expansion of π is
Question : The decimal expansion of π is : terminating non-terminating and non-recurring non-terminating and recurring doesn't exist Solution : The correct option is 2. non-terminating and non-recurring We know that $\pi$ is an irrational number and Irrational numbers have decimal expansions that neither terminate nor become periodic. So, correct answer is option 2....
Read More →Between any two rational numbers, there are infinitely many rational numbers
Question : Between any two rational numbers there is no rational number there is exactly one rational number there are infinitely many rational numbers there are only rational numbers and no irrational numbers Solution : The correct option is 3. there are infinitely many rational numbers Recall that to find a rational number between r and s, you can add $\mathrm{r}$ and $\mathrm{s}$ and divide the sum by 2 , that is $\frac{\mathrm{r}+\mathrm{s}}{2}$ lies between $\mathrm{r}$ and $\mathrm{s}$. Fo...
Read More →Find any five rational numbers between -3/2 and 5/3
Question : State true or false :Five rational numbers between $\frac{-3}{2}$ and $\frac{5}{3}$ are $\frac{-8}{6}, \frac{-7}{6}, 0, \frac{1}{6}, \frac{2}{6}$ True False Solution : The Correct option is 1. True To get the rational numbers between $\frac{-3}{2}$ and $\frac{5}{3}$ Take an LCM of these two numbers: $\frac{-9}{6}$ and $\frac{10}{6}$ All the numbers between $\frac{-9}{6}$ and $\frac{10}{6}$ form the answer Some of these numbers are $\frac{-8}{6}, \frac{-7}{6}, 0, \frac{1}{6}, \frac{2}{...
Read More →five rational numbers which are smaller than 2
Question : Following are the five rational numbers that are smaller than 2 $\Rightarrow 1, \frac{1}{2}, 0,-1, \frac{-1}{2}$If true then enter 1 and if false then enter 0 Solution : Correct option is 1 Any number in the form of $\frac{p}{q}$ which is less than 2 will form the answer. So given numbers are $1, \frac{1}{2}, 0,-1, \frac{-1}{2}$ rational number which are smaller than 2 So the statement is true....
Read More →Find five rational numbers between:2/3 and 4/5
Question : State true or false:Five rational numbers between$\frac{2}{3}$ and $\frac{4}{5}$ are $\frac{41}{60}, \frac{42}{60}, \frac{43}{60}, \frac{44}{60}, \frac{45}{60}$ True False Solution : Correct option is 1.True To get the rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$ Take an LCM of these two numbers: $\frac{10}{15}$ and $\frac{12}{15}$ Multiply numerator and denominator by $4: \frac{40}{60}$ and $\frac{48}{60}$ All the numbers between $\frac{40}{60}$ and $\frac{48}{60}$ form t...
Read More →Every rational number is a real number
Question : Every rational number is A natural number An integer A real number A whole number Solution : The correct option is 3. A real number Real number is a value that represents a quantity along the number line. Real number includes all rational and irrational numbers. Rational numbers are numbers that can be represented in the form $\frac{p}{q}$ where, $\mathrm{q} \neq 0$ and $\mathrm{p}, \mathrm{q}$ are integers. Therefore, a rational number is a subset of a real number. We know that ratio...
Read More →A number is an irrational if and only if its decimal representation is
Question : A number is irrational if and only if its decimal representation is : Non-terminating Non-terminating and repeating Non-terminating and non-repeating Terminating Solution : The correct option is 3. non-terminating and non-repeating According to the definition of an irrational number, If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. Hence, a number having non terminating and non-repeating...
Read More →There are numbers which cannot be written in the form p/q , where q ≠ 0 and both p, q are integers
Question : State true or false:There are numbers which cannot be written in the form p/q , where q ≠ 0 and both pq are integers. True False Solution : The correct option is 1. True The statement is true as there are Irrational numbers which don't satisfy the condition of rational numbers i.e irrational numbers cannot be written in the form of $_{\mathrm{q}}^{\mathrm{p}} $ , $\mathrm{q} \neq 0$, where $\mathrm{p}, \mathrm{q}$ are integers. Example, $\sqrt{3}, \sqrt{99}$...
Read More →Two Rational Numbers Between 2/3 and 5/3 are
Question : Two rational numbers between $\frac{2}{3}$ and $\frac{5}{3}$ are : $\frac{1}{6}$ and $\frac{2}{6}$ $\frac{1}{2}$ and $\frac{2}{1}$ $\frac{5}{6}$ and $\frac{7}{6}$ $\frac{2}{3}$ and $\frac{4}{3}$ Solution : Correct option is 3. $\frac{5}{6}$ and $\frac{7}{6}$ Changing the denominators of both numbers to 6, we get $\frac{2}{3}=\frac{4}{6} \quad \ \quad \frac{5}{3}=\frac{10}{6}$ $\frac{5}{6} \ \frac{7}{6}$ So, correct answer is option 3....
Read More →The value of 2√3 + √3 is equal to
Question: The value of $2 \sqrt{3}+\sqrt{3}$ is equal to : $2 \sqrt{6}$ $3 \sqrt{3}$ $4 \sqrt{6}$ 6 Solution : Correct option is 2. $3 \sqrt{3}$ $2 \sqrt{3}+\sqrt{3}=(2+1) \sqrt{3}=3 \sqrt{3}$...
Read More →In between two rational number there is/are
Question: In between two rational numbers there is/are : Only irrational number Exactly one rational number Infinitely many rational numbers Many irrational numbers Solution : The correct option is 1. Infinitely many rational numbers Recall that to find a rational number between r and s, you can add $\mathrm{r}$ and $\mathrm{s}$ and divide the sum by 2 , that is $\frac{\mathrm{r}+\mathrm{s}}{2}$ lies between $\mathrm{r}$ and $\mathrm{s}$. For example, $\frac{5}{2}$ is a number between 2 and 3 We...
Read More →The property under multiplication used in each of the following. -4/5 × 1 = 1 × -4/5 = -4/5
Question. The property under multiplication used in each of the following. -4/5 × 1 = 1 × -4/5 = -4/5 Commutative Property Associate Property Distributive property Identity Property Solution: The correct options are 1. Commutative Property and 4. Identity Property According to commutative property if a and b are real numbers then a x b = b x a According to Identity if a is any real number then a x 1 = 1 So correct answer will be options 1 and 4...
Read More →If additive inverse of 2/8 is -2/q , then find the value of p
Question. If the additive inverse of 2/8 is -2/q, then find the value of p Solution: The additive inverse of a number x is −x. For example, additive inverse of $\frac{1}{2}$ is $-\frac{1}{2}$ Here, for $\frac{2}{8}$ additive inverse is $-\frac{2}{8}$....
Read More →Tell what property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3
Choose the correct option for the following statement. The property allows you to compute $\frac{1}{3} \times\left(6 \times \frac{4}{3}\right)$ as $\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}$ is Associativity. The given statement is true. The given statement is false. Incomplete information None of these Solution: The correct option is 1 The given statement is true. For any element $\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathrm{A}$, associative property states that $\mathrm{a}(\mathrm...
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