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question_answer1)
Which of the following is not a rational number?
A)
\[\sqrt{2}\] done
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B)
\[\sqrt{4}\] done
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C)
\[\sqrt{9}\] done
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D)
\[\sqrt{16}\] done
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question_answer2)
Of which of the following is the set of natural numbers a subset?
A)
The set of even numbers. done
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B)
The set of odd numbers. done
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C)
The set of composite numbers. done
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D)
The set of real numbers. done
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question_answer3)
Which is an irrational number between \[\sqrt{2}\]and\[\sqrt{3}\]?
A)
\[{{2}^{\frac{1}{2}}}\] done
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B)
\[{{3}^{\frac{1}{4}}}\] done
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C)
\[{{6}^{\frac{1}{4}}}\] done
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D)
\[{{6}^{\frac{1}{8}}}\] done
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question_answer4)
What type of a number is\[\left( 6+\sqrt{2} \right)\left( 6-\sqrt{2} \right)\]?
A)
Rational number done
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B)
Irrational number done
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C)
Prime number done
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D)
Negative Integer done
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question_answer5)
What type of a number is\[{{\left( \sqrt{2}+\sqrt{3} \right)}^{2}}\]?
A)
A rational number done
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B)
An irrational number done
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C)
A fraction done
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D)
A decimal number done
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question_answer6)
Given \[X\]: Every fraction is a rational number and \[Y\]: Every rational number is a fraction. Which of the following is correct?
A)
\[X\] is False and \[Y\] is True. done
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B)
\[X\] is True and \[Y\] is False. done
clear
C)
Both \[X\] and \[Y\] are True. done
clear
D)
Both \[X\] and \[Y\] are False. done
clear
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question_answer7)
What is the rationalizing factor of\[\left( 2\sqrt[3]{5} \right)\]?
A)
\[\sqrt[3]{5}\] done
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B)
\[\sqrt[3]{{{5}^{2}}}\] done
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C)
\[{{5}^{2}}\] done
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D)
\[{{5}^{3}}\] done
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question_answer8)
What is the rationalizing factor of\[\sqrt[5]{{{a}^{2}}{{b}^{3}}{{c}^{4}}}\]?
A)
\[\sqrt[5]{{{a}^{3}}{{b}^{2}}c}\] done
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B)
\[\sqrt[4]{{{a}^{3}}{{b}^{2}}c}\] done
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C)
\[\sqrt[3]{{{a}^{3}}{{b}^{2}}c}\] done
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D)
\[\sqrt{{{a}^{3}}{{b}^{2}}c}\] done
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question_answer9)
What is the rational denominator of\[\frac{2\sqrt[3]{5}}{\sqrt[3]{9}}\]?
A)
\[1\] done
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B)
\[2\] done
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C)
\[3\] done
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D)
\[4\] done
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question_answer10)
Find the value of\[{{\left( \sqrt[6]{27}-\sqrt{6\frac{3}{4}} \right)}^{2}}\]
A)
\[\frac{\sqrt{3}}{2}\] done
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B)
\[\frac{3}{2}\] done
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C)
\[\frac{\sqrt{3}}{4}\] done
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D)
\[\frac{3}{4}\] done
clear
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question_answer11)
What is the product of\[\sqrt[3]{4}\]and\[\sqrt[3]{22}\]?
A)
\[2\sqrt[3]{11}\] done
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B)
\[\left( 3\sqrt{11} \right)\] done
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C)
\[4\sqrt{11}\] done
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D)
\[8\sqrt[3]{11}\] done
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question_answer12)
What is the quotient when \[\sqrt[6]{12}\] is divided by\[\sqrt{3}\sqrt[3]{2}\]?
A)
\[\frac{1}{\sqrt[2]{3}}\] done
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B)
\[\frac{1}{\sqrt[3]{3}}\] done
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C)
\[\frac{1}{\sqrt[4]{3}}\] done
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D)
\[\frac{1}{\sqrt[5]{3}}\] done
clear
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question_answer13)
If\[\frac{-4}{7}=\frac{-32}{x}\], what is the value of\[x\]?
A)
\[-56\] done
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B)
\[56\] done
clear
C)
\[-65\] done
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D)
\[65\] done
clear
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question_answer14)
Find the value of \[x-{{y}^{x-y}}\] when \[x=2\] and\[y=-2\].
A)
\[18\] done
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B)
\[-18\] done
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C)
\[14\] done
clear
D)
\[-14\] done
clear
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question_answer15)
If\[{{9}^{x+2}}=240+{{9}^{x}}\], find\[x\].
A)
\[0.5\] done
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B)
\[0.2\] done
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C)
\[0.4\] done
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D)
\[0.1\] done
clear
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question_answer16)
Which expression is equal to\[{{({{x}^{-1}}+{{y}^{-1}})}^{1}}\]?
A)
\[xy\] done
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B)
\[x+y\] done
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C)
\[\frac{xy}{x+y}\] done
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D)
\[\frac{x+y}{xy}\] done
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question_answer17)
If\[{{10}^{x}}=64\], what is the value of\[{{10}^{\frac{x}{2}+1}}\]?
A)
\[18\] done
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B)
\[42\] done
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C)
\[80\] done
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D)
\[81\] done
clear
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question_answer18)
If \[\frac{x}{{{x}^{1.5}}}=8{{x}^{-1}}\]and\[x>0\], find\[x\].
A)
\[\frac{\sqrt{2}}{4}\] done
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B)
\[2\sqrt{2}\] done
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C)
\[4\] done
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D)
\[125\] done
clear
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question_answer19)
If\[{{4}^{x}}-{{4}^{x-1}}=24\], what is the value of\[{{(2x)}^{x}}\]?
A)
\[5\sqrt{5}\] done
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B)
\[\sqrt{5}\] done
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C)
\[25\sqrt{5}\] done
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D)
\[125\] done
clear
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question_answer20)
If\[x=\sqrt{5}+2\], find the value of\[x-\frac{1}{x}\].
A)
\[2\sqrt{5}\] done
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B)
\[4\] done
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C)
\[2\] done
clear
D)
\[\sqrt{5}\] done
clear
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question_answer21)
If\[x=\frac{2}{3-\sqrt{7}}\], find the value of\[{{(x-3)}^{2}}\].
A)
\[1\] done
clear
B)
\[3\] done
clear
C)
\[6\] done
clear
D)
\[7\] done
clear
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question_answer22)
If\[x=7+4\sqrt{3}\]and\[xy=1\], what is the value of\[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}\]?
A)
\[64\] done
clear
B)
\[134\] done
clear
C)
\[194\] done
clear
D)
\[1/49\] done
clear
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question_answer23)
If\[\sqrt{5}=2.236\]and\[\sqrt{3}=1.732\], find the value of\[\frac{1}{\sqrt{5}-\sqrt{3}}\].
A)
\[3.968\] done
clear
B)
\[\frac{1}{3.968}\] done
clear
C)
\[1.984\] done
clear
D)
\[\sqrt{0.504}\] done
clear
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question_answer24)
Identify a rational number between \[-5\] and\[5\].
A)
\[0\] done
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B)
\[-7.3\] done
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C)
\[-5.7\] done
clear
D)
\[1.101100110001\]. done
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question_answer25)
The sum of the digits of a number is subtracted from the number, the resulting number is always divisible by which of the following numbers?
A)
\[2\] done
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B)
\[5\] done
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C)
\[8\] done
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D)
\[9\] done
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question_answer26)
Find the difference between \[1.\overline{4}\] and\[0.\overline{2}\].
A)
\[0.\overline{2}\] done
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B)
\[1.\overline{3}\] done
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C)
\[\frac{11}{9}\] done
clear
D)
\[\frac{12}{9}\] done
clear
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question_answer27)
If \[\sqrt{a}\] is an irrational number, what is\[a\]?
A)
Rational done
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B)
Irrational done
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C)
0 done
clear
D)
Real done
clear
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question_answer28)
Which of the following is an irrational number?
A)
\[\sqrt{9}\] done
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B)
\[\pi \] done
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C)
\[\frac{22}{7}\] done
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D)
\[2.5151515...\] done
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question_answer29)
Which of the following numbers is an irrational number?
A)
\[\sqrt{16}-4\] done
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B)
\[\left( 3-\sqrt{3} \right)\left( 3+\sqrt{3} \right)\] done
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C)
\[\sqrt{5}+3\] done
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D)
\[-\sqrt{25}\] done
clear
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question_answer30)
If\[x=2+{{2}^{1/3}}+{{2}^{2/3}}\], find the value of\[({{x}^{3}}-6{{x}^{2}}+6x)\].
A)
\[2\] done
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B)
\[4\] done
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C)
\[8\] done
clear
D)
\[6\] done
clear
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question_answer31)
If\[x=\frac{1}{2-\sqrt{3}}\], find the value of\[{{x}^{3}}-2{{x}^{2}}-7x+10\].
A)
\[14\] done
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B)
\[8\] done
clear
C)
\[4\] done
clear
D)
\[16\] done
clear
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question_answer32)
If\[a=3\]and\[b=5\], find the value of\[{{a}^{a}}+{{b}^{b}}\].
A)
\[512\] done
clear
B)
\[251\] done
clear
C)
\[513\] done
clear
D)
\[152\] done
clear
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question_answer33)
If\[p=3\]and\[q=5\], find the value of\[{{\left( \frac{1}{p}+\frac{1}{q} \right)}^{p}}\].
A)
\[\frac{3375}{512}\] done
clear
B)
\[\frac{512}{3375}\] done
clear
C)
\[\frac{512}{225}\] done
clear
D)
\[\frac{64}{225}\] done
clear
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question_answer34)
Find the value of\[\frac{1}{\sqrt{5}-\sqrt{4}}\].
A)
\[\sqrt{5}-\sqrt{4}\] done
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B)
\[\sqrt{5}+\sqrt{4}\] done
clear
C)
\[\frac{\sqrt{5}+\sqrt{4}}{9}\] done
clear
D)
\[\sqrt{4}-\sqrt{5}\] done
clear
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question_answer35)
Find the rational number for\[0.\overline{5}\].
A)
\[\frac{9}{5}\] done
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B)
\[\frac{5}{10}\] done
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C)
\[\frac{5}{9}\] done
clear
D)
\[\frac{10}{5}\] done
clear
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question_answer36)
Identify the simplest form of\[\frac{5\sqrt{3}+3\sqrt{5}}{5\sqrt{3}-3\sqrt{5}}\].
A)
\[6+\sqrt{15}\] done
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B)
\[4+\sqrt{15}\] done
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C)
\[4+\sqrt{3}\] done
clear
D)
\[6+\sqrt{5}\] done
clear
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question_answer37)
Find the value of\[\frac{{{(0.6)}^{0}}-{{(0.1)}^{-1}}}{{{\left( \frac{3}{8} \right)}^{-1}}{{\left( \frac{3}{2} \right)}^{3}}+{{\left( \frac{-1}{3} \right)}^{-1}}}\].
A)
\[\frac{-2}{3}\] done
clear
B)
\[\frac{3}{2}\] done
clear
C)
\[-\frac{3}{2}\] done
clear
D)
\[\frac{2}{3}\] done
clear
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question_answer38)
\[m\] and \[n\] are integers and\[\sqrt{mn}=10\]. Which of the following cannot be a value of\[m+n\]?
A)
\[25\] done
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B)
\[52\] done
clear
C)
\[101\] done
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D)
\[50\] done
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question_answer39)
If\[2.5252525...=\frac{p}{q}\](in the lowest form) what is the value of\[\frac{q}{p}\]?
A)
\[0.4\] done
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B)
\[0.42525\] done
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C)
\[0.0396\] done
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D)
\[0.396\] done
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question_answer40)
If\[{{x}^{x\sqrt{x}}}={{\left( x\sqrt{x} \right)}^{x}}\], find the value of\[x\].
A)
\[\frac{3}{2}\] done
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B)
\[\frac{2}{9}\] done
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C)
\[\frac{9}{4}\] done
clear
D)
\[\frac{4}{9}\] done
clear
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question_answer41)
Simplify\[\frac{{{a}^{\frac{1}{2}}}+{{a}^{-\frac{1}{2}}}}{1-a}+\frac{1-{{a}^{-\frac{1}{2}}}}{1+\sqrt{a}}\].
A)
\[1\] done
clear
B)
\[0\] done
clear
C)
\[\frac{2}{1-a}\] done
clear
D)
\[1+a\] done
clear
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question_answer42)
Which symbol is used to denote a collection of all positive integers?
A)
\[N\] done
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B)
\[W\] done
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C)
\[Z\] done
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D)
\[Q\] done
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question_answer43)
Find the value of \[0.9999.......\] in the form of\[\frac{p}{q}\](\[p,\,\,q\in Z\]and\[q\ne 0\])
A)
\[\frac{1}{9}\] done
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B)
\[\frac{2}{9}\] done
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C)
\[\frac{9}{10}\] done
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D)
\[1\] done
clear
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question_answer44)
If\[x=\sqrt[3]{2+\sqrt{3}}\], find the value of\[{{x}^{3}}+\frac{1}{{{x}^{3}}}\].
A)
\[2\] done
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B)
\[4\] done
clear
C)
\[8\] done
clear
D)
\[9\] done
clear
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question_answer45)
Find the simplest rationalising factor of\[{{5}^{1/3}}+{{5}^{-1/3}}\]
A)
\[{{5}^{2/3}}+1+{{5}^{-2/3}}\] done
clear
B)
\[{{5}^{1/3}}-{{5}^{-1/3}}\] done
clear
C)
\[{{5}^{2/3}}-1+{{5}^{-2/3}}\] done
clear
D)
\[{{5}^{2/3}}+1-{{5}^{-2/3}}\] done
clear
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