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question_answer1)
If \[{{2}^{x-3}}{{.3}^{2x-8}}=36,\] then the value of \[x\]is______.
A)
2 done
clear
B)
5 done
clear
C)
3 done
clear
D)
1 done
clear
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question_answer2)
If \[N=\frac{\sqrt{\sqrt{5}+2}+\sqrt{5-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}},\] then N equals ____.
A)
1 done
clear
B)
\[2\sqrt{2}-1\] done
clear
C)
\[\frac{\sqrt{5}}{2}\] done
clear
D)
\[\frac{2}{\sqrt{\sqrt{5}+1}}\] done
clear
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question_answer3)
Express the mixed recurring decimal 4.32 in the form \[\frac{p}{q}.\]
A)
\[\frac{389}{90}\] done
clear
B)
\[\frac{329}{90}\] done
clear
C)
\[\frac{29}{90}\] done
clear
D)
\[\frac{233}{990}\] done
clear
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question_answer4)
If \[x=(7+4\sqrt{3}),\]then \[\left( x+\frac{1}{x} \right)=\_\_\_\_\_.\]
A)
\[8\sqrt{3}\] done
clear
B)
14 done
clear
C)
49 done
clear
D)
48 done
clear
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question_answer5)
\[\frac{7\sqrt{3}}{(\sqrt{10}+\sqrt{3})}-\frac{2\sqrt{5}}{(\sqrt{6}+\sqrt{5})}-\frac{3\sqrt{2}}{(\sqrt{15}+3\sqrt{2})}=\_\_\_\_\_.\]
A)
1 done
clear
B)
2 done
clear
C)
\[\frac{1}{2}\] done
clear
D)
3 done
clear
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question_answer6)
The rationalizing factor of\[\sqrt[5]{{{a}^{2}}{{b}^{3}}{{c}^{4}}}\]is ______.
A)
\[\sqrt[5]{{{a}^{3}}{{b}^{2}}c}\] done
clear
B)
\[\sqrt[4]{{{a}^{3}}{{b}^{2}}c}\] done
clear
C)
\[\sqrt[3]{{{a}^{3}}{{b}^{2}}c}\] done
clear
D)
\[\sqrt{{{a}^{3}}{{b}^{2}}c}\] done
clear
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question_answer7)
Rational number \[\frac{-18}{5}\] lies between consecutive integers ____.
A)
-2 and-3 done
clear
B)
-3 and-4 done
clear
C)
-4 and -5 done
clear
D)
-5 and -6 done
clear
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question_answer8)
An irrational number between \[\frac{1}{7}\]and \[\frac{2}{7}\] is _____.
A)
\[\frac{1}{2}\left( \frac{1}{7}+\frac{2}{7} \right)\] done
clear
B)
\[\left( \frac{1}{7}\times \frac{2}{7} \right)\] done
clear
C)
\[\sqrt{\frac{1}{7}\times \frac{2}{7}}\] done
clear
D)
None of these done
clear
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question_answer9)
The denominator of \[\frac{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}+\frac{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}\]is ______.
A)
\[{{a}^{2}}\] done
clear
B)
\[{{b}^{2}}\] done
clear
C)
\[{{a}^{2}}-{{b}^{2}}\] done
clear
D)
\[\frac{4{{a}^{2}}-2{{b}^{2}}}{{{b}^{2}}}\] done
clear
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question_answer10)
The ascending order of the surds \[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4},\] is ____.
A)
\[\sqrt[9]{4},\sqrt[6]{3},\sqrt[3]{2}\] done
clear
B)
\[\sqrt[9]{4},\sqrt[3]{2},\sqrt[6]{3}\] done
clear
C)
\[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4}\] done
clear
D)
\[\sqrt[6]{3},\sqrt[9]{4},\sqrt[3]{2}\] done
clear
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question_answer11)
The greater number among \[\sqrt{17}-\sqrt{12}\] and \[\sqrt{11}-\sqrt{6}\]is_____.
A)
\[\sqrt{17}-\sqrt{12}\] done
clear
B)
\[\sqrt{11}-\sqrt{6}\] done
clear
C)
Both are equal done
clear
D)
Can't be compared done
clear
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question_answer12)
The value of \[x,\]if \[{{5}^{x-3}}{{.3}^{2x-8}}=225\] is______.
A)
3 done
clear
B)
4 done
clear
C)
2 done
clear
D)
5 done
clear
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question_answer13)
The value of \[\frac{1}{3}\] of \[{{15}^{27}}\] is ____.
A)
\[{{5}^{27}}\] done
clear
B)
\[~{{15}^{9}}\] done
clear
C)
\[~5\times {{15}^{26}}\] done
clear
D)
\[~5\times {{3}^{9}}\] done
clear
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question_answer14)
If \[x=2-\sqrt{3}\]then the value of \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] and \[{{x}^{2}}-\frac{1}{{{x}^{2}}}\]respectively, are____.
A)
\[14,8\sqrt{3}\] done
clear
B)
\[-14,-8\sqrt{3}\] done
clear
C)
\[14,-8\sqrt{3}\] done
clear
D)
\[-14,\,8\sqrt{3}\] done
clear
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question_answer15)
Which of the following statements is INCORRECT?
A)
Every integer is a rational number. done
clear
B)
Every natural number is an integer. done
clear
C)
Every natural number is a real number. done
clear
D)
Every real number is a rational number. done
clear
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question_answer16)
If \[\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}=(a-b\sqrt{3}),\] find the values of a and b.
A)
\[a=1,b=2\] done
clear
B)
a = 2,b = 1 done
clear
C)
a = 2, b = 3 done
clear
D)
a = 3, b = 2 done
clear
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question_answer17)
Which of the following numbers has the terminating decimal representation?
A)
\[\frac{5}{12}\] done
clear
B)
\[\frac{8}{35}\] done
clear
C)
\[\frac{7}{24}\] done
clear
D)
\[\frac{13}{80}\] done
clear
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question_answer18)
The number \[x=1.242424....\]can be expressed in the form \[x=\frac{p}{q},\]where p and q q are positive integers having no common factors. Then p + q equals ____.
A)
72 done
clear
B)
74 done
clear
C)
41 done
clear
D)
53 done
clear
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question_answer19)
If \[x\]and y are positive real numbers, then which of the following is CORRECT?
A)
\[x>y\Rightarrow -x>-y\] done
clear
B)
\[x>y\Rightarrow -x<-y\] done
clear
C)
\[x>y\Rightarrow \frac{1}{x}>\frac{1}{y}\] done
clear
D)
\[x>y\Rightarrow \frac{1}{x}<\frac{-1}{y}\] done
clear
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question_answer20)
If \[x=1-\sqrt{2},\]then find the value of \[{{\left( x-\frac{1}{x} \right)}^{2}}.\]
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
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question_answer21)
The value of \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\]\[\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}\]is _____.
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
4 done
clear
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question_answer22)
Which of the following statements is INCORRECT?
A)
If 'a' is a rational number and 'b' is irrational, then a + b is irrational. done
clear
B)
The product of a non-zero rational number with an irrational number is always irrational. done
clear
C)
Addition of any two irrational numbers can be rational. done
clear
D)
Division of any two integers is an integer. done
clear
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question_answer23)
Fill in the blanks.
(i) The decimal form of an irrational number is neither P nor Q. |
(ii) There are R rational numbers between any two consecutive integers. |
(iii) Every rational number is S. |
A)
B)
C)
D)
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question_answer24)
Read the statements carefully.
Statement 1: Every point on the number line represent a unique real number. |
Statement 2: Irrational numbers cannot be represented on a number line. |
Which of the following options hold?
A)
Both Statement-1 and Statement-2 are true. done
clear
B)
Statement-1 is true but Statement-2 is false. done
clear
C)
Statement-1 is false but Statement-2 is true. done
clear
D)
Both Statement-1 and Statement-2 are false. done
clear
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question_answer25)
Match the following,
Column -I | Column -II |
(a) If \[\frac{3}{x+8}=\frac{4}{6-x},\]then \[x\]is ______. | (i) 3 |
(b) if, \[\frac{{{2}^{x-1}}{{.4}^{2x+1}}}{{{8}^{x-1}}}=64,\] | (ii) \[-2\] |
(c) if \[{{4}^{x}}-{{4}^{x}}^{-1}=24\] | (iii)\[-2\] |
(d) \[{{4}^{x+1}}=256,\]then \[x\]is | (iv) 1 |
A)
\[(a)\to (i);(b)\to (ii);(c)\to (iii);(d)\to (iv)\] done
clear
B)
\[(a)\to (iii);(b)\to (iv);(c)\to (i);(d)\to (ii)\] done
clear
C)
\[(a)\to (i);(b)\to (iv);(c)\to (ii);(d)\to (iii)\] done
clear
D)
\[(a)\to (iii);(b)\to (iv);(c)\to (iii);(d)\to (i)\] done
clear
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