-
question_answer1)
Find the value of \[\sqrt{\mathbf{12+2}\sqrt{\mathbf{6}}\mathbf{+2}\sqrt{\mathbf{21}}\mathbf{+2}\sqrt{\mathbf{14}}}\]
A)
\[\sqrt{2}+\sqrt{3}+\sqrt{5}\] done
clear
B)
\[\sqrt{3}+\sqrt{2}+\sqrt{5}\] done
clear
C)
\[3+\sqrt{2}+\sqrt{1}\] done
clear
D)
\[\sqrt{2}+\sqrt{3}+\sqrt{7}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer2)
Find the least value from \[\sqrt[4]{2},\sqrt[6]{3},\sqrt[9]{5},\sqrt[12]{7}\]
A)
\[\sqrt[4]{2}\] done
clear
B)
\[\sqrt[6]{3}\] done
clear
C)
\[\sqrt[9]{5}\] done
clear
D)
\[\sqrt[12]{7}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer3)
Identify the irrational number among the following 0.019019019019..........., 0.235230523005230005..........., \[\frac{\mathbf{19}}{\mathbf{100000000000}}\], \[\mathbf{0}\mathbf{.}\overline{\mathbf{2958}}\]
A)
0.019019019019...... done
clear
B)
0.235230523005230005......... done
clear
C)
\[\frac{19}{100000000000}\] done
clear
D)
\[0.\overline{2958}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer4)
Simplify:\[\mathbf{(}\sqrt{\mathbf{20}}\mathbf{+}\sqrt{\mathbf{1125}}\mathbf{-}\sqrt{\mathbf{567}}\mathbf{)}\]\[\mathbf{(}\sqrt{\mathbf{500}}\mathbf{+}\sqrt{\mathbf{245}}\mathbf{+9}\sqrt{\mathbf{7}})\]
A)
2012 done
clear
B)
878 done
clear
C)
1445 done
clear
D)
567 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer5)
Solve: \[\sqrt[12]{32}\times \sqrt[32]{16}\times \sqrt[24]{2048}\]
A)
2 done
clear
B)
8 done
clear
C)
16 done
clear
D)
32 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer6)
Find the value of \[\left( \sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}} \right)\]
A)
0 done
clear
B)
1 done
clear
C)
\[\sqrt{2}\] done
clear
D)
\[2\sqrt{2}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer7)
Which one is different among the following? |
\[^{\mathbf{9}}\sqrt{\mathbf{3(}{{\mathbf{2}}^{\mathbf{8}}}\mathbf{-13)}}{{\mathbf{,}}^{\mathbf{3}}}\sqrt{\mathbf{9}}\mathbf{,}{{\mathbf{ }}^{\mathbf{9}}}\sqrt{\mathbf{729}}\mathbf{, }\frac{\mathbf{3}}{{{\mathbf{3}}^{\mathbf{1/3}}}}\] |
A)
\[^{9}\sqrt{3({{2}^{8}}-13)}\] done
clear
B)
\[^{3}\sqrt{9}\] done
clear
C)
\[^{9}\sqrt{729}\] done
clear
D)
\[\frac{3}{{{3}^{1/3}}}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer8)
If r is a rational number and s is an irrational number, then which one of the following is true?
A)
\[(r+s)(r-s)\] will always be an irrational number. done
clear
B)
\[\frac{(r+s)}{(r-s)}\] will always be a rational number. done
clear
C)
rs will always be an irrational number. done
clear
D)
\[\frac{r}{s}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer9)
Which one of following statements is correct?
A)
\[\pi \] is not a rational number. done
clear
B)
\[{{\pi }^{2}}\]is an irrational number. done
clear
C)
3.2325325325..... is equal to\[\frac{32293}{9990}\]. done
clear
D)
All of the above done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer10)
Simplify: \[\frac{{{\mathbf{(}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{)}}^{\mathbf{1/5}}}{{\mathbf{x}}^{\mathbf{1/3}}}}{{{\mathbf{x}}^{\mathbf{2/3}}}{{\mathbf{x}}^{\mathbf{-11/15}}}}\]
A)
\[\sqrt[15]{{{x}^{13}}}\] done
clear
B)
\[\frac{\text{1}}{{{x}^{1/15}}}\] done
clear
C)
x done
clear
D)
1 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer11)
After rationalizing \[\mathbf{E=}\frac{\mathbf{1}}{\sqrt{\mathbf{2}}\mathbf{+}\sqrt{\mathbf{3}}\mathbf{-}\sqrt{\mathbf{5}}}\], the value of \[\mathbf{4}\sqrt{\mathbf{3}}\mathbf{E}\]is _________
A)
\[\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{\sqrt{3}}\] done
clear
B)
\[2+\sqrt{6}-\sqrt{10}\] done
clear
C)
\[2+\sqrt{6}+\sqrt{10}\] done
clear
D)
\[\frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{3}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer12)
\[\frac{\sqrt{\mathbf{5}\sqrt{\mathbf{5}\sqrt{\mathbf{5}\sqrt{\mathbf{5}\sqrt{\mathbf{5}}}}}}}{\sqrt{\mathbf{5}\sqrt{\mathbf{5}\sqrt{\mathbf{5}}}}}\]is equal to _________
A)
\[{{5}^{3/32}}\] done
clear
B)
\[{{5}^{7/32}}\] done
clear
C)
\[{{5}^{21/32}}\] done
clear
D)
\[{{5}^{5/32}}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer13)
If pqr = 1, then find the value of \[\left( \frac{\mathbf{1}}{\mathbf{1+p+}{{\mathbf{q}}^{\mathbf{-1}}}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{1+q+}{{\mathbf{r}}^{\mathbf{-1}}}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{1+r+}{{\mathbf{p}}^{\mathbf{-1}}}} \right)\]
A)
\[pq+qr+rp\] done
clear
B)
1 done
clear
C)
pq + qr done
clear
D)
p/q done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer14)
If \[\frac{{{\mathbf{2}}^{\mathbf{3n}}}}{\mathbf{8}}\mathbf{+1+3}\times \frac{{{\mathbf{2}}^{\mathbf{2n}}}}{\mathbf{2}}\mathbf{+3}\times \frac{{{\mathbf{2}}^{\mathbf{2n}}}}{\mathbf{4}}\mathbf{=4913}\], then find the value of n.
A)
3 done
clear
B)
10 done
clear
C)
5 done
clear
D)
8 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer15)
If \[\mathbf{A=}\sqrt{\mathbf{13}}\mathbf{-}\sqrt{\mathbf{5}}\] and \[\mathbf{B=}\sqrt{\mathbf{17}}\mathbf{-}\sqrt{\mathbf{13}}\], then _________
A)
\[A>B\] done
clear
B)
\[A<B\] done
clear
C)
\[A=B\] done
clear
D)
\[A<2B\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer16)
If two fractions are p and q such that both lies between 0 and 1, then ________
A)
The product of p and q will always be greater than both p and q separately. done
clear
B)
The division of p and q i.e. p/q will always be greater than 1. done
clear
C)
The product of p and q will always be greater than sum of p and q. done
clear
D)
The product of p and q will always be less than either of the fractions p or q. done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer17)
\[\mathbf{1}{{\mathbf{0}}^{\mathbf{34}}}\mathbf{-7}\] is divisible by _________
A)
9 done
clear
B)
2 done
clear
C)
3 done
clear
D)
both B and C done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer18)
If\[\frac{\sqrt{\sqrt{\sqrt{{{\sqrt{\mathbf{5+2}}}^{\mathbf{x}}}}}}}{{{\mathbf{2}}^{\mathbf{x}}}\mathbf{-1}}\mathbf{=}\frac{\mathbf{1}}{{{\mathbf{3}}^{\mathbf{7/8}}}}\], then find the value of x.
A)
4 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer19)
If \[\mathbf{x=}\frac{\sqrt{\mathbf{7}}\mathbf{+}\sqrt{\mathbf{5}}}{\sqrt{\mathbf{7}}\mathbf{-}\sqrt{\mathbf{5}}}\] and \[\mathbf{y=}\frac{\sqrt{\mathbf{7}}\mathbf{-}\sqrt{\mathbf{5}}}{\sqrt{\mathbf{7}}\mathbf{+}\sqrt{\mathbf{5}}}\], then find the value of \[\frac{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+xy+}{{\mathbf{y}}^{\mathbf{2}}}}{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-xy+}{{\mathbf{y}}^{\mathbf{2}}}}\]
A)
\[\frac{137}{143}\] done
clear
B)
\[\frac{143}{137}\] done
clear
C)
\[\frac{117}{128}\] done
clear
D)
\[\frac{128}{117}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer20)
If \[\mathbf{P=2}\sqrt{\mathbf{7}}\mathbf{-3}\sqrt{\mathbf{3}}\] and \[\mathbf{Q=}\frac{\mathbf{1}}{\mathbf{P}}\], then find the value of\[{{\mathbf{P}}^{\mathbf{4}}}\mathbf{-}{{\mathbf{Q}}^{\mathbf{4}}}\].
A)
\[2110\sqrt{3}\] done
clear
B)
\[-\,1440\sqrt{7}\] done
clear
C)
\[2210\sqrt{7}\] done
clear
D)
\[-\,2640\sqrt{21}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer21)
If \[\mathbf{p=}\frac{\sqrt{\mathbf{17}}\mathbf{+}\sqrt{\mathbf{15}}}{\sqrt{\mathbf{17}}\mathbf{-}\sqrt{\mathbf{15}}}\] and \[\mathbf{q=}\frac{\mathbf{1}}{\mathbf{p}}\], then the value of \[\mathbf{3}{{\mathbf{p}}^{\mathbf{2}}}\mathbf{-5pq+3}{{\mathbf{q}}^{\mathbf{2}}}\]is _________
A)
3117 done
clear
B)
3061 done
clear
C)
3177 done
clear
D)
2861 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer22)
If \[\mathbf{x=}{{\mathbf{p}}^{\mathbf{1/3}}}\mathbf{+}{{\mathbf{p}}^{\mathbf{-}}}^{\mathbf{1/3}}\] and \[\mathbf{y=}{{\mathbf{p}}^{\mathbf{1/3}}}\mathbf{-}{{\mathbf{p}}^{\mathbf{-}}}^{\mathbf{1/3}}\], then find the value of \[\frac{{{\mathbf{(}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{)}}^{\mathbf{3}}}}{\mathbf{(}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+xy)(}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{-xy)}}\]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer23)
If \[\sqrt{\mathbf{x}}\mathbf{=}{{\mathbf{a}}^{\mathbf{1/3}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{-1/3}}}\] and \[\sqrt{\mathbf{y}}\mathbf{=}{{\mathbf{a}}^{\mathbf{1/3}}}\mathbf{-}{{\mathbf{a}}^{\mathbf{-1/3}}}\], then find the value of \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{y}}^{\mathbf{2}}}\]
A)
\[2({{a}^{2/3}}+{{a}^{-2/3}})\] done
clear
B)
\[4({{a}^{1/3}}+{{a}^{-1/3}})\] done
clear
C)
\[8({{a}^{2/3}}+{{a}^{-2/3}})\] done
clear
D)
\[16({{a}^{1/3}}+{{a}^{-1/3}})\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer24)
\[\frac{^{\mathbf{5}}\sqrt{\mathbf{3}}{{\mathbf{.}}^{\mathbf{4}}}{{\sqrt{\mathbf{3}}}^{\mathbf{6}}}\mathbf{.}\sqrt{\mathbf{9}}}{\sqrt{\mathbf{3}\sqrt{\mathbf{3}\sqrt{\mathbf{3}}}}}\]equals to _______
A)
\[{{3}^{11/119}}\] done
clear
B)
\[{{3}^{-11/120}}\] done
clear
C)
\[{{3}^{103/119}}\] done
clear
D)
\[{{3}^{105/119}}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer25)
If \[\mathbf{a=}\sqrt{\frac{\sqrt{\mathbf{3}}\mathbf{-1}}{\sqrt{\mathbf{3}}\mathbf{+1}}}\] then find the value of \[\mathbf{a+}\frac{\mathbf{1}}{\mathbf{a}}\].
A)
6 done
clear
B)
\[\sqrt{3}\] done
clear
C)
3 done
clear
D)
\[\sqrt{6}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer26)
If \[\mathbf{x=17+12}\sqrt{\mathbf{2}}\] then the value of \[{{\mathbf{x}}^{\mathbf{1/4}}}\mathbf{-}{{\mathbf{x}}^{\mathbf{-1/4}}}\] is equal to _______
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer27)
If \[{{\mathbf{x}}^{\mathbf{1/4}}}\mathbf{+}{{\mathbf{x}}^{\mathbf{-1/4}}}\mathbf{=2}\sqrt{\mathbf{2}}\] then find the value of\[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-}\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{2}}}}\].
A)
\[1152\sqrt{2}\] done
clear
B)
\[\sqrt{2}-1\] done
clear
C)
\[816\sqrt{2}\] done
clear
D)
\[\sqrt{2}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer28)
If \[\sqrt{\frac{\sqrt{\mathbf{5}}\mathbf{-}\sqrt{\mathbf{3}}}{\sqrt{\mathbf{5}}\mathbf{+}\sqrt{\mathbf{3}}}\mathbf{+}\frac{\sqrt{\mathbf{5}}\mathbf{+}\sqrt{\mathbf{3}}}{\sqrt{\mathbf{5}}\mathbf{-}\sqrt{\mathbf{3}}}}\], then find the value of \[\sqrt{\sqrt{\sqrt{\mathbf{x}}}}\].
A)
\[{{(\sqrt{5}+\sqrt{3})}^{13/8}}\] done
clear
B)
\[{{2}^{3/16}}\] done
clear
C)
\[{{3}^{1/16}}\] done
clear
D)
\[{{5}^{1/8}}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer29)
If \[\mathbf{A=}\frac{\sqrt{\sqrt{\sqrt{\sqrt{\mathbf{2+}\sqrt{\mathbf{3}}}}}}}{\sqrt{\sqrt{\sqrt{\sqrt{\mathbf{2-}\sqrt{\mathbf{3}}}}}}}\], then find the value of A8.
A)
\[{{(2-\sqrt{3})}^{1/2}}\] done
clear
B)
\[{{(2+\sqrt{3})}^{1/4}}\] done
clear
C)
\[{{\left( \frac{2+\sqrt{3}}{2-\sqrt{3}} \right)}^{1/4}}\] done
clear
D)
\[2+\sqrt{3}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer30)
If \[{{\mathbf{x}}^{\mathbf{1/8}}}\mathbf{=m}\] and \[{{\mathbf{x}}^{\mathbf{1/4}}}\mathbf{=n}\] and n = 4 m then find the value of\[\sqrt{\mathbf{x}}\].
A)
512 done
clear
B)
216 done
clear
C)
324 done
clear
D)
256 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer31)
Find the value of \[{{\mathbf{(729)}}^{\mathbf{0}\mathbf{.16}}}\times {{\mathbf{(27)}}^{\mathbf{0}\mathbf{.18}}}\]
A)
\[\sqrt{3}\] done
clear
B)
\[3\sqrt{3}\] done
clear
C)
27 done
clear
D)
81 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer32)
If \[{{\left[ \sqrt{\mathbf{2}}{{\left( \mathbf{1}{{\mathbf{6}}^{\mathbf{1/4}}}\mathbf{+777}{{\mathbf{6}}^{\mathbf{1/5}}} \right)}^{\mathbf{4}}} \right]}^{\mathbf{n}}}\mathbf{=4}\sqrt{\mathbf{2}}\], then find value of n.
A)
\[\frac{1}{4}\] done
clear
B)
\[\frac{1}{6}\] done
clear
C)
\[\frac{1}{5}\] done
clear
D)
\[\frac{1}{3}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer33)
Which of the following is a rational number between \[\mathbf{0}\mathbf{.12}\overline{\mathbf{7}}\] and\[\mathbf{0}\mathbf{.18}\overline{\mathbf{3}}\]?
A)
\[\frac{206}{1620}\] done
clear
B)
\[\frac{295}{1620}\] done
clear
C)
\[\frac{299}{1620}\] done
clear
D)
\[\frac{315}{1620}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer34)
How many rational numbers are possible in between\[\frac{\mathbf{1779}}{\mathbf{3001}}\] & \[\frac{\mathbf{1780}}{\mathbf{3001}}\]?
A)
10 done
clear
B)
1 done
clear
C)
infinite done
clear
D)
1000 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer35)
Which among the following is an rational number between \[\frac{\mathbf{7203}}{\mathbf{12005}}\]and\[\frac{\mathbf{8788}}{\mathbf{10985}}\]?
A)
0.6001000100001........ done
clear
B)
0.590020002......... done
clear
C)
0.81025002500025........ done
clear
D)
0.635463546354....... done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer36)
Simplify \[\mathbf{ }\frac{\sqrt{\mathbf{13+}\sqrt{\mathbf{5+}\sqrt{\mathbf{10+}\sqrt{\mathbf{12+2}\sqrt{\mathbf{144}}}}}}}{\sqrt{\mathbf{6+}\sqrt{\mathbf{97+}\sqrt{\mathbf{4+}\sqrt{\mathbf{37-4}\sqrt{\mathbf{9}}}}}}}\]
A)
1 done
clear
B)
2 done
clear
C)
\[\sqrt{2}\] done
clear
D)
\[\sqrt{5}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer37)
If \[\mathbf{x=}\sqrt{\mathbf{13}}\mathbf{-}\sqrt{\mathbf{11}}\] and \[\mathbf{y=}\sqrt{\mathbf{13}}\mathbf{+}\sqrt{\mathbf{11}}\], then find the value of \[\mathbf{(}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+80}\sqrt{\mathbf{11}}\mathbf{)-(}{{\mathbf{y}}^{\mathbf{3}}}\mathbf{-20}\sqrt{\mathbf{11}}\mathbf{)}\]
A)
1 done
clear
B)
2 done
clear
C)
0 done
clear
D)
\[\sqrt{11}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer38)
Simplify \[\frac{{{\mathbf{(0}\mathbf{.00001)}}^{\mathbf{0}\mathbf{.20}}}\times {{\mathbf{(0}\mathbf{.0016)}}^{\mathbf{0}\mathbf{.25}}}\times {{\mathbf{(0}\mathbf{.64)}}^{\mathbf{0}\mathbf{.50}}}}{{{\mathbf{(0}\mathbf{.2)}}^{\mathbf{4}}}}\]
A)
1 done
clear
B)
10 done
clear
C)
0.8 done
clear
D)
0.16 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer39)
\[\sqrt{\mathbf{11+4}\sqrt{\mathbf{7}}}\mathbf{-}\sqrt{\mathbf{8-2}\sqrt{\mathbf{7}}}\]is equal to ______
A)
0 done
clear
B)
3 done
clear
C)
1 done
clear
D)
\[\sqrt{7}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer40)
If\[{{\left[ \frac{{{\mathbf{2}}^{{{\mathbf{n}}^{\mathbf{3}}}\mathbf{-3}{{\mathbf{n}}^{\mathbf{2}}}}}}{\mathbf{2}}\mathbf{.}{{\mathbf{2}}^{\mathbf{3n}}} \right]}^{\mathbf{1/3}}}\mathbf{+}{{\left[ \mathbf{4}\mathbf{.}{{\mathbf{2}}^{{{\mathbf{n}}^{\mathbf{2}}}\mathbf{+2n}}} \right]}^{\mathbf{1/2}}}\mathbf{=640}\], then find the value of n.
A)
6 done
clear
B)
7 done
clear
C)
8 done
clear
D)
10 done
clear
E)
None of these done
clear
View Solution play_arrow