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question_answer1)
The value of \[\frac{{{2}^{2001}}+{{2}^{1999}}}{{{2}^{2000}}-{{2}^{1998}}}\], is _____.
A)
2 done
clear
B)
\[10/3\] done
clear
C)
\[{{2}^{1000}}+1\] done
clear
D)
\[\text{10}\] done
clear
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question_answer2)
When simplified, \[{{\text{(}{{\text{x}}^{-1}}+{{y}^{-1}})}^{-1}}\] is equal to_____.
A)
\[x+y\] done
clear
B)
\[\frac{xy}{x+y}\] done
clear
C)
\[xy\] done
clear
D)
\[\frac{1}{xy}\] done
clear
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question_answer3)
The value of \[x+x({{x}^{x}})\] at \[x=2\] is __.
A)
10 done
clear
B)
16 done
clear
C)
18 done
clear
D)
36 done
clear
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question_answer4)
Simplify; \[\begin{align} & {{\left( \frac{{{x}^{a}}}{{{x}^{b}}} \right)}^{({{a}^{2}}+{{b}^{2}}+ab)}}\times {{\left( \frac{{{x}^{b}}}{{{x}^{c}}} \right)}^{({{b}^{2}}+{{c}^{2}}+cb)}}\times {{\left( \frac{{{x}^{c}}}{{{x}^{a}}} \right)}^{({{c}^{2}}+{{a}^{2}}+ca)}} \\ & \\ \end{align}\]
A)
1 done
clear
B)
\[{{(a+b+c)}^{3}}\] done
clear
C)
\[{{\text{a}}^{\text{2}}}\text{+}{{\text{b}}^{\text{2}}}\text{+}{{\text{c}}^{\text{2}}}\] done
clear
D)
0 done
clear
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question_answer5)
If (\[{{(6x)}^{6}}={{6}^{{{2}^{3}}}}\], then find the value of x.
A)
1 done
clear
B)
\[\sqrt{6}\] done
clear
C)
\[\sqrt[3]{6}\] done
clear
D)
\[\sqrt[6]{6}\] done
clear
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question_answer6)
Find the value of\[{{\text{(0}\text{.000064)}}^{\frac{5}{6}}}\div {{\text{(0}\text{.00032)}}^{\frac{6}{5}}}\].
A)
0.2 done
clear
B)
0.4 done
clear
C)
5 done
clear
D)
2.5 done
clear
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question_answer7)
If \[x={{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{2}{3} \right)}^{-4}}\], find the value of \[{{x}^{2}}\].
A)
\[{{\left( \frac{4}{3} \right)}^{12}}\] done
clear
B)
\[{{\left( \frac{2}{3} \right)}^{12}}\] done
clear
C)
\[{{\left( \frac{3}{2} \right)}^{12}}\] done
clear
D)
\[{{\left( \frac{3}{4} \right)}^{12}}\] done
clear
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question_answer8)
If \[{{a}^{x}}={{b}^{y}}={{c}^{z}}\] and \[{{b}^{2}}=ac\], then y equals
A)
\[\frac{2xz}{x+z}\] done
clear
B)
\[\frac{xz}{2(x-z)}\] done
clear
C)
\[\frac{xz}{2(z-x)}\] done
clear
D)
\[\frac{2xz}{(x-z)}\] done
clear
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question_answer9)
If \[\frac{10}{3}\times {{3}^{x}}-{{3}^{x-1}}=81\], then the value of x is____.
A)
2 done
clear
B)
1 done
clear
C)
3 done
clear
D)
0 done
clear
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question_answer10)
Which of the following values are equal? (P) \[{{1}^{4}}\] (Q) \[{{4}^{0}}\] (R) \[{{0}^{4}}\] (S) \[{{4}^{1}}\]
A)
P and Q done
clear
B)
Q and R done
clear
C)
P and R done
clear
D)
P and S done
clear
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question_answer11)
The value of \[{{({{7}^{-1}}-{{8}^{-1}})}^{-1}}-{{({{3}^{-1}}-{{4}^{-1}})}^{-1}}\] is
A)
56 done
clear
B)
12 done
clear
C)
68 done
clear
D)
44 done
clear
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question_answer12)
When \[5\times {{10}^{-3}}-2000\times {{10}^{-6}}\] is expressed in standard form, we will get
A)
\[3\times {{10}^{-2}}\] done
clear
B)
\[3\times {{10}^{-3}}\] done
clear
C)
\[3\times {{10}^{3}}\] done
clear
D)
\[3\times {{10}^{2}}\] done
clear
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question_answer13)
If \[{{3}^{(x-y)}}=27\] and \[{{3}^{(x+y)}}=243\], then x is equal to ____.
A)
0 done
clear
B)
2 done
clear
C)
4 done
clear
D)
6 done
clear
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question_answer14)
Number of prime factors in \[{{(216)}^{\frac{3}{5}}}\times {{(2500)}^{\frac{2}{5}}}\times {{(300)}^{\frac{1}{5}}}\] is _______.
A)
6 done
clear
B)
9 done
clear
C)
8 done
clear
D)
None of these done
clear
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question_answer15)
Find \[x\], if \[{{\left( \frac{5}{11} \right)}^{-3}}\times {{\left( \frac{5}{11} \right)}^{5}}={{\left( \frac{5}{11} \right)}^{x}}\]
A)
3 done
clear
B)
4 done
clear
C)
8 done
clear
D)
2 done
clear
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question_answer16)
The size of a red blood cell is 0.000007 m and the size of a plant cell is 0.00001275 m. Find the ratio of the size of red blood cell to that of plant cell.
A)
13 : 56 done
clear
B)
28:51 done
clear
C)
31 : 39 done
clear
D)
22 : 31 done
clear
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question_answer17)
Pluto is 5913000000 km away from the Sun. Express this distance in standard form.
A)
\[5.913\times {{10}^{-11}}\] done
clear
B)
\[5.913~\times {{10}^{-9}}\] done
clear
C)
\[\text{5}\text{.913}\times \text{1}{{\text{0}}^{\text{6}}}\] done
clear
D)
\[\text{5}\text{.913}\times \text{1}{{\text{0}}^{9}}\] done
clear
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question_answer18)
The cell of bacteria doubles itself after every 1 hour. How many cells will there be after 8 hours?
A)
200 times of the original done
clear
B)
\[{{\text{2}}^{\text{10}}}\] times of the original done
clear
C)
\[{{\text{2}}^{\text{8}}}\] times of the original done
clear
D)
\[{{\text{2}}^{\text{6}}}\] times of the original done
clear
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question_answer19)
At the end of the 20th century, the world's population was approximately\[6.125\times {{10}^{9}}\]. Express this population in usual form.
A)
\[6.125\times {{10}^{10}}\] done
clear
B)
6125000000 done
clear
C)
\[6125\times {{10}^{5}}\] done
clear
D)
612500000 done
clear
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question_answer20)
Weight of moon is \[(7.346\times {{10}^{22}})kg\] and weight of Earth is \[\text{5,9724}\times \text{1}{{\text{0}}^{\text{24}}}\text{ 7 kg}\]. What is the total weight of both in standard form?
A)
\[\text{6}\text{.04}\times \text{1}{{\text{0}}^{\text{24}}}\text{kg}\] done
clear
B)
\[\text{7}\text{.08}\times \text{1}{{\text{0}}^{\text{22}}}\text{kg}\] done
clear
C)
\[\text{5}\text{.98}\times \text{1}{{\text{0}}^{24}}\text{kg}\] done
clear
D)
\[\text{6}\text{.44}\times \text{1}{{\text{0}}^{\text{24}}}\text{ kg}\] done
clear
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question_answer21)
Simplify: \[\frac{{{\left[ \frac{2}{3} \right]}^{3}}\times {{\left[ \frac{2}{3} \right]}^{-2}}\times {{\left[ {{\left( \frac{1}{2} \right)}^{2}} \right]}^{-2}}\times \frac{1}{24}}{{{\left( \frac{2}{3} \right)}^{-5}}\times {{\left( \frac{3}{2} \right)}^{-12}}}\]
A)
\[{{\left( \frac{2}{3} \right)}^{-4}}\] done
clear
B)
\[\frac{32}{3}\] done
clear
C)
\[\frac{243}{16}\] done
clear
D)
\[\frac{243}{32}\] done
clear
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question_answer22)
Solve for y, if \[\frac{{{\left( \frac{1}{9} \right)}^{2y-1}}{{(.0081)}^{1/3}}}{\sqrt{243}}={{\left( \frac{1}{3} \right)}^{2y-5}}\sqrt[3]{\frac{{{27}^{y-1}}}{10000}}\]
A)
\[\frac{1}{2}\] done
clear
B)
\[-\frac{19}{18}\] done
clear
C)
\[\frac{3}{10}\] done
clear
D)
\[\frac{12}{17}\] done
clear
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question_answer23)
Fill in the blanks.
(i) If \[{{m}^{2}}={{27}^{2/3}}\times {{16}^{-3/2}}\]then m = P . |
(ii) If \[ab=1\]then \[\frac{1}{1+{{a}^{-1}}}+\frac{1}{1+{{b}^{-1}}}=\] Q . |
(iii) If x = \[({{8}^{2/3}}\cdot {{32}^{-2/5}})\]then \[{{x}^{-5}}=\] R |
A)
B)
C)
D)
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question_answer24)
Match the following.
Column - I | Column - II |
(P) \[{{\left( {{6}^{-1}}+{{\left( \frac{3}{2} \right)}^{-1}} \right)}^{-1}}\] | (i) \[-\frac{4}{13}\] |
(Q) \[{{\left\{ {{\left( \frac{4}{3} \right)}^{-1}}{{\left( \frac{1}{4} \right)}^{-1}} \right\}}^{-1}}\] | (ii) \[\frac{9}{32}\] |
(R) \[\left[ {{\left( \frac{1}{3} \right)}^{-3}}-{{\left( \frac{1}{2} \right)}^{-3}} \right]\div {{\left( \frac{1}{4} \right)}^{-3}}\] | (iii) \[\frac{6}{5}\] |
(S) \[({{3}^{-1}}\times {{4}^{-1}})\times {{\left( \frac{2}{3} \right)}^{-3}}\] | (iv) \[\frac{19}{64}\] |
A)
(P)\[\to \](iii); (Q)\[\to \](i); (R)\[\to \](iv); (S)\[\to \](ii) done
clear
B)
(P)\[\to \](iv): (Q)\[\to \](i); (R)\[\to \](ii); (S)\[\to \](iii) done
clear
C)
(P)\[\to \](ii); (Q)\[\to \](iii); (R)\[\to \](iv); (S)\[\to \](i) done
clear
D)
(P)\[\to \](iii); (Q)\[\to \](i); (R)\[\to \](ii); (S)\[\to \](iv) done
clear
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question_answer25)
If \[a=({{2}^{-2}}-{{2}^{-3}})\], \[b=({{2}^{-3}}-{{2}^{-4}})\] and\[c=({{2}^{-4}}-{{2}^{-2}})\] then find : (i) \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\] (ii) \[10\text{ abc}\]
A)
B)
C)
D)
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