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question_answer1)
\[{{2}^{3}}+{{2}^{3}}+{{2}^{3}}+{{2}^{3}}\]is equal to ____.
A)
\[{{2}^{5}}\] done
clear
B)
\[{{2}^{12}}\] done
clear
C)
281 done
clear
D)
216 done
clear
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question_answer2)
The value of \[\frac{{{\left( -\frac{1}{2} \right)}^{5}}}{{{\left( -\frac{1}{2} \right)}^{4}}}+\frac{\left( -\frac{1}{8} \right)}{\left( -\frac{1}{4} \right)}\] is ____.
A)
2 done
clear
B)
0 done
clear
C)
1 done
clear
D)
\[-1\] done
clear
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question_answer3)
\[\left\{ {{\left( \frac{1}{3} \right)}^{-3}}-{{\left( \frac{1}{2} \right)}^{-3}} \right\}\div {{\left( \frac{1}{4} \right)}^{-3}}=?\]
A)
\[\frac{19}{64}\] done
clear
B)
\[\frac{64}{19}\] done
clear
C)
\[\frac{27}{16}\] done
clear
D)
\[\frac{16}{27}\] done
clear
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question_answer4)
The value of \[(-8)\times (-8)\times (-8)\times (-8)+(-8)\]\[\times (-8)\times (-8)\times (-8)\] is ____.
A)
\[-2{{(8)}^{5}}\] done
clear
B)
\[-{{(2)}^{16}}\] done
clear
C)
\[-{{(4)}^{8}}\] done
clear
D)
All of these done
clear
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question_answer5)
If \[{{\left( \frac{5}{3} \right)}^{-5}}\times {{\left( \frac{5}{3} \right)}^{11}}={{\left( \frac{5}{3} \right)}^{8+x}},\] then x=?
A)
\[\frac{-1}{2}\] done
clear
B)
\[-2\] done
clear
C)
\[2\] done
clear
D)
\[\frac{1}{2}\] done
clear
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question_answer6)
The value of \[\left( \frac{{{a}^{-2}}\times {{b}^{-3}}}{{{a}^{-3}}\times {{b}^{-4}}} \right)\] is ________.
A)
\[{{a}^{-1}}\times b\] done
clear
B)
\[a\times {{b}^{-1}}\] done
clear
C)
\[{{(ab)}^{-1}}\] done
clear
D)
\[ab\] done
clear
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question_answer7)
\[{{\left\{ {{\left( \frac{3}{4} \right)}^{-1}}-{{\left( \frac{1}{4} \right)}^{-1}} \right\}}^{-1}}=?\]
A)
\[\frac{3}{8}\] done
clear
B)
\[\frac{-3}{8}\] done
clear
C)
\[\frac{8}{3}\] done
clear
D)
\[\frac{-8}{3}\] done
clear
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question_answer8)
Select the CORRECT match.
A)
B)
C)
D)
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question_answer9)
If \[{{\left( \frac{5}{9} \right)}^{4}}\times {{\left( \frac{5}{9} \right)}^{-10}}={{\left( \frac{5}{9} \right)}^{-4}}{{\left( \frac{5}{9} \right)}^{2a-1}},\]then the value of a is _____.
A)
1 done
clear
B)
\[\frac{-5}{2}\] done
clear
C)
\[\frac{-5}{4}\] done
clear
D)
\[\frac{-1}{2}\] done
clear
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question_answer10)
Which of the following is equivalent to \[7.7\times {{10}^{-6}}\]?
A)
\[0.00000077\] done
clear
B)
\[0.0000077\] done
clear
C)
\[0.000077\] done
clear
D)
\[0.00077\] done
clear
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question_answer11)
If \[{{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{3}{2} \right)}^{a+5}}={{\left( \frac{3}{2} \right)}^{8}},\]then a=____.
A)
\[-1\] done
clear
B)
0 done
clear
C)
1 done
clear
D)
2 done
clear
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question_answer12)
The number which is multiplied by \[{{(-8)}^{-1}}\]to obtain a product equal to \[{{10}^{-1}}\] is ____.
A)
\[-\frac{4}{5}\] done
clear
B)
\[-\frac{3}{5}\] done
clear
C)
\[-\frac{1}{5}\] done
clear
D)
\[-\frac{5}{4}\] done
clear
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question_answer13)
The value of \[\frac{{{6}^{12}}\times {{(35)}^{28}}\times {{(15)}^{16}}}{{{(14)}^{12}}\times {{(21)}^{11}}\times {{5}^{28}}}\] is??.
A)
\[{{2}^{6}}\times {{3}^{16}}\times {{5}^{12}}\] done
clear
B)
\[{{3}^{17}}\times {{5}^{16}}\times {{7}^{5}}\] done
clear
C)
\[{{2}^{6}}\times {{5}^{16}}\times {{7}^{12}}\] done
clear
D)
\[{{2}^{7}}\times {{3}^{17}}\times {{7}^{5}}\] done
clear
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question_answer14)
The value of \[{{a}^{b}}-{{b}^{a}},\]if \[a=3,\text{ }b=7\]is
A)
1825 done
clear
B)
1840 done
clear
C)
1844 done
clear
D)
1850 done
clear
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question_answer15)
The value of \[{{\left( \frac{23}{25} \right)}^{0}}\times {{\left( \frac{-1}{2} \right)}^{5}}\times {{2}^{3}}\times {{\left( \frac{3}{4} \right)}^{2}}\]is
A)
\[-\frac{9}{64}\] done
clear
B)
\[\frac{9}{64}\] done
clear
C)
\[\frac{64}{9}\] done
clear
D)
\[-\frac{64}{9}\] done
clear
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question_answer16)
A rectangular piece of land is to be sold off in smaller pieces. The total area of the land is 217 sq. miles. The pieces to the cut out are 162 sq. miles in size. How many smaller pieces of the land can be sold at the given size?
A)
215 done
clear
B)
164 done
clear
C)
29 done
clear
D)
None of these done
clear
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question_answer17)
Pooja spends about Rs.40000 each month on utensils hold. If she has about \[1\times {{10}^{8}}\] utensils, what is the total amount of money (in Rs.) spent on the households in one month?
A)
\[40\times {{10}^{8}}\] done
clear
B)
40000 done
clear
C)
\[4.0\times {{10}^{14}}\] done
clear
D)
\[4.0\times {{10}^{12}}\] done
clear
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question_answer18)
All the planets revolve around the Sun in elliptical orbits. Uranus's farthest distance from the Sun is approximately \[3.004\times {{10}^{9}}\text{ }km\]and its closest distance is approximately \[2.7499\times {{10}^{9}}km\]km. What is the average distance of Uranus from the Sun?
A)
\[(2.476\times {{10}^{9}})\,km\] done
clear
B)
\[(2.8765\times {{10}^{9}})\,km\] done
clear
C)
\[(2.876\times {{10}^{8}})\,km\] done
clear
D)
None of these done
clear
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question_answer19)
There are three places A, B, C in a straight line as shown below. If distance between place A and B is \[(2.4\times {{10}^{6}})m\] and distance between 8 and C is \[(5.2\times {{10}^{5}})m,\] then find the distance between place A and C in standard form.
A)
\[(292\times {{10}^{6}})km\] done
clear
B)
\[(2.92\times {{10}^{6}})km\] done
clear
C)
\[(292\times {{10}^{5}})km\] done
clear
D)
\[(2.92\times {{10}^{4}})\,m\] done
clear
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question_answer20)
Mr Gupta asked two of his students to solve the expression \[{{\left( \frac{9{{a}^{3}}{{b}^{-8}}}{81{{a}^{-5}}{{b}^{2}}} \right)}^{-\frac{1}{2}}}\]and write the answer on blackboard. Aryan wrote the answer as \[3{{a}^{-4}}{{b}^{5}}\] whereas Ayan wrote the answer as \[\frac{3{{b}^{5}}}{{{a}^{4}}}\]. Who wrote the correct answer?
A)
Aryan done
clear
B)
Ayan done
clear
C)
Both of them done
clear
D)
None of these done
clear
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question_answer21)
Match the following.
Column-l | Column-II |
(P) \[\left[ {{({{5}^{3}})}^{2}}\times {{5}^{5}} \right]\div {{5}^{9}}\] | (i) \[{{(-6)}^{3}}\] |
(Q) \[{{(-6)}^{5}}\div {{(6)}^{2}}\] | (ii) 2 |
(R) \[({{5}^{0}}+{{3}^{0}})\div ({{8}^{0}})\] | (iii) 1 |
(S) \[{{(7/19)}^{0}}\] | (iv) 25 |
A)
(P)\[\to \](i), (Q)\[\to \](ii), (R)\[\to \](iii), (S)\[\to \](iv) done
clear
B)
(P)\[\to \](ii), (Q)\[\to \](iii), (r)\[\to \](iv), (S)\[\to \](i) done
clear
C)
(P)\[\to \](iv), (Q)\[\to \](i). (R)\[\to \](ii), (S)\[\to \](iii) done
clear
D)
(P)\[\to \](iv), (Q)\[\to \](ii), (R)\[\to \](i), (S)\[\to \](iii) done
clear
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question_answer22)
Compare the following and put the correct sign.
I. \[{{({{3}^{2}})}^{3}}\] |
II. \[{{({{8}^{4}})}^{\frac{1}{2}}}\] |
III. \[{{({{3}^{1/3}})}^{9}}\] |
A)
B)
C)
D)
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question_answer23)
Which of the following statements is true?
Statement 1: \[x={{\left[ \frac{2}{3} \right]}^{4}}\div {{\left[ \frac{2}{3} \right]}^{2}},\] then value of \[{{x}^{2}}+2x+3\]is 0. |
Statement 2: If \[{{\left[ -\frac{1}{2} \right]}^{4}}\times {{(-2)}^{8}}={{(-2)}^{4x}}\] then\[x=1\]. |
A)
Only Statement-1 done
clear
B)
Only Statement-2 done
clear
C)
Both Statement-1 and Statement-2 done
clear
D)
Neither Statement-1 nor Statement-2 done
clear
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question_answer24)
State T for true and T' for false.
(P) If x and y are non-zero rational numbers and m is a positive integer, then \[{{x}^{m}}\times {{y}^{m}}={{(xy)}^{2m}}\] and \[{{x}^{m}}\div {{y}^{m}}={{\left( \frac{x}{y} \right)}^{1}}.\] |
(Q) Standard form of 38000000 is\[3.8\times {{10}^{7}}\]. |
(R) The base and power in \[{{(-16\times 2)}^{4}}\]is \[-32\] and 4 respectively. |
(S) \[{{6}^{2}}\] is greater than \[{{2}^{6}}\]. |
A)
B)
C)
D)
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question_answer25)
Fill in the blanks.
(i) A number is said to be in the ___ form. if it is expressed as the product of a number between 1 and 10 and the integral power of 10. |
(ii) \[{{2}^{0}}\times {{3}^{0}}+{{1}^{0}}\times 3=\_\_\_\] |
(iii) \[\left( {{\left( {{2}^{2}} \right)}^{2}}\times {{7}^{2}} \right)\div \left( {{8}^{3}}\times 7 \right)=\_\_\_\_\_\_\_\_\_.\] |
A)
B)
C)
D)
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