question_answer 1)
\[{{\left( \frac{{{\mathbf{x}}^{\mathbf{-3}}}}{{{\mathbf{y}}^{\mathbf{3}}}} \right)}^{\mathbf{2/3}}}\mathbf{\times }{{\left( \frac{{{\mathbf{x}}^{\mathbf{3}}}}{{{\mathbf{y}}^{\mathbf{-3}}}} \right)}^{\mathbf{2/3}}}\]is equal to
A)
\[\frac{{{x}^{4}}}{{{y}^{-4}}}\] done
clear
B)
\[\frac{{{y}^{4}}}{{{x}^{-4}}}\] done
clear
C)
\[\frac{{{x}^{-}}^{4}}{{{y}^{4}}}\] done
clear
D)
\[\frac{1}{{{x}^{2}}{{y}^{2}}}\] done
clear
E)
None of these done
clear
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question_answer 2)
Which among the following is not equal to 1?
A)
\[\frac{{{2}^{8}}\times 32}{8\times 1024}\] done
clear
B)
\[[{{(-2)}^{6}}\times {{2}^{-4}}]\div \frac{{{(-2)}^{8}}}{64}\] done
clear
C)
\[\frac{{{3}^{-1/3}}}{81}\times \frac{{{3}^{-11/3}}}{{{3}^{-8}}}\] done
clear
D)
\[\frac{{{3}^{-5/4}}\times {{3}^{-15/4}}}{{{(2+7)}^{-2}}}\] done
clear
E)
None of these done
clear
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question_answer 3)
The standard form of the number 56789 is _________.
A)
5.6789 x 103 done
clear
B)
56.789 x 103 done
clear
C)
5.6789 x 104 done
clear
D)
5678.9 x 10 done
clear
E)
None of these done
clear
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question_answer 4)
Which one among the following is correct?
A)
\[{{\left( 5+5 \right)}^{5}}={{5}^{5}}+{{5}^{5}}\] done
clear
B)
\[{{3}^{5}}>{{5}^{3}}\] done
clear
C)
one billion \[=\text{ }{{10}^{9}}\] done
clear
D)
one hour = 3600 minutes done
clear
E)
None of these done
clear
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question_answer 5)
Which one among the following is wrong statement?
A)
\[{{a}^{m}}+{{a}^{m}}=\text{ }{{a}^{2}}^{m}\], where a is a non-zero rational number and m is a positive integer. done
clear
B)
\[{{a}^{p}}\text{ }\times \text{ }{{a}^{q}}=\text{ }{{a}^{pq}}\], where p, q are positive integer. done
clear
C)
\[{{4}^{6}}\] is greater than \[~{{8}^{5}}\] done
clear
D)
\[{{2}^{n}}>\text{ }{{n}^{2}}\], where n is a natural number greater than 2. done
clear
E)
None of these done
clear
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question_answer 6)
Which one among the following is the largest? \[{{\mathbf{3}}^{\mathbf{1/12}}}\mathbf{,}\,{{\mathbf{6}}^{\mathbf{1/6}}}\mathbf{,}\,{{\mathbf{9}}^{\mathbf{1/4}}}\mathbf{,}\,{{\mathbf{2}}^{\mathbf{1/16}}}\mathbf{,}\,{{\mathbf{5}}^{\mathbf{1/6}}}\]
A)
\[{{3}^{1/12}}\] done
clear
B)
\[{{6}^{1/6}}\] done
clear
C)
\[{{9}^{1/4}}\] done
clear
D)
\[{{2}^{1/16}}\] done
clear
E)
None of these done
clear
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question_answer 7)
The value of \[\frac{\mathbf{10}{{\mathbf{0}}^{\mathbf{98}}}\mathbf{+10}{{\mathbf{0}}^{\mathbf{100}}}}{\mathbf{10}{{\mathbf{0}}^{\mathbf{98}}}}\]+1 is equal to________.
A)
10001 done
clear
B)
10002 done
clear
C)
1001 done
clear
D)
1002 done
clear
E)
None of these done
clear
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question_answer 8)
Find the value of K, where K is an integer and \[{{\mathbf{2}}^{\mathbf{K+5}}}\mathbf{\times }{{\mathbf{6}}^{\mathbf{2K-3}}}\mathbf{=}\frac{{{\mathbf{3}}^{\mathbf{-8}}}}{\mathbf{1}{{\mathbf{2}}^{\mathbf{6}}}\mathbf{\times }{{\mathbf{2}}^{\mathbf{3}}}}\]
A)
-5 done
clear
B)
-6 done
clear
C)
5 done
clear
D)
-8 done
clear
E)
None of these done
clear
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question_answer 9)
If\[\mathbf{~}{{\mathbf{2}}^{\mathbf{2002}}}\mathbf{- }{{\mathbf{2}}^{\mathbf{1996}}}\mathbf{- }{{\mathbf{2}}^{\mathbf{1992}}}\mathbf{+ }{{\mathbf{2}}^{\mathbf{1991}}}\mathbf{= K}\mathbf{.}{{\mathbf{2}}^{\mathbf{1991}}}\], then the value of K is ________.
A)
2012 done
clear
B)
4024 done
clear
C)
2015 done
clear
D)
4012 done
clear
E)
None of these done
clear
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question_answer 10)
If \[{{\mathbf{a}}^{\mathbf{2}}}+\text{ }{{\mathbf{b}}^{\mathbf{2}}}+\text{ }{{\mathbf{c}}^{\mathbf{2}}}=\text{ }\mathbf{4abc}\], then find the value of \[{{\left[ {{\mathbf{4}}^{\frac{\mathbf{1}}{\mathbf{bc}}}} \right]}^{\mathbf{a}}}{{\left[ {{\mathbf{4}}^{\frac{\mathbf{1}}{\mathbf{ac}}}} \right]}^{\mathbf{b}}}{{\left[ {{\mathbf{4}}^{\frac{\mathbf{1}}{\mathbf{ab}}}} \right]}^{\mathbf{c}}}\] .
A)
5 abc done
clear
B)
4abc done
clear
C)
64 done
clear
D)
256 done
clear
E)
None of these done
clear
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question_answer 11)
The least value among \[{{8}^{28}},\text{ }{{512}^{9}},\] \[{{\mathbf{(}\sqrt{\mathbf{2}}\mathbf{)}}^{\mathbf{182}}}\] , \[{{4}^{42}},\text{ }{{32}^{16}}\text{ }\] is_________
A)
\[{{8}^{28~}}\] done
clear
B)
\[~{{512}^{9}}\] done
clear
C)
\[{{(\sqrt{2})}^{182}}\] done
clear
D)
\[~{{32}^{16}}\] done
clear
E)
None of these done
clear
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question_answer 12)
What should be multiplied to \[{{3}^{-9}}\] so that the product may be equal to 2187?
A)
\[{{3}^{15}}\] done
clear
B)
\[{{3}^{16}}\] done
clear
C)
\[{{3}^{14}}\] done
clear
D)
\[{{3}^{13}}\] done
clear
E)
None of these done
clear
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question_answer 13)
Which one among the following statements is true?
A)
\[{{6}^{5}}>{{5}^{6}}\] done
clear
B)
\[~{{2}^{12}}<{{12}^{3}}\] done
clear
C)
\[{{4}^{6}}>{{6}^{4}}~\] done
clear
D)
\[{{3}^{6}}<{{6}^{3~}}\] done
clear
E)
None of these done
clear
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question_answer 14)
If \[{{\mathbf{p}}^{\mathbf{q}}}=\text{ }{{\mathbf{q}}^{\mathbf{p}}}\] then find\[{{\mathbf{p}}^{\mathbf{3}}}+\text{ }{{\mathbf{q}}^{\mathbf{3}}}\], where p and q are distinct natural numbers.
A)
72 done
clear
B)
152 done
clear
C)
208 done
clear
D)
728 done
clear
E)
None of these done
clear
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question_answer 15)
If \[{{\left( \frac{\mathbf{m}}{\mathbf{n}} \right)}^{\mathbf{3/8}}}\mathbf{+}{{\left( \frac{\mathbf{n}}{\mathbf{m}} \right)}^{\mathbf{3/8}}}\mathbf{=9}\] then find the value of \[\,{{\left( \frac{\mathbf{m}}{\mathbf{n}} \right)}^{\mathbf{3/4}}}\mathbf{+}{{\left( \frac{\mathbf{n}}{\mathbf{m}} \right)}^{\mathbf{3/4}}}\].
A)
79 done
clear
B)
72 done
clear
C)
83 done
clear
D)
84 done
clear
E)
None of these done
clear
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question_answer 16)
If \[{{\mathbf{3}}^{\mathbf{X}}}\text{ }=\text{ }\mathbf{2700}\] then find the value of \[{{\mathbf{3}}^{\mathbf{x+2}}}\mathbf{+}{{\mathbf{3}}^{\mathbf{x-2}}}\]
A)
25600 done
clear
B)
24600 done
clear
C)
2200 done
clear
D)
2400 done
clear
E)
None of these done
clear
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question_answer 17)
If \[{{\mathbf{4}}^{\mathbf{x}}}\mathbf{ = }{{\mathbf{2}}^{\mathbf{y}}}\mathbf{ = 1}{{\mathbf{6}}^{\mathbf{z}}}\mathbf{= 256}\], then find the value of \[{{\mathbf{x}}^{\mathbf{2}}}+\text{ }{{\mathbf{y}}^{\mathbf{2}}}+\text{ }{{\mathbf{z}}^{\mathbf{2}}}+\text{ }\mathbf{2xy}\text{ }+\text{ }\mathbf{2yz}\text{ }+\text{ }\mathbf{2zx}.\]
A)
120 done
clear
B)
196 done
clear
C)
186 done
clear
D)
190 done
clear
E)
None of these done
clear
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question_answer 18)
A teacher distributes 2209 toffees equally among n number students. If each student gets n toffees, find n.
A)
37 done
clear
B)
27 done
clear
C)
47 done
clear
D)
57 done
clear
E)
None of these done
clear
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question_answer 19)
Which among the following is the ascending order of
\[{{2}^{1024}},\text{ }{{5}^{512}},\text{ }{{7}^{256}}\text{ }and\text{ }{{81}^{128}}.~~~\]
A)
\[{{5}^{512}}>\text{ }{{2}^{1024}}>\text{ }{{7}^{256}}>\text{ }{{81}^{128}}\] done
clear
B)
\[{{7}^{256}}<\text{ }{{81}^{128}}<\text{ }{{2}^{1024}}<\text{ }{{5}^{512}}\] done
clear
C)
\[{{7}^{256}}<\text{ }{{81}^{128}}<\text{ }{{5}^{512}}<\text{ }{{2}^{1024}}\] done
clear
D)
\[{{2}^{1024}}>\text{ }{{5}^{512}}>\text{ }{{81}^{128}}>\text{ }{{7}^{256}}\] done
clear
E)
None of these done
clear
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question_answer 20)
Evaluate: \[{{\left[ \mathbf{1}\text{ }+\text{ }\mathbf{8}\text{ }+\text{ }\mathbf{27}\text{ }+\text{ }\mathbf{64}\text{ }+\text{ }\mathbf{125}\text{ }+\text{ }\mathbf{216}\text{ }+\text{ }\mathbf{343} \right]}^{\mathbf{3/4}}}\]
A)
\[34\sqrt{3}\] done
clear
B)
\[56\sqrt{7}\] done
clear
C)
\[28\sqrt{7}\] done
clear
D)
\[34\sqrt{7}\] done
clear
E)
None of these done
clear
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question_answer 21)
Find the value of
A)
49 done
clear
B)
79 done
clear
C)
43 done
clear
D)
81 done
clear
E)
None of these done
clear
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question_answer 22)
If\[{{\mathbf{x}}^{{{\mathbf{(3+m)}}^{\mathbf{2}}}}}\mathbf{\times }\,\,{{\mathbf{x}}^{\mathbf{3-m}}}^{^{\mathbf{2}}}\mathbf{ }{{\mathbf{x}}^{\mathbf{24}}}\], then value of m is ___________.
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer 23)
Simplify: \[{{\left( \frac{\mathbf{512}}{\mathbf{125}} \right)}^{\mathbf{2/3}}}\mathbf{\div }{{\left( \frac{\mathbf{64}}{\mathbf{125}} \right)}^{\mathbf{1/3}}}\mathbf{\times }{{\left( \frac{\mathbf{125}}{\mathbf{8}} \right)}^{\mathbf{2/3}}}\]
A)
40 done
clear
B)
20 done
clear
C)
25 done
clear
D)
45 done
clear
E)
None of these done
clear
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question_answer 24)
If \[\mathbf{3600 = }{{\mathbf{2}}^{\mathbf{m}}}\,\mathbf{x }{{\mathbf{3}}^{\mathbf{n}}}\mathbf{ x}\,{{\mathbf{5}}^{\mathbf{p}}}\], then find the value of \[\frac{\mathbf{512}}{{{\mathbf{(16)}}^{\mathbf{(m+n)-p}}}}\]
A)
\[{{2}^{-7}}\] done
clear
B)
\[~{{2}^{7}}\] done
clear
C)
\[~{{2}^{8}}\] done
clear
D)
\[~{{2}^{-8}}\] done
clear
E)
None of these done
clear
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question_answer 25)
The least integer value of a which satisfies \[{{\mathbf{a}}^{\mathbf{4}}}>\text{ }\mathbf{2400}\] is _________.
A)
7 done
clear
B)
6 done
clear
C)
5 done
clear
D)
8 done
clear
E)
None of these done
clear
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question_answer 26)
Which one among the following is the greatest?
\[{{5}^{-4}},\text{ }{{2}^{-4}},\text{ }{{3}^{-4}},\text{ }{{4}^{-4}},\text{ }{{6}^{-4}}\]
A)
\[{{5}^{-4}}~\] done
clear
B)
\[{{6}^{-4}}\] done
clear
C)
\[~{{2}^{-4}}~\] done
clear
D)
\[~{{4}^{-\,4\text{ }~}}\] done
clear
E)
None of these done
clear
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question_answer 27)
\[{{\left( \mathbf{0}.\mathbf{0256} \right)}^{\mathbf{1/4}}}\] =__________.
A)
0.4 done
clear
B)
0.04 done
clear
C)
0.02 done
clear
D)
0.2 done
clear
E)
None of these done
clear
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question_answer 28)
If \[{{\mathbf{2}}^{\mathbf{m-7}}}=\text{ }\mathbf{32}\], then find the value of \[{{\mathbf{2}}^{\mathbf{m-3}}}\].
A)
256 done
clear
B)
512 done
clear
C)
1024 done
clear
D)
2048 done
clear
E)
None of these done
clear
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question_answer 29)
If \[{{\mathbf{p}}^{\mathbf{q}}}\mathbf{ x }{{\mathbf{q}}^{\mathbf{p}}}\mathbf{ = 30375}\], then find the value of \[\mathbf{3p}\text{ }+\text{ }\mathbf{2q}\] (where, p and q are natural numbers greater than 1).
A)
19 done
clear
B)
21 done
clear
C)
23 done
clear
D)
24 done
clear
E)
None of these done
clear
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question_answer 30)
If \[\mathbf{m = }{{\mathbf{7}}^{\mathbf{-}}}^{\mathbf{7}}\mathbf{- }{{\mathbf{7}}^{\mathbf{7}}}\mathbf{and n = }{{\mathbf{7}}^{\mathbf{7}}}\mathbf{- }{{\mathbf{7}}^{\mathbf{-}}}^{\mathbf{7}}\], then find the value of \[\frac{\mathbf{m}}{\mathbf{n}}\mathbf{-}\frac{\mathbf{n}}{\mathbf{m}}\].
A)
1 done
clear
B)
2 done
clear
C)
0 done
clear
D)
-1 done
clear
E)
None of these done
clear
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question_answer 31)
Solve: \[{{\mathbf{(}\sqrt{\mathbf{260}}\mathbf{-}\sqrt{\mathbf{64}}\mathbf{)}}^{\mathbf{3/2}}}\,{{\mathbf{(}\sqrt{\mathbf{260}}\mathbf{+}\sqrt{\mathbf{64}}\mathbf{)}}^{\mathbf{3/2}}}\]
A)
2343 done
clear
B)
2744 done
clear
C)
1834 done
clear
D)
2656 done
clear
E)
None of these done
clear
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question_answer 32)
If\[{{\mathbf{3}}^{\mathbf{8}}}{{^{\mathbf{x}}}^{\mathbf{-}}}^{\mathbf{32}}\mathbf{= }{{\mathbf{4}}^{\mathbf{28}}}^{\mathbf{-7x}}\], then find the value of x.
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
6 done
clear
E)
None of these done
clear
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question_answer 33)
Which one of the following statements is correct?
A)
\[{{a}^{x}}+{{a}^{x}}=\text{ }{{a}^{2x}}\], where a is non-zero rational number and x is a positive integer. done
clear
B)
\[{{b}^{x}}\times {{c}^{x}}=\left( b+c \right),~~\] where b and c are non-zero rational numbers and x is a positive integer. done
clear
C)
\[{{a}^{x}}\times {{a}^{y}}={{a}^{xy}},\] where a is a non-zero rational number and x, y are positive integer. done
clear
D)
\[{{p}^{mn}}\div {{q}^{mn}}={{\left( \frac{p}{q} \right)}^{mn}}\], where p and q are non-zero rational numbers and m and n are positive integer. done
clear
E)
None of these done
clear
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question_answer 34)
By what number should \[{{\left( -8 \right)}^{-9}}\text{ }\] be divided so that the quotient may be equal to\[{{\left( -\text{ }8 \right)}^{-6}}\]?
A)
\[{{8}^{3}}\] done
clear
B)
\[~{{\left( -8 \right)}^{-3}}\] done
clear
C)
\[~{{\left( -8 \right)}^{3}}\] done
clear
D)
\[~{{8}^{-3}}\] done
clear
E)
None of these done
clear
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question_answer 35)
Choose the correct descending order for the following:
\[{{4}^{5+6}},{{({{4}^{5}})}^{6}},{{4}^{8}}\times {{4}^{4}},\frac{{{4}^{6}}}{{{4}^{-7}}},{{4}^{10}}\times {{4}^{0}}\].
A)
\[{{\left( {{4}^{5}} \right)}^{6}}>\text{ }{{4}^{8}}\times {{4}^{4}}>\frac{{{4}^{6}}}{{{4}^{-7}}}>{{4}^{5+6}}>{{4}^{10}}\times {{4}^{0}}\] done
clear
B)
\[{{({{4}^{5}})}^{6}}>\frac{{{4}^{6}}}{{{4}^{-7}}}>{{4}^{8}}\times {{4}^{4}}>{{4}^{5+6}}>{{4}^{10}}\times {{4}^{0}}\] done
clear
C)
\[{{4}^{8}}\times \,{{4}^{4}}>{{({{4}^{5}})}^{6}}>\frac{{{4}^{6}}}{{{4}^{-7}}}>\text{ }{{4}^{10}}\times {{4}^{0}}>{{4}^{5+6}}\] done
clear
D)
\[{{4}^{8}}\times {{4}^{4}}<{{({{4}^{5}})}^{6}}<\frac{{{4}^{6}}}{{{4}^{-7}}}<{{4}^{10}}\times {{4}^{0}}<{{4}^{5+6}}\] done
clear
E)
None of these done
clear
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question_answer 36)
If \[{{\mathbf{a}}^{\mathbf{b}}}^{^{\mathbf{c}}}\mathbf{= 6561}\], where a, b and c are positive integers, then find the minimum possible value of \[\mathbf{a}\text{ }+\text{ }\mathbf{b}\text{ }+\text{ }\mathbf{c}\].
A)
6 done
clear
B)
11 done
clear
C)
8 done
clear
D)
9 done
clear
E)
None of these done
clear
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question_answer 37)
If \[{{\mathbf{4}}^{\mathbf{-2X}}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{4096}}\,\,\mathbf{and}\,\,\mathbf{1}{{\mathbf{1}}^{\mathbf{y}}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{1331}}\] then find the value of\[\mathbf{x}\text{ }-\text{ }\mathbf{y}\].
A)
0 done
clear
B)
1 done
clear
C)
3 done
clear
D)
6 done
clear
E)
None of these done
clear
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question_answer 38)
Solve for \[\mathbf{x},\text{ }{{\left( \mathbf{243} \right)}^{\mathbf{x+5}}}=\text{ }{{\left( \mathbf{2187} \right)}^{\mathbf{3x-1}}}\]
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer 39)
If \[\mathbf{5000 > }{{\mathbf{x}}^{\mathbf{4}}}\]then the greatest possible integer value of x is _________.
A)
5 done
clear
B)
6 done
clear
C)
7 done
clear
D)
8 done
clear
E)
None of these done
clear
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question_answer 40)
Simplify: \[\frac{\sqrt{\mathbf{216}}\mathbf{+}\sqrt{\mathbf{96}}}{\sqrt{\mathbf{5}{{\mathbf{0}}^{\mathbf{2}}}\mathbf{-1}{{\mathbf{0}}^{\mathbf{2}}}}}\]
A)
1 done
clear
B)
\[\frac{1}{4}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
2 done
clear
E)
None of these done
clear
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