If\[\sqrt{2+\sqrt{x}}=3\], then find the value of x.
A)
9
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B)
\[\sqrt{7}\]
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C)
49
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D)
5
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E)
None of these
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Evaluate:\[\sqrt{136+\sqrt{51+\sqrt{169}}}\]
A)
18
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B)
21
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C)
12
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D)
9
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E)
None of these
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Simplify: \[\frac{6{{a}^{2}}b{{c}^{-3}}}{4a{{b}^{-3}}{{c}^{2}}~~}\div \frac{5{{a}^{-3}}{{b}^{2}}{{c}^{-1}}}{3a{{b}^{-2}}{{c}^{3}}}\]
A)
\[\frac{9}{10}ac\]
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B)
\[\frac{9}{10}ac-1\]
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C)
\[\frac{9}{10}a{{c}^{2}}\]
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D)
\[\frac{9}{10}ac3\]
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E)
None of these
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If\[~\mathbf{x}+\mathbf{y}=\mathbf{10}\]and\[~{{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{58}\], then find the value of\[~{{\mathbf{x}}^{\mathbf{3}}}+{{\mathbf{y}}^{\mathbf{3}}}\].
A)
225
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B)
630
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C)
1000
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D)
370
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E)
None of these
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Find the value of\[\left( \mathbf{3}{}^\circ +{{\mathbf{4}}^{-\mathbf{1}}} \right)\times {{\mathbf{2}}^{\mathbf{2}}}\].
A)
3
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B)
5
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C)
7
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D)
1
done
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E)
None of these
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If \[\mathbf{P}:\mathbf{Q}:\mathbf{R}=\mathbf{2}:\mathbf{3}:\mathbf{4}\]and\[{{\mathbf{P}}^{\mathbf{2}}}+{{\mathbf{Q}}^{\mathbf{2}}}+{{\mathbf{R}}^{\mathbf{2}}}=\mathbf{11600}\], then find\[\mathbf{P}+\mathbf{Q}-\mathbf{R}\], where P, Q and R are whole numbers.
A)
16
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B)
20
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C)
22
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D)
11
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E)
None of these
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If \[{{3}^{3x+5}}\times {{2}^{3x+3}}=9\], then find the value of x.
A)
0
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B)
1
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C)
-1
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D)
2
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E)
None of these
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Simplify: \[{{\left( \frac{{{x}^{-3}}}{{{y}^{2}}} \right)}^{-3}}{{\left( \frac{{{x}^{-3}}}{{{y}^{5}}} \right)}^{2}}\]
A)
\[\frac{1}{{{y}^{4}}}\]
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B)
\[\frac{{{x}^{2}}}{{{y}^{3}}}\]
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C)
\[\frac{{{x}^{3}}}{{{y}^{4}}}\]
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D)
\[\frac{1}{{{y}^{2}}}\]
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E)
None of these
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If \[\frac{b-a}{a}=\frac{7}{8}\], then find the value of \[\frac{a}{b}\]
A)
\[\frac{7}{15}\]
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B)
\[\frac{8}{15}\]
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C)
\[\frac{-7}{15}\]
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D)
\[\frac{-8}{15}\]
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E)
None of these
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Find the altitude AD of an isosceles\[~\Delta \mathbf{ABC}\] with sides 2a, 2a and a, if AB = AC.
A)
\[a\sqrt{15}\]
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B)
\[\frac{a\sqrt{15}}{2}\]
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C)
\[\frac{a\sqrt{5}}{3}\]
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D)
\[\frac{a\sqrt{15}}{7}\]
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E)
None of these
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If \[\frac{11}{x}-\frac{7}{y}=1\]and\[\frac{9}{x}-\frac{4}{y}=6\]then find\[\mathbf{x}+\mathbf{y}\]
A)
\[\frac{3}{5}\]
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B)
\[\frac{5}{6}\]
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C)
\[\frac{1}{2}\]
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D)
\[\frac{3}{7}\]
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E)
None of these
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If \[{{\mathbf{a}}^{x}}=\mathbf{b},\text{ }{{\mathbf{b}}^{y}}=\mathbf{c}\]and\[~{{\mathbf{c}}^{\mathbf{7}}}=a\], then xyz is equal to:
A)
0
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B)
abc
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C)
1
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D)
\[\frac{1}{abc}\]
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E)
None of these
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A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. In how many days will they finish it together?
A)
10 days
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B)
15 days
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C)
12 days
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D)
13 days
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E)
None of these
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Compare\[~{{\mathbf{2}}^{\mathbf{21}}}\]and\[~{{\mathbf{3}}^{\mathbf{14}}}\]and identify the correct option.
A)
221>314
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B)
221<314
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C)
221=314
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D)
All of these
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E)
None of these
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Find the least 4-digit number which is a perfect square.
A)
1016
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B)
1036
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C)
1024
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D)
1044
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E)
None of these
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Find the value of\[~{{\left( \mathbf{x}+\mathbf{3} \right)}^{\mathbf{3}}}-{{\left( \mathbf{x}-\mathbf{3} \right)}^{\mathbf{3}}}\].
A)
\[1-{{x}^{3}}\]
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B)
0
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C)
\[18\times 2+54\]
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D)
\[18\times 2\]
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E)
None of these
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Insert the symbols '+' and '-' in the boxes such that
.
A)
\[\left( -,+,-,-,- \right)\]
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B)
\[\left( -,+,+,+,+ \right)\]
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C)
\[\left( +,+,-,-,+ \right)\]
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D)
Both B and C
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E)
None of these
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Find the possible values of x, when\[\sqrt{x}+~\frac{87}{\sqrt{x}}=\mathbf{32}\].
A)
6 and 58
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B)
9 and 841
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C)
3 and 29
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D)
18 and 1682
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E)
None of these
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One angle of a quadrilateral is\[~\mathbf{116}{}^\circ \]and the remaining three angles are in the ratio 1:2:1. Find the greatest angle of the quadrilateral.
A)
\[118{}^\circ \]
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B)
\[11{}^\circ \]
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C)
\[122{}^\circ \]
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D)
\[132{}^\circ \]
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E)
None of these
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The sum of three consecutive even numbers is 330, then find\[\frac{3}{4}\]th of the greatest number.
A)
112
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B)
72
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C)
140
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D)
84
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E)
None of these
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If \[\frac{x}{2y}=\frac{3}{4}\], then find the value of\[\frac{2x+y}{x-2y}\].
A)
\[\frac{1}{7}\]
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B)
7
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C)
7.2
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D)
3.2
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E)
None of these
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Rudra gets 98 marks in his exam, which is equal to 56% of the total marks. What is the maximum marks?
A)
175
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B)
180
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C)
150
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D)
160
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E)
None of these
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Evaluate: \[{{27}^{\frac{-4}{3}}}\times {{9}^{\frac{3}{2}}}\times {{81}^{\frac{1}{4}}}\]
A)
3
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B)
1
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C)
9
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D)
1
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E)
None of these
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