Domain of the function \[f(x)=lo{{g}_{2}}\left( -{{\log }_{1/2}}\left( 1+\frac{1}{4\sqrt{x}} \right)-1 \right)\]is
A)
\[\left( 0,1 \right)\]
done
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B)
\[(0,1]\]
done
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C)
\[\left[ 1,\infty \right)\]
done
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D)
\[(1,\infty )\]
done
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The greatest value of the function \[f(x)=ta{{n}^{-1}}x-\frac{1}{2}logx\,in\left[ \frac{1}{\sqrt{3}},\sqrt{3} \right]\]is:
A)
\[\frac{\pi }{6}-\frac{1}{4}log3\]
done
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B)
\[\frac{\pi }{3}+\frac{1}{4}.log3\]
done
clear
C)
\[\frac{\pi }{3}+\frac{1}{4}log3\]
done
clear
D)
\[\frac{\pi }{3}-\frac{1}{4}log3\]
done
clear
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\[\int {{e}^{3\log x{{({{x}^{4}}+1)}^{-1}}dx}}\]is equal to:
A)
\[\frac{1}{4}log\left( {{x}^{4}}+1 \right)+c\]
done
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B)
\[log\left( 1+{{x}^{4}} \right)+c\]
done
clear
C)
\[-log\left( {{x}^{4}}+1 \right)+c\]
done
clear
D)
\[-\frac{1}{4}log\left( 1+{{x}^{4}} \right)+c\]
done
clear
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\[\int\limits_{0}^{\frac{\pi }{2}}{\mathbf{co}{{\mathbf{s}}^{\mathbf{5}}}\left( \frac{x}{2} \right).\mathbf{sinx}.\mathbf{dx}}\] is equal to:
A)
\[\frac{2}{7}.\left( 1-\frac{1}{8\sqrt{2}} \right)\]
done
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B)
\[\frac{-4}{7}.\left( 1-\frac{1}{8\sqrt{2}} \right)\]
done
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C)
\[\frac{4}{7}.\left( 1+\frac{1}{8\sqrt{2}} \right)\]
done
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D)
\[\frac{4}{7}.\left( 1-\frac{1}{8\sqrt{2}} \right)\]
done
clear
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The solution of \[\frac{dy}{dx}+\sqrt{\frac{1-{{y}^{2}}}{1+{{x}^{2}}}}=0\] is
A)
\[si{{n}^{-1}}x.si{{n}^{-1}}y=c\]
done
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B)
\[si{{n}^{-1}}x-si{{n}^{-1}}y=c\]
done
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C)
\[si{{n}^{-1}}x+si{{n}^{-1}}y=c\]
done
clear
D)
\[si{{n}^{-1}}x=c.si{{n}^{-1}}y\]
done
clear
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Lf \[\Delta \]=
, then A is equal to
A)
0
done
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B)
1
done
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C)
2
done
clear
D)
4
done
clear
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If \[\left| \overrightarrow{a} \right|=3,\left| \overrightarrow{b} \right|=1,\left| \overrightarrow{c} \right|=4\] and\[\overrightarrow{\mathbf{a}}+\mathbf{\vec{b}}+\mathbf{\vec{c}}=\mathbf{0}\],then \[\mathbf{\vec{a}}.\mathbf{\vec{b}}+\mathbf{\vec{b}}.\mathbf{\vec{c}}+\mathbf{\vec{c}}.\mathbf{\vec{a}}\] =?
A)
10
done
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B)
\[-10\]
done
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C)
13
done
clear
D)
\[-13\]
done
clear
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The equation of a plane that passes through \[\left( \mathbf{2},-\mathbf{3},\mathbf{1} \right)\]and is perpendicular to the line joining the points \[\left( \mathbf{3},\mathbf{4},-\mathbf{1} \right)\] and \[\left( \mathbf{2},-\mathbf{1},\mathbf{5} \right)\] is:
A)
\[x+5y-6z+19=0\]
done
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B)
\[x+5y-6z-19=0\]
done
clear
C)
\[x-5y-6z+19=0\]
done
clear
D)
\[x+5y+6z+19=0\]
done
clear
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If A and B be two events such that \[\mathbf{P}\left( \mathbf{A}\cap \mathbf{B} \right)=\mathbf{0}.\mathbf{32},\text{ }\mathbf{P}\left( B \right)=\mathbf{0}.\mathbf{5}\], then \[\mathbf{P}\left( \frac{A}{B} \right)\]is equal to:
A)
0.64
done
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B)
0.65
done
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C)
0.61
done
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D)
0.63
done
clear
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\[\mathbf{co}{{\mathbf{s}}^{-1}}\left( \frac{1}{2} \right)+2si{{n}^{-1}}\left( \frac{1}{2} \right)\]- is equal to:
A)
\[\frac{\pi }{6}\]
done
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B)
\[\frac{\pi }{4}\]
done
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C)
\[\frac{\pi }{3}\]
done
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D)
\[\frac{2\pi }{3}\]
done
clear
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If \[\mathbf{A}=\left[ \begin{align} & a\,\,\,\,b \\ & b\,\,\,\,b \\ \end{align} \right]\] and \[{{\mathbf{A}}^{2}}=\left[ \begin{align} & \alpha \,\,\,\,\beta \\ & \beta \,\,\,\,\alpha \\ \end{align} \right]\]4, then
A)
\[\alpha ={{a}^{2}}+{{b}^{2}},\beta =ab\]
done
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B)
\[\alpha ={{a}^{2}}+{{b}^{2}},\beta ={{a}^{2}}-{{b}^{2}}\]
done
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C)
\[\alpha ={{a}^{2}}+{{b}^{2}},\beta =2ab\]
done
clear
D)
\[\alpha ={{a}^{2}}-{{b}^{2}},\beta ={{a}^{2}}+{{b}^{2}}\]
done
clear
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The projection of the line segment joining the points \[\left( -\mathbf{1},\mathbf{0},\mathbf{3} \right)\] and \[\left( \mathbf{2},\mathbf{5},\mathbf{1} \right)\] on the line whose direction ratio are \[\mathbf{6},\mathbf{2},\mathbf{3}\] is:
A)
\[\frac{11}{7}\]
done
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B)
\[\frac{21}{7}\]
done
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C)
\[\frac{22}{7}\]
done
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D)
\[\frac{17}{7}\]
done
clear
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The degree of the differential equation of all tangent lines to the parabola \[{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{4ax}\] is:
A)
1
done
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B)
2
done
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C)
3
done
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D)
4
done
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The set of points of discontinuity of the function \[\mathbf{f}\left( \mathbf{x} \right)=\mathbf{log}\left( \mathbf{x} \right)\]is
A)
\[\left\{ 0 \right\}\]
done
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B)
\[\left\{ 1,-1 \right\}\]
done
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C)
\[\left\{ -\infty ,\infty \right\}\]
done
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D)
None of these
done
clear
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If f(x) be a periodic function of period a, then \[\int\limits_{0}^{na}{\mathbf{f}\left( \mathbf{x} \right)}\]is equal to:
A)
\[n.\int\limits_{0}^{n}{\mathbf{f}\left( \mathbf{x} \right)}.dx\]
done
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B)
\[\int\limits_{0}^{a}{\mathbf{f}\left( \mathbf{x} \right)}.dx\]
done
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C)
\[(n+1)\int\limits_{0}^{a}{\mathbf{f}\left( \mathbf{x} \right)}.dx\]
done
clear
D)
\[(n-1).\int\limits_{0}^{a}{\mathbf{f}\left( \mathbf{x} \right)}.dx\]
done
clear
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A bag contains 6 red and 3 white balls. Four balls are drawn one by one and not replaced. The probability that they are alternatively of different colour is:
A)
\[\frac{1}{42}\]
done
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B)
\[\frac{5}{42}\]
done
clear
C)
\[\frac{1}{6}\]
done
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D)
\[\frac{2}{21}\]
done
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If the chance that a ship will arrive safely at a port, is \[\frac{9}{10}\], the chance that out of 5 ships expected to arrive at the port, at least 4 will arrive safely, is
A)
\[\frac{91854}{100000}\]
done
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B)
\[\frac{91827}{100000}\]
done
clear
C)
\[\frac{91881}{100000}\]
done
clear
D)
None of these
done
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If
, then x
A)
\[\frac{-9\pm \sqrt{53}}{2}\]
done
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B)
\[\frac{-7\pm \sqrt{53}}{2}\]
done
clear
C)
\[\frac{-5\pm \sqrt{53}}{2}\]
done
clear
D)
None of these
done
clear
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The function \[\mathbf{f}\left( \mathbf{x} \right)={{\mathbf{x}}^{\mathbf{9}}}+\mathbf{3}{{\mathbf{x}}^{\mathbf{7}}}+\mathbf{64}\]is increasing on:
A)
\[\left( 0,\infty \right)\]
done
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B)
\[\left( -\infty ,0 \right)\]
done
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C)
\[\left( -\infty ,\infty \right)\]
done
clear
D)
None of these
done
clear
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\[\int {{e}^{x}}\left( tanx+se{{c}^{2}} \right)dx\] is equal to
A)
\[{{e}^{x}}.secx+c\]
done
clear
B)
\[{{e}^{x}}.tanx+c\]
done
clear
C)
\[{{e}^{x}}.se{{c}^{2}}x+c\]
done
clear
D)
\[{{e}^{x}}+tanx+c\]
done
clear
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