\[sin\left[ ta{{n}^{-1}}\frac{1-{{x}^{2}}}{2x}+co{{s}^{-1}}\frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right]=\]
A)
1
done
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B)
\[-1\]
done
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C)
0
done
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D)
\[\infty \]
done
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The tangent to the curve \[\mathbf{5}{{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{1}\]at \[\left( \frac{1}{3}.\frac{-2}{3} \right)\]passes through the point
A)
\[\left( 0,0 \right)\]
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B)
\[\left( 1,1 \right)\]
done
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C)
\[\left( 1,-1 \right)\]
done
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D)
\[\left( -1,1 \right)\]
done
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\[\int{log(x+\sqrt{{{x}^{2}}+{{a}^{2}}}).dx}\].is equal to
A)
\[xlog(x+\sqrt{{{x}^{2}}+{{a}^{2}}})+\sqrt{{{x}^{2}}+{{a}^{2}}}+c\]
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B)
\[xlog(x+\sqrt{{{x}^{2}}+{{a}^{2}}})-\sqrt{{{x}^{2}}+{{a}^{2}}}+c\]
done
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C)
\[x.log(x+\sqrt{{{x}^{2}}+{{a}^{2}}})-\sqrt{{{x}^{2}}+{{a}^{2}}}+c\]
done
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D)
None of these
done
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\[\int\limits_{-20\pi }^{20\pi }{\left| \mathbf{cosx} \right|.\mathbf{dx}}\] is equal to:
A)
20
done
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B)
40
done
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C)
60
done
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D)
80
done
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If A is symmetric as well as skew symmetric matrix, then A is:
A)
null
done
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B)
diagonal
done
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C)
triangular
done
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D)
None of these
done
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If
and \[\mathbf{a},\mathbf{b},c\]care distinct, then the product\[\mathbf{abc}\]is equal to
A)
0
done
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B)
1
done
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C)
\[-1\]
done
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D)
2
done
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If \[\vec{a}\] and \[\vec{b}\]be two perpendicular vectors, then
A)
\[(\vec{a}+\vec{b})={{a}^{-2}}+{{b}^{-2}}\]
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B)
\[(\vec{a}-\vec{b})={{a}^{-2}}+{{b}^{-2}}\]
done
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C)
\[{{(\vec{a}-\vec{b})}^{2}}={{\left( \vec{a}+\vec{b} \right)}^{2}}\]
done
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D)
All of these
done
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Perpendicular distance of the point \[\left( \mathbf{3},\mathbf{4},\mathbf{5} \right)\] from y-axis, is:
A)
4
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B)
5
done
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C)
\[\sqrt{26}\]
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D)
\[\sqrt{34}\]
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The probability that a leap year will have 53 Saturdays or 53 Sundays is
A)
\[\frac{3}{7}\]
done
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B)
\[\frac{2}{7}\]
done
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C)
\[\frac{1}{7}\]
done
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D)
None of these
done
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The value of integral\[\int\limits_{-1}^{1}{{{\sin }^{15}}x.dx}\]is:
A)
1
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B)
0
done
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C)
\[\frac{14}{15}\times \frac{12}{13}\times \frac{10}{11}\times \frac{8}{9}\times \frac{6}{7}\times \frac{4}{5}\times \frac{2}{3}\]
done
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D)
None of these
done
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If A is the square matrix such that \[{{A}^{2}}=I\] (where I =identity matrix), then \[{{\mathbf{A}}^{-\mathbf{1}}}=\]
A)
A
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B)
2A
done
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C)
\[A+1\]
done
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D)
None of these
done
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If \[\mathbf{n}=\mathbf{10},\overline{\mathbf{x}}=\mathbf{12},\sum {{\mathbf{x}}^{\mathbf{2}}}=\mathbf{1530}\], then the coefficient of variance is:
A)
\[20%\]
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B)
\[25%\]
done
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C)
\[30%\]
done
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D)
\[35%\]
done
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The degree and order of the differential equation of the family of all parabolas whose axis is x- axis, are respectively
A)
\[2,1\]
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B)
\[1,2\]
done
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C)
\[2,3\]
done
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D)
\[3,2\]
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If \[\mathbf{f}\left( \mathbf{x} \right)\]is a continuous function and \[g\left( \mathbf{x} \right)\]be discontinuous, then
A)
\[f\left( x \right)+g\left( x \right)\]be discontinuous
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B)
\[f\left( x \right)-g\left( x \right)\]be continuous
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C)
\[f\left( x \right)=g\left( x \right)\forall x\]
done
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D)
None of these
done
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\[\int\limits_{0}^{2\pi }{\sqrt{1+sin\frac{x}{2}}.dx=}\]
A)
2
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B)
4
done
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C)
6
done
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D)
8
done
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The probability that at least one of the events \[\mathbf{A}\And \mathbf{B}\] occurred is 0.7 and they occurs simultaneously with probability 0.2. Then \[\mathbf{p}(A)+\mathbf{P}\left( B \right)=\]
A)
1.2
done
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B)
1.1
done
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C)
0.1
done
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D)
1.5
done
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The solution of the differential equation, \[(1+{{y}^{2}})-\left( x+{{e}^{{{\tan }^{-1}}y}} \right)\frac{dy}{dx}=0\].is
A)
\[(x-2)=k{{e}^{{{\tan }^{-1}}y}}\]
done
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B)
\[2x{{e}^{{{\tan }^{-1}}y}}={{e}^{2{{\tan }^{-1}}y}}+k\]
done
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C)
\[x.{{e}^{-{{\tan }^{-1}}y}}=ta{{n}^{-1y}}+k\]
done
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D)
\[x.{{e}^{2{{\tan }^{-1}}y}}=ta{{n}^{-1y}}+k\]
done
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If \[A=\left[ \begin{align} & 2\,\,\,\,\,0\,\,\,\,\,0 \\ & 0\,\,\,\,\,2\,\,\,\,\,0 \\ & 0\,\,\,\,\,0\,\,\,\,\,2 \\ \end{align} \right]\],then \[{{\mathbf{A}}^{\mathbf{5}}}\]is equal to:
A)
\[16A\]
done
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B)
15A
done
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C)
32A
done
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D)
8A
done
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Area bounded by parabola \[{{y}^{2}}=4ax\] and the line \[x=2y\] is
A)
\[\frac{4}{3}\]
done
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B)
\[\frac{3}{4}\]
done
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C)
\[\frac{2}{3}\]
done
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D)
\[\frac{1}{2}\]
done
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\[\int\limits_{0}^{\pi }{x.si{{n}^{6}}x.co{{s}^{4}}xdx}\]
A)
\[\frac{{{\pi }^{2}}}{512}\]
done
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B)
\[\frac{3{{\pi }^{2}}}{512}\]
done
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C)
\[\frac{5{{\pi }^{2}}}{512}\]
done
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D)
\[\frac{7{{\pi }^{2}}}{512}\]
done
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