\[\tan ({{\cos }^{-1}}x)\]is equal to:
A)
\[\pm \sqrt{\frac{1+x}{{{x}^{2}}}},x\ne 0\]
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B)
\[\pm \sqrt{\frac{1+{{x}^{2}}}{{{x}^{2}}}},x\ne 0\]
done
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C)
\[\frac{-x}{\sqrt{1+{{x}^{2}}}}\]
done
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D)
\[\sqrt{\frac{1-{{x}^{2}}}{x}},x\ne 0\]
done
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The maximum value of \[{{x}^{1/x}},x>0\]is:
A)
\[{{\left( \frac{1}{e} \right)}^{e}}\]
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B)
\[{{e}^{\frac{1}{e}}}\]
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C)
1
done
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D)
0
done
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\[\int{\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}.}}dx\] is equal to:
A)
\[2\sqrt{1-x}+{{\cos }^{-1}}\sqrt{x}+\sqrt{x-{{x}^{2}}}+c\]
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B)
\[-2\sqrt{1-x}+{{\cos }^{-1}}\sqrt{x}+\sqrt{x-{{x}^{2}}}+c\]
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C)
\[2\sqrt{1-x}-{{\cos }^{-1}}\sqrt{x}-\sqrt{x-{{x}^{2}}}+c\]
done
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D)
None of these
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\[\int\limits_{0}^{3}{\left[ \sqrt{x} \right]}.dx\] is equal to:
A)
1
done
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B)
\[-1\]
done
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C)
2
done
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D)
\[-2\]
done
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Which of the following is correct?
A)
B'AB is symmetric if A is symmetric.
done
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B)
B'AB is skew symmetric if A is skew symmetric.
done
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C)
B'AB is symmetric, if A is skew symmetric.
done
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D)
Both and
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If \[l,m,n\] are the\[{{p}^{th}},{{q}^{th}}\]and \[{{r}^{th}}\]term of a G.P. If all terms are positive, then
is equal to
A)
0
done
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B)
1
done
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C)
2
done
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D)
3
done
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The area of the parallelogram whose diagonals are given by the vectors \[\mathbf{3\hat{i}}+\mathbf{\hat{J}}-\mathbf{2\hat{k}}\] and \[\mathbf{\hat{i}}-\mathbf{2}\hat{j}+\mathbf{4\hat{k}}\] is:
A)
4
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B)
8
done
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C)
\[5\sqrt{3}\]
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D)
\[10\sqrt{3}\]
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The ratio in which the line joining \[\left( \mathbf{1},\mathbf{2},\mathbf{3} \right)\] and \[\left( -\mathbf{3},\mathbf{4},-\mathbf{5} \right)\] is divided by \[\mathbf{xy}\]plane is:
A)
\[5:3\]
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B)
\[2:3\]
done
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C)
\[3:2\]
done
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D)
\[3:5\]
done
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If S is the sample space and \[\mathbf{P}\left( A \right)=\frac{1}{3}\mathbf{P}\left( B \right)\]and \[\mathbf{S}=\mathbf{A}\cup \mathbf{B}\], where A and B are two mutually exclusive events, then \[\mathbf{P}\left( A \right)=\]
A)
\[\frac{1}{3}\]
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B)
\[\frac{1}{4}\]
done
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C)
\[\frac{1}{2}\]
done
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D)
\[\frac{2}{3}\]
done
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\[\int{\left( \sqrt{\mathbf{tanx}}+\sqrt{\mathbf{cotx}} \right).\mathbf{dx}}\] is equal to:
A)
\[\sqrt{2}.{{\sin }^{-1}}(\operatorname{si}nx-cosx)+c\]
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B)
\[{{\sin }^{-1}}(\operatorname{si}nx-cosx)+c\]
done
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C)
\[\sqrt{2}.{{\cos }^{-1}}(\operatorname{si}nx-cosx)+c\]
done
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D)
\[2.{{\cos }^{-1}}(\operatorname{si}nx-cosx)+c\]
done
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\[A=\left[ \begin{align} & 2\,\,\,\,0\,\,\,\,7 \\ & 7\,\,\,\,0\,\,\,\,5 \\ & 0\,\,\,\,0\,\,\,\,3 \\ \end{align} \right]\], then \[{{\mathbf{A}}^{\mathbf{2}}}\]is equal to:
A)
A
done
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B)
2A
done
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C)
? 2A
done
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D)
\[-A\]
done
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The solution of the differential equation,\[{{\left( \mathbf{1}+\mathbf{x} \right)}^{\mathbf{2}}}\frac{dy}{dx}+{{\mathbf{y}}^{\mathbf{2}}}+\mathbf{1}=0\]is
A)
\[ta{{n}^{-1}}x+ta{{n}^{-1}}y=ta{{n}^{-1}}c\]
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B)
\[ta{{n}^{-1}}x-ta{{n}^{-1}}y=ta{{n}^{-1}}c\]
done
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C)
\[-ta{{n}^{-1}}x+ta{{n}^{-1}}y=ta{{n}^{-1}}c\]
done
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D)
None of these
done
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Interval where the function \[\mathbf{log}\left( 1+\mathbf{x} \right)\]is continuous, is
A)
\[\left( -\infty ,-1 \right)\]
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B)
\[\left( -1,\infty \right)\]
done
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C)
\[\left( 0,\infty \right)\]
done
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D)
\[\left( -\infty ,0 \right)\]
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\[\mathbf{si}{{\mathbf{n}}^{-1}}\frac{2a}{1+{{a}^{2}}}+\mathbf{si}{{\mathbf{n}}^{-1}}\frac{2b}{1+{{b}^{2}}}=\mathbf{2ta}{{\mathbf{n}}^{-1}}\mathbf{x}\]
A)
\[x=\frac{a-b}{1+ab}\]
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B)
\[x=\frac{a+b}{1-ab}\]
done
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C)
\[x=\frac{{{a}^{2}}-{{b}^{2}}}{1+ab}\]
done
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D)
None of these
done
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Two events A and B have probability 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is
A)
0.39
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B)
0.61
done
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C)
0.72
done
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D)
0.28
done
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Let R is a relation on N defined by \[\mathbf{x}+\mathbf{2y}=\mathbf{8}\]. Then, the domain of R is
A)
\[\left\{ 2,4,6,8 \right\}\]
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B)
\[\left\{ 2,4,6 \right\}\]
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C)
\[\left\{ 2,4,8 \right\}\]
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D)
\[\left\{ 1,2,3,4 \right\}\]
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A man alternately tosses a coin and throws a die beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 in the dice is
A)
\[\frac{3}{4}\]
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B)
\[\frac{1}{2}\]
done
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C)
\[\frac{1}{3}\]
done
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D)
None of these
done
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The area bounded by the parabola \[{{y}^{2}}=4ax\] and \[{{\mathbf{x}}^{\mathbf{2}}}=\mathbf{4ay}\] is
A)
\[\frac{8{{a}^{2}}}{3}\]
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B)
\[\frac{16{{a}^{2}}}{3}\]
done
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C)
\[8{{a}^{3}}\]
done
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D)
None of these
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If \[\mathbf{\vec{a}}\] and \[\mathbf{\vec{b}}\] are unit vectors inclined at an angle \[\theta \] ,then the value of
is:
A)
\[2sin\theta \]
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B)
\[2.sin\frac{\theta }{2}\]
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C)
\[cos\theta \]
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D)
\[\frac{1}{2}.cos\frac{\theta }{2}\]
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If OACB is a parallelogram with \[\overrightarrow{\mathbf{OC}}=\mathbf{\vec{a}}\] and \[\overrightarrow{\mathbf{AB}}=\mathbf{\vec{b}}\], then OA is equal to:
A)
\[\frac{1}{2}\left( \vec{a}+\vec{b} \right)\]
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B)
\[\frac{1}{2}\left( \vec{a}-\vec{b} \right)\]
done
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C)
\[\vec{a}-\vec{b}\]
done
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D)
None of these
done
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