The principal value of the amplitude of \[\left( \mathbf{1}+\mathbf{i} \right)\]is:
A)
\[\frac{\pi }{4}\]
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B)
p
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C)
\[\frac{\pi }{2}\]
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D)
\[\frac{3\pi }{4}\]
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If A and B are two independent events such that \[\mathbf{P}\left( A \right)>\mathbf{0}\]and \[P(B)\ne 1\], then \[P\left( \frac{\overline{A}}{\overline{B}} \right)\]. is to:
A)
\[\frac{P(\overline{A})}{P(\overline{B})}\]
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B)
\[\frac{1-P(A\cup B)}{P(B)}\]
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C)
\[1-P\left( \frac{A}{B} \right)\]
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D)
\[1-P\left( \frac{A}{\overline{B}} \right)\]
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If \[\mathbf{lo}{{\mathbf{g}}_{2}},\mathbf{log}\left( {{\mathbf{2}}^{x}}-\mathbf{1} \right)\]and \[\mathbf{log}({{2}^{x}}+\mathbf{3})\]are in A.P. then x =....
A)
\[\frac{5}{2}\]
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B)
\[log_{3}^{2}\]
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C)
\[\frac{7}{2}\]
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D)
\[log_{2}^{5}\]
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The value of \[\mathbf{tan}{{\mathbf{1}}^{{}^\circ }},\mathbf{tan}{{\mathbf{2}}^{{}^\circ }},\mathbf{tan}{{\mathbf{3}}^{{}^\circ }}...\mathbf{tan}\text{ }\mathbf{8}{{\mathbf{9}}^{{}^\circ }}\]is equal to:
A)
0
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B)
\[-1\]
done
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C)
\[~-2\]
done
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D)
1
done
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\[\underset{x\to 0}{\mathop{lim}}\,{{\log }_{\tan x}}(sinx)\]equal to:
A)
0
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B)
\[-1\]
done
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C)
¥
done
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D)
1
done
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If \[\mathbf{y}=\frac{x}{1+\tan x}\]then \[\frac{dy}{dx}\] is equal to;
A)
\[\frac{1+\tan x-x.{{\sec }^{2}}x}{{{(1+\tan x)}^{2}}}\]
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B)
\[\frac{1+\tan x+x.{{\sec }^{2}}x}{{{(1+\tan x)}^{2}}}\]
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C)
\[\frac{1-\tan x-x.{{\sec }^{2}}x}{{{(1+\tan x)}^{2}}}\]
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D)
None of these
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In what ratio, the line joining \[\left( -\mathbf{1},\mathbf{1} \right)\] and \[\left( \mathbf{5},\mathbf{7} \right)\] is divided by the line \[\mathbf{x}+\mathbf{y}=\mathbf{4}?\]
A)
\[2:1\]
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B)
\[1:2\]
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C)
\[2:3\]
done
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D)
\[3:2\]
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If the roots of \[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{bx}+\mathbf{c}=\mathbf{0}\]are two consecutive integers, then \[{{b}^{2}}-4ac\]is
A)
1
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B)
2
done
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C)
0
done
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D)
3
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The number of ways in which 5 different beads can be string into a necklace is:
A)
12
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B)
14
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C)
60
done
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D)
24
done
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The series\[3\log 2+\frac{1}{4}-\frac{1}{2}{{\left( \frac{1}{4} \right)}^{2}}+\frac{1}{3}{{\left( \frac{1}{4} \right)}^{3}}+....\] is equal to:
A)
\[log5\]
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B)
\[log2\]
done
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C)
\[log6\]
done
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D)
\[\log 10\]
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Let \[\mathbf{A}=\left\{ \left( \mathbf{x},\mathbf{y} \right)/\mathbf{y}={{\mathbf{e}}^{x}},\mathbf{x}\in \mathbf{R} \right\}\] \[B=\left\{ \left( \mathbf{x},\mathbf{y} \right)/\mathbf{y}={{\mathbf{e}}^{-x}},\mathbf{x}\in \mathbf{R} \right\}\].then
A)
done
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B)
done
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C)
done
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D)
None of these
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Let \[\mathbf{F}:\mathbf{R}\to \mathbf{R}\] be defined by \[f(x)=3x-4\] \[{{f}^{-1}}(x)\]
A)
\[~\frac{x}{3}-4~\]
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B)
\[\frac{x+4}{3}\]
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C)
\[3x+4\]
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D)
None of these
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If \[\overline{\mathbf{x}}\] is the mean of\[{{x}_{1}},{{x}_{2}},{{x}_{3}},.....{{x}_{n}}\]. Then the algebraic sum of the deviation about X is:
A)
\[n\overline{x}\]
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B)
\[\frac{\overline{x}}{n}\]
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C)
0
done
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D)
1
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The eccentricity of the conjugate hyperbola of hyperbola \[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{3}{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{1}\]is
A)
1
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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 middle term in the expansion is \[{{\left( \frac{2{{x}^{2}}}{3}+\frac{3}{2{{x}^{2}}} \right)}^{10}}\]is:
A)
252
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B)
352
done
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C)
452
done
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D)
250
done
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A and B throw a dice The probability that A's throw is not greater than B's is:
A)
\[\frac{7}{12}\]
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B)
\[\frac{5}{12}\]
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C)
\[\frac{1}{6}\]
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D)
\[\frac{1}{5}\]
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\[{{\log }_{3}}^{2},{{\log }_{6}}^{2},{{\log }_{12}}^{2}\]are in:
A)
A.P.
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B)
H.P.
done
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C)
G.P.
done
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D)
None of these
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\[x=\sqrt{-1-\sqrt{-1\sqrt{-1......}}}to\,\infty =\]
A)
1
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B)
w
done
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C)
\[-1\]
done
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D)
0
done
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If \[x=\sqrt{7+4\sqrt{3}}\]then \[x+\frac{1}{x}\]is equal to
A)
2
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B)
3
done
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C)
4
done
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D)
6
done
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The sum of the series \[lo{{g}_{4}}^{2}-lo{{g}_{8}}^{2}+lo{{g}_{10}}^{2}.....\]up to \[\infty \]is:
A)
\[lo{{g}_{e}}2-1\]
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B)
\[1-lo{{g}_{e}}2\]
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C)
\[1+lo{{g}_{e}}2\]
done
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D)
e
done
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