\[z=\left( \frac{-1}{2}+\frac{\sqrt{3}}{2}i \right)\] is equal to
A)
1
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B)
w
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C)
\[{{w}^{2}}\]
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D)
None of these
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Three identical dice are rolled. The probability that the same number will appear an each of them is:
A)
\[\frac{1}{6}\]
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B)
\[\frac{1}{36}\]
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C)
\[\frac{1}{18}\]
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D)
\[\frac{3}{28}\]
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In a A.P. of 81 terms, the 4th terms is 10. Then the sum of the series:
A)
\[10\times 41\]
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B)
\[\frac{10\times 41}{2}\]
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C)
\[10\times 81\]
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D)
\[41\times 81\]
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If \[\mathbf{cosec}\theta +\mathbf{cot}\theta =\frac{11}{2}\],then tan \[\theta \]is equal to:
A)
\[\frac{1}{6}\]
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B)
\[\frac{3}{28}\]
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C)
\[\frac{1}{18}\]
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D)
\[\frac{44}{117}\]
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The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\mathbf{x}}^{\mathbf{7}}}-\mathbf{2}{{\mathbf{x}}^{\mathbf{5}}}+\mathbf{1}}{{{x}^{3}}-3{{x}^{2}}+2}\]is equal to
A)
0
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B)
1
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C)
¥
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D)
\[-1\]
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What is the value of \[\frac{dy}{dx}\mathbf{at}\text{ }\mathbf{x}=-\mathbf{1}\]when \[\left( siny \right)sin\frac{\pi x}{2}+\frac{\sqrt{3}}{2}.{{\sec }^{-1}}\left( 2x \right)+{{2}^{x}}.tan\left( log\left( x+2 \right) \right)=0\]
A)
\[\frac{3}{\pi \sqrt{{{\pi }^{2}}-3}}\]
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B)
\[\frac{2}{\pi \sqrt{{{\pi }^{2}}-2}}\]
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C)
\[\frac{-3}{\pi \sqrt{{{\pi }^{2}}+3}}\]
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D)
None of these
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The three points \[\mathbf{A}\left( \mathbf{a},-\mathbf{1} \right),\mathbf{B}\left( \mathbf{2},\mathbf{1} \right)\]and \[\mathbf{C}\left( \mathbf{4},\mathbf{5} \right)\]are collinear points then value of a is:
A)
\[a=2\]
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B)
\[a=3\]
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C)
\[a=1\]
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D)
\[a=0\]
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If a, b are roots of the equations \[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{5x}+\mathbf{1}=\mathbf{0}\]then the value of \[{{\mathbf{a}}^{\mathbf{3}}}+{{\mathbf{b}}^{\mathbf{3}}}\]is
A)
115
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B)
110
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C)
120
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D)
125
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If there are 15 person in a party, and if each of them shake hands with each other. Then the number of handshakes happen in the party is:
A)
110
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B)
75
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C)
120
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D)
105
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\[\frac{1}{2}{{x}^{2}}+\frac{2}{3}{{x}^{3}}+\frac{3}{4}{{x}^{4}}+\frac{4}{5}{{x}^{5}}+.....\]is
A)
\[\frac{-x}{1+x}+log\left( 1+x \right)\]
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B)
\[\frac{x}{1+x}+log\left( 1+x \right)\]
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C)
\[\frac{x}{1-x}+log\left( 1+x \right)\]
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D)
\[\frac{1+x}{1-x}+log\left( 1+x \right)\]
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If A and B be two non-empty sets, then \[\mathbf{A}\cap \left( \mathbf{A}\cup \mathbf{B} \right)'\]equals
A)
A
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B)
\[\phi \]
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C)
B
done
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D)
None of these
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Let \[\mathbf{R}=\left\{ \left( \mathbf{a},\mathbf{a} \right),\left( b,b \right),\left( \mathbf{c},\mathbf{c} \right),\left( \mathbf{a},\mathbf{b} \right) \right\}\]be a relation on set\[\mathbf{A}=\left\{ \mathbf{A},b,\mathbf{c} \right\}\]. Then R is:
A)
symmetric relation
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B)
Identity relation
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C)
Reflexive relation
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D)
Antisymmetric relation
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The one which is the measure of the central is:
A)
Mean deviation
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B)
Coefficient of correlation
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C)
Standard deviation
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D)
Mode
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The normal to the parabola \[{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{4ax}\] from the points \[\left( \mathbf{5a},\mathbf{2a} \right)\] are
A)
\[2x+y=12a\]
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B)
\[2y+x=12a\]
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C)
\[2x-y=12a\]
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D)
\[2y-x=12a\]
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Constant term of the expansion of \[{{\left( \mathbf{x}-\frac{1}{x} \right)}^{10}}\]is
A)
152
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B)
\[-152\]
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C)
252
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D)
\[-252\]
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A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that they are of the same colour is:
A)
\[\frac{5}{18}\]
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B)
\[\frac{4}{9}\]
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C)
\[\frac{5}{9}\]
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D)
\[\frac{7}{9}\]
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If\[\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{a}+\frac{1}{c}\] then \[\mathbf{a},\mathbf{b},\mathbf{c}\]are in:
A)
A.P.
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B)
G.P.
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C)
H.P.
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D)
None of these
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The equation of the circle whose center is (1,2) and which passes through the point (4,6)
A)
\[{{x}^{2}}+{{y}^{2}}+2x-4y-20=0\]
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B)
\[{{x}^{2}}+{{y}^{2}}-2x-4y-20=0\]
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C)
\[{{x}^{2}}+{{y}^{2}}+2x+4y-20=0\]
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D)
\[{{x}^{2}}+{{y}^{2}}-2x-2y-20=0\]
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Domain of\[{{e}^{x}}=1+x+\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}+....\infty \]is
A)
\[\left( 1,\infty \right)\]
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B)
\[\left( 0,\infty \right)\]
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C)
\[\left( -\infty ,0 \right)\]
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D)
\[\left( -\infty ,-\infty \right)\]
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[A] \[\because \]\[\underset{x\to 2}{\mathop{\lim }}\,\frac{{{2}^{x}}-{{x}^{2}}}{{{x}^{x}}-{{2}^{2}}}\]is equal to:
A)
\[\frac{{{\log }_{2}}-1}{{{\log }_{2}}+1}\]
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B)
\[\pm 1\]
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C)
\[\frac{{{\log }_{2}}+1}{{{\log }_{2}}-1}\]
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D)
\[-1\]
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