In a committee, 50 people speak Hindi, 20 speak English and 10 speak both Hindi and English then how many speak at least one of these two language?
A)
40
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B)
50
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C)
60
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D)
80
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If A, B and C are non-empty subsets of a set, then \[\left( \mathbf{A}-\mathbf{B} \right)\cup \left( \mathbf{B}-\mathbf{A} \right)\] equal
A)
\[\left( A\cup B \right)-B\]
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B)
\[A-\left( A\cap B \right)\]
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C)
\[\left( A\cup B \right)-\left( A\cap B \right)\]
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D)
\[\left( A\cap B \right)\cup \left( A\cup B \right)\]
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\[\mathbf{P}\left( A \right)=\mathbf{0}.\mathbf{25}\]and \[\mathbf{P}\left( B \right)=\mathbf{0}.\mathbf{50}\]and \[\mathbf{P}\left( \mathbf{A}\cap \mathbf{B} \right)=\mathbf{0}.\mathbf{14}\]then \[\mathbf{P}\left( \mathbf{A}'\cap \mathbf{B}' \right)=?\]
A)
\[\frac{11}{100}\]
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B)
\[\frac{39}{100}\]
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C)
\[\frac{35}{100}\]
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D)
\[\frac{22}{100}\]
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The value of \[{{(e)}^{1/2}}\] will be
A)
1.444
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B)
1.546
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C)
1.349
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D)
1.648
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The coefficient of \[{{\mathbf{x}}^{\mathbf{3}}}\]in \[{{\left( \sqrt{{{\mathbf{x}}^{\mathbf{5}}}}+\frac{3}{\sqrt{{{x}^{3}}}} \right)}^{6}}\] is
A)
120
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B)
540
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C)
150
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D)
250
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The modulus of \[\frac{{{(3+2i)}^{2}}}{4-3i}\]is
A)
\[\frac{13}{5}\]
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B)
\[\frac{11}{5}\]
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C)
\[\frac{9}{5}\]
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D)
\[\frac{7}{5}\]
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The interior angles of a polygon are in arithmetic progression. The smallest angle is \[\mathbf{12}{{\mathbf{0}}^{{}^\circ }}\] and the common difference is\[{{\mathbf{5}}^{{}^\circ }}\]. What will be the number of sides of the polygon
A)
8
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B)
9
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C)
10
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D)
7
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\[\underset{x\to \infty }{\mathop{lim}}\,{{\left( cos\frac{x}{n} \right)}^{n}}\] is equal to
A)
e
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B)
\[\frac{1}{e}\]
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C)
0
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D)
1
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\[\frac{{{d}^{2}}x}{d{{y}^{2}}}\] equal to
A)
\[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{-1}}\]
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B)
\[-{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{-1}}.{{\left( \frac{dy}{d{{x}^{2}}} \right)}^{-3}}\]
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C)
\[\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)\times {{\left( \frac{dy}{dx} \right)}^{2}}\]
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D)
\[-\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right).{{\left( \frac{dy}{dx} \right)}^{-3}}\]
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If \[\mathbf{y=1}{{\mathbf{0}}^{\mathbf{x}}}\] is the reflection of \[\mathbf{y}=\mathbf{lo}{{\mathbf{g}}_{10}}\mathbf{x}\] in the line whose equations is:
A)
\[\mathbf{y}=-x\]
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B)
\[\mathbf{y}=x\]
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C)
\[x-2y=0\]
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D)
\[x+2y=0\]
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The length of major axis of ellipse is 26 and its foci is \[\left( \pm \text{ }\mathbf{5},\mathbf{0} \right)\] then equation of ellipse be
A)
\[\frac{{{x}^{2}}}{144}+\frac{{{y}^{2}}}{169}=1\]
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B)
\[\frac{{{x}^{2}}}{169}-\frac{{{y}^{2}}}{144}=-1\]
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C)
\[\frac{{{x}^{2}}}{169}+\frac{{{y}^{2}}}{144}=-1\]
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D)
\[-\frac{{{x}^{2}}}{169}-\frac{{{y}^{2}}}{144}=-1\]
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The equation of the common tangent to the curves \[{{y}^{2}}=8x\] and \[\mathbf{xy}\text{=}-\mathbf{1}\]is-
A)
\[2y=x+8\]
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B)
\[y=x+2\]
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C)
\[y=2x+1\]
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D)
\[3y=9x+2\]
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If the quadratic equations \[{{x}^{2}}+ax+b=0\]and \[{{\mathbf{x}}^{2}}+\mathbf{bx}+\mathbf{a}=\mathbf{0}\]have a common root then the numerical value of \[\left( \mathbf{a}+\mathbf{b} \right)\] is:
A)
1
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B)
\[-1\]
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C)
0
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D)
2
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The points \[\left( \mathbf{3},\mathbf{3} \right),\left( \mathbf{h},\mathbf{0} \right)\]and \[\left( \mathbf{0},\mathbf{k} \right)\]are collinear if
A)
\[\frac{1}{h}+\frac{1}{k}=\frac{1}{3}\]
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B)
\[\frac{1}{k}-\frac{1}{h}=\frac{1}{3}\]
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C)
\[h+k=3\]
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D)
\[\frac{1}{h}-\frac{1}{k}=\frac{1}{3}\]
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If \[y=si{{n}^{-1}}\left( \frac{5x+12\sqrt{1-{{x}^{2}}}}{13} \right)\] then \[\frac{dy}{dx}\]is equa.to
A)
\[\frac{1}{\sqrt{1-{{x}^{2}}}}\]
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B)
\[\frac{-1}{\sqrt{1-{{x}^{2}}}}\]
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C)
\[\frac{2}{\sqrt{1-{{x}^{2}}}}\]
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D)
\[\frac{-2}{\sqrt{1-{{x}^{2}}}}\]
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If \[\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\phi =\mathbf{2ta}{{\mathbf{n}}^{\mathbf{2}}}\phi +1\],then \[cos2\phi +si{{n}^{2}}\phi \]is equal to
A)
0
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B)
\[-1\]
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C)
1
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D)
2
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The most stable measure of the central tendency Is:
A)
the mode
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B)
the mean
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C)
the median
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D)
None of these
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A group of 10 items has A.M 6, if the arithmetic mean of 4 of these items Is 7.5 the of the remaining items is:
A)
5
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B)
3
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C)
3.5
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D)
4.5
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The value of k for which the circles \[{{x}^{2}}+{{y}^{2}}-~3x+ky-5=0\]and \[4{{x}^{2}}+4{{y}^{2}}-12x-y-9=0\]became concentric is
A)
\[-\frac{1}{6}\]
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B)
\[\frac{1}{6}\]
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C)
\[-\frac{1}{4}\]
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D)
\[\frac{1}{4}\]
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If \[\mathbf{f}\left( \mathbf{x} \right)=\frac{\mathbf{1}-\mathbf{cosx}}{\mathbf{1}-\mathbf{sinx}}\] then \[f'\left( \frac{\pi }{2} \right)\]is equal to
A)
1
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B)
0
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C)
\[\infty \]
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D)
does not exist
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