\[\sqrt{i}-\sqrt{-i}\] is equal to
A)
(a) \[i\sqrt{2}\]
done
clear
B)
(b) \[\frac{i}{i\sqrt{2}}\]
done
clear
C)
(c) 0
done
clear
D)
(d) \[-i\sqrt{2}\]
done
clear
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Two events A and B have probability 0.25 and 0.50 respectively. Probability that both A and E occur simultaneously is 0.14. Then the probability that neither A nor B occurs is:
A)
(a) 0.11
done
clear
B)
(b) 0.25
done
clear
C)
(c) 0.39
done
clear
D)
(d) 0.45
done
clear
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The middle term in the following arithmetic progression \[20,16,12........\text{ }176\] is:
A)
(a) \[-46\]
done
clear
B)
(b)\[-76\]
done
clear
C)
(c) \[-80\]
done
clear
D)
(d) \[-70\]
done
clear
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If \[\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\theta =\mathbf{1}-{{\mathbf{e}}^{\mathbf{2}}}\], then sec \[\theta +\mathbf{ta}{{\mathbf{n}}^{\mathbf{3}}}\theta \] cosec \[\theta \]is equal to:
A)
(a) \[{{\left( 1-{{e}^{2}} \right)}^{\frac{3}{2}}}\]
done
clear
B)
(b) \[{{\left( 2-{{e}^{2}} \right)}^{\frac{1}{2}}}\]
done
clear
C)
(c) \[{{\left( 2-{{e}^{2}} \right)}^{\frac{3}{2}}}\]
done
clear
D)
(d) None of these
done
clear
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\[\underset{x\to 0}{\mathop{\lim }}\,\frac{ex+{{e}^{-x}}2.cosx-4}{{{x}^{4}}}\]is equal to:
A)
(a) 0
done
clear
B)
(b) 1
done
clear
C)
(c) \[\frac{1}{6}\]
done
clear
D)
(d) \[\frac{-1}{6}\]
done
clear
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The derivative of \[\mathbf{se}{{\mathbf{c}}^{-\mathbf{1}}}\left( \frac{-1}{2{{x}^{2}}+1} \right)\]with respect to \[\sqrt{1-{{\mathbf{x}}^{\mathbf{2}}}}\]at \[\mathbf{x}=\frac{1}{2}\]is equal to:
A)
(a) 4
done
clear
B)
(b) \[-4\]
done
clear
C)
(c) 2
done
clear
D)
(d) \[-2\]
done
clear
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If \[\mathbf{A}\left( \mathbf{l},\mathbf{2} \right),\mathbf{B}\left( \mathbf{4},\mathbf{6} \right),\mathbf{C}\left( \mathbf{5},\mathbf{7} \right)\]and \[\mathbf{D}\left( \mathbf{a},\mathbf{b} \right)\]are the vertices of parallelogram ABCD then
A)
(a) \[a=2,b=3\]
done
clear
B)
(b) \[a=2,b=4\]
done
clear
C)
(c) \[a=3,b=4\]
done
clear
D)
(d) \[a=3,b=5\]
done
clear
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If x is real, then the maximum value of \[\mathbf{5}+\mathbf{4x}-{{\mathbf{x}}^{\mathbf{2}}}\]is
A)
(a) 7
done
clear
B)
(b) 8
done
clear
C)
(c) 9
done
clear
D)
(d) 10
done
clear
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If 7 points out of 12 are in the same straight line, then the number of triangles formed is
A)
(a) 180
done
clear
B)
(b) 185
done
clear
C)
(c) 181
done
clear
D)
(d) 190
done
clear
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The value of \[1-log2+\frac{{{(log2)}^{2}}}{2}-\frac{{{\left( log2 \right)}^{3}}}{3}+.....\]is
A)
(a) 2
done
clear
B)
(b) \[\frac{1}{2}\]
done
clear
C)
(c) \[log3\]
done
clear
D)
(d) 1
done
clear
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If A and B are two sets, then \[\mathbf{A}\cap \left( \mathbf{A}\cup \mathbf{B} \right)\]equals
A)
(a) A
done
clear
B)
(b) B
done
clear
C)
(c) f
done
clear
D)
(d) None of these
done
clear
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If \[f(x)=\frac{x-1}{x+1}\]then f(2x) is equal to:
A)
(a) \[\frac{f\left( x \right)+1}{f\left( x \right)+3}\]
done
clear
B)
(b) \[\frac{3f\left( x \right)+1}{f\left( x \right)+3}\]
done
clear
C)
(c) \[\frac{f\left( x \right)+3}{f\left( x \right)+1}\]
done
clear
D)
(d) \[\frac{f\left( x \right)+3}{3f\left( x \right)+1}\]
done
clear
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The mean deviation from the mean of A.P. \[\mathbf{a},\mathbf{a}+\mathbf{d},\mathbf{a}+\mathbf{2d}....\mathbf{a}+\mathbf{2}\]and is:
A)
(a) \[\frac{n(n+1).d}{2n+1}\]
done
clear
B)
(b) \[n(n+1).d\]
done
clear
C)
(c) \[\frac{n(n-1).d}{2n+1}\]
done
clear
D)
(d) \[\frac{n(n+1).d}{2n}\]
done
clear
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In an ellipse the distance between its foci is 6 and length of its minor axis is 8. Then Its eccentricity is:
A)
(a) \[\frac{5}{3}\]
done
clear
B)
(b) \[\frac{1}{2}\]
done
clear
C)
(c) \[\frac{3}{5}\]
done
clear
D)
(d) \[\frac{3}{4}\]
done
clear
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In the expansion of \[\left( 3x-\frac{1}{{{x}^{2}}} \right)\],the 5th term from the end is:
A)
(a) \[\frac{16486}{{{x}^{8}}}\]
done
clear
B)
(b) \[\frac{13486}{{{x}^{8}}}\]
done
clear
C)
(c) \[\frac{17010}{{{x}^{8}}}\]
done
clear
D)
(d) \[\frac{16010}{{{x}^{8}}}\]
done
clear
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An integer is chosen at random from the first two hundred digits. The probability that the integer chosen is divisible by 6 or 8 is:
A)
(a) \[\frac{3}{4}\]
done
clear
B)
(b) \[\frac{1}{2}\]
done
clear
C)
(c) \[\frac{1}{4}\]
done
clear
D)
(d) \[\frac{2}{3}\]
done
clear
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If \[\mathbf{a},\mathbf{b},\mathbf{c}\] are in A.P. and \[{{\mathbf{a}}^{\mathbf{2}}},{{\mathbf{b}}^{\mathbf{2}}},{{\mathbf{c}}^{\mathbf{2}}}\]are in H.P. then:
A)
(a) \[2b=30+c\]
done
clear
B)
(b) a=b=c
done
clear
C)
(c) \[{{b}^{2}}=\sqrt{\frac{ac}{8}}\]
done
clear
D)
(d) None of these
done
clear
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If \[\mathbf{siny}=\mathbf{x}.\sin \left( \mathbf{a}+\mathbf{y} \right)\],then \[\frac{dx}{dy}\]is
A)
(a) \[\frac{\sin a}{\sin a.{{\sin }^{2}}(a+y)}\]
done
clear
B)
(b) \[\frac{{{\sin }^{2}}(a-y)}{\sin a}\]
done
clear
C)
(c) \[\sin a.{{\sin }^{2}}(a+y)\]
done
clear
D)
(d) \[\frac{{{\sin }^{2}}(a+y)}{\sin a}\]
done
clear
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\[\underset{x\to 0}{\mathop{\lim }}\,{{\left[ \tan \left( \frac{\pi }{4}+x \right) \right]}^{\frac{1}{x}}}\]is equal to
A)
(a) e
done
clear
B)
(b) \[\frac{1}{e}\]
done
clear
C)
(c) e2
done
clear
D)
(d) e3
done
clear
View Answer play_arrow
Let \[f(x)=\frac{\alpha .x}{x+1},x\ne -1\], then for what value of a Is \[\left\{ \mathbf{f}\left\{ \mathbf{f}\left( \mathbf{x} \right) \right\} \right\}=\mathbf{x}?\]
A)
(a) 1
done
clear
B)
(b) \[-1\]
done
clear
C)
(c) \[\sqrt{2}\]
done
clear
D)
(d) \[-\sqrt{2}\]
done
clear
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