tan \[\left[ \mathbf{ilog}\frac{a-ib}{a+ib} \right]\]is equal to.
A)
\[\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\]
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B)
\[\frac{{{a}^{2}}-{{b}^{2}}}{2ab}\]
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C)
\[\frac{2ab}{{{a}^{2}}-{{b}^{2}}}\]
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D)
\[ab\]
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A speaks truth in 60% of the cases and B in boy of the case. The percentage of cases they are likely to contradict each other in stating the same fact is
A)
36%
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B)
42%
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C)
48%
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D)
None of these
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The number of odd numbers between 60 & 360 is
A)
148
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B)
150
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C)
160
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D)
153
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If \[\mathbf{sinx}+\mathbf{cosx}=\mathbf{a}\]then. \[si{{r}^{6}}x+co{{s}^{6}}x\]is equal to.
A)
\[\frac{1}{4}(4+3.({{a}^{2}}-{{1}^{2}}))\]
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B)
\[\frac{1}{4}[4-3.({{a}^{2}}-{{1}^{2}})]\]
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C)
\[\frac{1}{4}[4-2.({{a}^{2}}+{{1}^{2}})]\]
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D)
\[\frac{1}{4}[4-3.{{({{a}^{2}}+1)}^{2}}]\]
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If \[\mathbf{f}\left( \mathbf{2} \right)=\mathbf{2},\mathbf{f}'\left( \mathbf{2} \right)=1\]then \[\underset{x\to 2}{\mathop{Lt}}\,\frac{2{{x}^{2}}-4f(x)}{x-2}\]is equal to
A)
4
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B)
\[-2\]
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C)
\[-4\]
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D)
2
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If \[y=\frac{\cos x}{1+\sin x}\]then \[\frac{dy}{dx}\]at \[x=\frac{\pi }{2}\]is equal to.
A)
\[\frac{1}{2}\]
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B)
\[\frac{-1}{2}\]
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C)
-1
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D)
0
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What will be the equation of a straight which is equidistant from parallel lines \[\mathbf{9x}+\mathbf{6y}-\mathbf{7}=\mathbf{0}\] and \[\mathbf{3x}+\mathbf{2y}+\mathbf{6}=\mathbf{0}.\]
A)
\[21x+18y+11=0\]
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B)
\[18x+21y-11=0\]
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C)
\[18x+21y+11=0\]
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D)
\[21x+18y-11=0\]
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The solution of \[\mathbf{6}+\mathbf{x}-{{\mathbf{x}}^{\mathbf{2}}}>\mathbf{0}\]is
A)
\[-1<x<2\]
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B)
\[~-2<x<3\]
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C)
\[-2<x<-1\]
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D)
None of these
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A man has gat 6 friends. Then the number of ways in which the can invite or of his friends to dinner, is
A)
63
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B)
65
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C)
61
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D)
60
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The sum of the series \[\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}......\] up to \[\infty \] is equal to.
A)
\[lo{{g}_{e}}2\]
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B)
\[lo{{g}_{e}}2-1\]
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C)
\[2.lo{{g}_{e}}2\]
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D)
\[2.lo{{g}_{e}}2-1\]
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A set contains n elements. The power set contains -
A)
n elements
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B)
\[{{2}^{n}}\]elements
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C)
\[{{n}^{2}}\]elements
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D)
\[{{2}^{(n-1)}}\]elements
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If \[f(x)=\frac{\mathbf{3x}+\mathbf{1}}{\mathbf{5x}-\mathbf{3}}\].then
A)
\[{{f}^{-1}}(x)=-f(x)\]
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B)
\[f\,of\left( x \right)=f\left( x \right)\]
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C)
\[{{f}^{-1}}(x)=-f(x)\]
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D)
\[{{f}^{-1}}(x)=\frac{1}{20}f(x)\]
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Sum of the absolute deviation about median is-
A)
least
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B)
zero
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C)
greatest
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D)
None of these
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Coefficient of x4 in the expansion of \[{{\left( \mathbf{1}+\mathbf{x}+{{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{x}}^{\mathbf{4}}} \right)}^{\mathbf{11}}}\] is -
A)
605
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B)
810
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C)
990
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D)
910
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The slope of the normal at the point \[\left( \mathbf{a}{{\mathbf{t}}^{\mathbf{2}}},\mathbf{2at} \right)\] of the parabola \[{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{4ax}\] is
A)
\[\frac{1}{t}\]
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B)
t
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C)
\[-t\]
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D)
\[{{t}^{2}}\]
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The roots of the equation \[{{2}^{x+2}}{{.3}^{\frac{3x}{x-1}}}=9\]are given by
A)
\[lo{{g}_{2}}\left( \frac{2}{3} \right),-2\]
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B)
\[-3,3\]
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C)
\[-2,1-\frac{\log 3}{\log 2}\]
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D)
\[-2,1-{{\log }_{2}}3\]
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A coin & a dice is thrown. If A denotes the event head & even face and B denotes the event tail & multiple of 3. Then-
A)
\[P(A)=\frac{1}{4}\]
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B)
\[P(B)=\frac{1}{5}\]
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C)
\[P(A)=\frac{1}{3}\]
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D)
\[P(B)=\frac{2}{3}\]
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\[\underset{x\to 0}{\mathop{Lt}}\,\frac{{{e}^{{{x}^{2}}}}-\cos x}{{{x}^{2}}}\]is
A)
\[\frac{2}{3}\]
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B)
\[\frac{1}{2}\]
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C)
\[\frac{3}{2}\]
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D)
2
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If w is an imaginary cube root of unity then \[\left( 1-w \right)\left( 1-{{w}^{2}} \right)\left( 1-{{w}^{4}} \right)\left( 1-{{w}^{5}} \right)\]is equal to
A)
3
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B)
6
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C)
9
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D)
12
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Root of the equation- \[{{\mathbf{3}}^{\mathbf{x-1}}}\mathbf{+}{{\mathbf{3}}^{\mathbf{1-x}}}\mathbf{=2}\]
A)
\[x=0\]
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B)
\[x=1\]
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C)
\[x=2\]
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D)
\[x=-1\]
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