The principle value of \[co{{t}^{-1}}(-1)\]is;
A)
\[\frac{\pi }{4}\]
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B)
\[\frac{3\pi }{4}\]
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C)
\[\frac{-\pi }{4}\]
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D)
\[\frac{5\pi }{4}\]
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If \[\mathbf{h}\left( \mathbf{x} \right)=\mathbf{f}\left( \mathbf{x} \right)+\mathbf{f}\left( -\mathbf{x} \right)\], then h(x) has get an extreme value at a point where \[\mathbf{f}'\left( \mathbf{x} \right)\]is:
A)
zero
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B)
odd function
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C)
even function
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D)
None of these
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\[\int{{{7}^{{{7}^{{{7}^{x}}}}}}}{{.7}^{{{7}^{^{x}}}}}{{.7}^{^{^{x}}}}.dx\]is equal to
A)
\[\frac{{{7}^{{{7}^{{{7}^{x}}}}}}}{(\log 7)}+c\]
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B)
\[\frac{{{7}^{{{7}^{{{7}^{x}}}}}}}{{{(\log 7)}^{2}}}+c\]
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C)
\[\frac{{{7}^{{{7}^{{{7}^{x}}}}}}}{{{(\log 7)}^{3}}}+c\]
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D)
None of these
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\[\int\limits_{0}^{2\pi }{\sqrt{\frac{1-\cos 2x}{2}}}.dx\]Is equal to:
A)
2
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B)
\[-2\]
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C)
4
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D)
\[-4\]
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The root of the equation
are independent of
A)
a
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B)
p
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C)
Y
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D)
All of these
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If
then x is equal to:
A)
2
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B)
7
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C)
\[-9\]
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D)
All of these
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If the vectors, \[\mathbf{\vec{a}}=\mathbf{2\hat{i}}-\mathbf{3\hat{J}}+\mathbf{4\hat{k}},\mathbf{\hat{b}}=\mathbf{\hat{i}}+\mathbf{2\hat{J}}-\mathbf{\hat{k}}\]and \[\mathbf{\vec{c}}=\mathbf{x\hat{i}}-\mathbf{\hat{j}}+\mathbf{2\hat{k}}\] are coplanar, then x=
A)
0
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B)
1
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C)
\[\frac{5}{8}\]
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D)
\[\frac{8}{5}\]
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The ratio in which the plane \[\mathbf{x}-\mathbf{2y}+\mathbf{3z}=\mathbf{17}\]divides the line joining the points \[\left( \mathbf{2},-\mathbf{4},\mathbf{7} \right)\] and \[\left( \mathbf{3},-\mathbf{5},\mathbf{8} \right)\] is:
A)
\[3:10\]
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B)
\[10:3\]
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C)
\[2:3\]
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D)
\[3:2\]
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\[\int{\frac{\sqrt{1+\sqrt{x}}}{x}}.dx\]equal to:
A)
\[2\sqrt{1+\sqrt{x}}-2\log \left( \frac{\sqrt{1+\sqrt{x}}-1}{\sqrt{1+\sqrt{x}}+1} \right)+c\]
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B)
\[4\sqrt{1+\sqrt{x}}-2\log \left( \frac{\sqrt{1+\sqrt{x}}-1}{\sqrt{1+\sqrt{x}}+1} \right)+c\]
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C)
\[4\sqrt{1+\sqrt{x}}-2\log \left( \frac{\sqrt{1+\sqrt{x}}-1}{\sqrt{1+\sqrt{x}}+1} \right)+c\]
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D)
\[2\sqrt{1+\sqrt{x}}+2\log \left( \frac{\sqrt{1+\sqrt{x}}-1}{\sqrt{1+\sqrt{x}}+1} \right)+c\]
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If A and B are two events, then \[\mathbf{P}\left( \mathbf{A}\cap \mathbf{B} \right)=\]
A)
\[P\left( \overline{A} \right).P\left( \overline{B} \right)\]
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B)
\[1-P\left( \overline{A} \right)-P\left( \overline{B} \right)\]
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C)
\[P\left( B \right)-P\left( A\cap B \right)\]
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D)
\[P\left( A \right)+P\left( B \right)-P\left( A\cap B \right)\]
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Corner points of the feasible region for an LPP are \[\left( \mathbf{0},\mathbf{2} \right),\left( \mathbf{3},\mathbf{0} \right),\left( \mathbf{6},\mathbf{0} \right),\left( \mathbf{6},\mathbf{8} \right)\] and\[\left( \mathbf{0},\mathbf{5} \right)\]. If \[\mathbf{F}=\mathbf{4x}+\mathbf{6y}\]be the objective function, then minimum value of F occurs at
A)
\[\left( 0,2 \right)\]only
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B)
\[\left( 3,0 \right)\]only
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C)
the mid point of the line segment joining the points \[\left( 0,2 \right)\] and \[\left( 3,0 \right)\] only
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D)
any point on the line segment joining the points \[\left( 0,2 \right)\] and \[\left( 3,0 \right)\]
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The solution of \[{{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{y}}^{\mathbf{2}}}\frac{dy}{dx}=\mathbf{4}\], is:
A)
\[{{x}^{3}}-{{y}^{3}}=12x+c'\]
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B)
\[{{x}^{3}}+{{y}^{3}}=12x+c'\]
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C)
\[{{y}^{3}}+{{x}^{3}}=12x+c'\]
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D)
None of these
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If \[f(x)=\left\{ \begin{align} & \underline{\left| x \right|},x\ne 0 \\ & 0,\,\,\,\,\,x=0 \\ \end{align} \right.\], where f(x) is signum function then the function is:
A)
continuous as well differentiable at \[x=0\]
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B)
continuous but not differentiable at \[x=0\]
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C)
neither differentiable nor continuous at \[x=0\]
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D)
differentiable but continuous at \[x=0\]
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If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is:
A)
\[\frac{11}{16}\]
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B)
\[\frac{15}{16}\]
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C)
\[\frac{1}{2}\]
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D)
None of these
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The sum of square of deviation for 10 observations taken from 50 is 250. The coefficient of variance is:
A)
10%
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B)
20%
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C)
30%
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D)
40%
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If \[ta{{n}^{-1}}\left( \frac{x+1}{x-1} \right)+ta{{n}^{-1}}\left( \frac{x-1}{x} \right)=ta{{n}^{-1}}(-7)\], then \[\mathbf{x}=\]
A)
1
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B)
2
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C)
\[-2\]
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D)
\[-1\]
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If \[\mathbf{\vec{a}}\] and \[\mathbf{\vec{b}}\] represent the diagonals of rhombus, then
A)
\[\vec{a}.\vec{b}=0\]
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B)
\[\vec{a}\times \vec{b}=0\]
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C)
\[\vec{a}.\vec{b}=1\]
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D)
\[\vec{a}\times \vec{b}=\vec{b}\]
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The area bounded by \[\mathbf{y}=\mathbf{2}-{{\mathbf{x}}^{\mathbf{2}}}\]and \[\mathbf{x}+\mathbf{y}=\mathbf{0}\]is:
A)
\[\frac{9}{2}\] sq. unit
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B)
\[\frac{7}{2}\]sq. unit
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C)
7 sq. unit
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D)
9 sq. unit
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A is a matrix such that \[{{\mathbf{A}}^{\mathbf{3}}}=\mathbf{I}\], then \[{{\mathbf{A}}^{-\mathbf{1}}}\]=
A)
A
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B)
A2
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C)
A3
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D)
None of these
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\[\int{{{\mathbf{e}}^{x}}\left( \frac{1-\sin x}{1-\cos x} \right).\mathbf{dx}=}\]
A)
\[-{{e}^{x}}.cot\frac{x}{2}+c\]
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B)
\[{{e}^{x}}.\tan +c\]
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C)
\[{{e}^{x}}.\cot \frac{x}{2}+c\]
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D)
\[-{{e}^{x}}.\tan \frac{x}{2}+c\]
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