MCQ Questions for Class 11 Commerce Applied Mathematics Differentiation Quiz 11

If $$x+y=\sin(x+y)$$ then $$\dfrac{dy}{dx}$$=

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$$\dfrac{1}{2}$$
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$$0$$
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$$-1$$
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$$\dfrac{1}{3}$$

$$\sqrt { 1 - x ^ { 4 } } + \sqrt { 1 - y ^ { 4 } } = a \left( x ^ { 2 } - y ^ { 2 } \right)$$ , then $$\frac { d y } { d x } = \frac { x } { y } \sqrt { \frac { 1 - y ^ { 4 } } { 1 - x ^ { 4 } } }$$.

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True
0%
False

If $$x^{2}+y^{2}=4$$, then the value of $$\dfrac{dy}{dx}$$ at the point $$(0,2)$$ is:

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$$0$$
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$$-32$$
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$$4$$
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$$-2$$

If $$x$$ $$sin$$ $$y$$$$=3 sin y$$ $$+$$ $$4 cos y$$, then $$\frac { dy }{ dx } =$$

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$$\frac { { -sin }^{ 2 }y }{ 4 } $$
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$$\frac { { sin }^{ 2 }y }{ 4 } $$
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$$\frac { { -cos }^{ 2 }y }{ 4 } $$
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$$\frac { { cos }^{ 2 }y }{ 4 } $$

If $$x+y=t-\dfrac{1}{t},x^{2}+y^{2}=t^{2}+\dfrac{1}{t^{2}}, $$ then $$\dfrac{dy}{dx}$$ is equal to

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$$\dfrac{-y}{x}$$
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$$-\dfrac{1}{x}$$
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$$\dfrac{1}{x^{2}}$$
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$$-\dfrac{1}{x^{2}}$$

If $$X={ { { { e }^{ y+e } }^{ y+e } }^{ y+e } }^{ y+...\infty }$$, then $$\dfrac {dy}{dx}$$ is

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$$\dfrac {X}{1+X}$$
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$$\dfrac {1}{X}$$
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$$\dfrac {1-X}{X}$$
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None of these

If $$a{x^2} + 2hxy + b{y^2} = 0$$ then $$\frac{{dy}}{{dx}}$$ is equal to

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$$\frac{y}{x}$$
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$$\frac{x}{y}$$
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$$ - \frac{x}{y}$$
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none of these

If $$y=a\ \sin\ x+b\ \cos\ x$$, then $$y^{2}+\left ( \dfrac{dy}{dx} \right )^{2}$$ is

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function of $$x$$
0%
function of $$y$$
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function of $$x$$ and $$y$$
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constant

If $$y=y(x)$$ and it follows the relation $$e^{xy^{2}}+y\cos(x^{2})=5$$ then $$y'(0)$$ is equal to

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$$4$$
0%
$$-16$$
0%
$$-4$$
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$$16$$

If $$y=a^{{a}^{{x}}}$$, then $$\dfrac {dy}{dx}=$$

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$$y.a^{x}{(\log a)}^{2}$$
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$$y.a^{x}.\log a$$
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$${(y.a^{x})}^{2}$$
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$$(y.a^{x})$$

Let $$f$$ be a differentiable function satisfying the condition $$f(\dfrac{x}{y})=\dfrac{f(x)}{f(y)}$$, for all $$x,y\neq 0\ \epsilon \ R$$ and $$f(y)\neq 0$$. If $$f'(1)=2$$ then $$f'(x)$$ is equal to

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$$2f(x)$$
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$$\dfrac{2f(x)}{x}$$
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$$2xf(x)$$
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$$\dfrac{2f(x)}{2}$$

$$f\left( x \right) =\sqrt { 1+\sqrt { 6+\sqrt { 5+{ x }^{ 2 } } } }$$, then $$f'(2)=$$

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$$1$$
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$$\dfrac {1}{12}$$
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$$\dfrac {1}{36}$$
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$$None$$

Let $$f(x)$$ be differentiable function such that $$f\left(\dfrac{x+y}{1-xy}\right)=f(x)+f(y) \forall x$$ and $$y$$. If $$\underset { x\rightarrow 0 }{ lt } \dfrac { f\left( x \right) }{ x } =\dfrac { 1 }{ 3 }$$ then $$f(1)$$ equals

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$$\dfrac{1}{4}$$
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$$\dfrac{1}{6}$$
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$$\dfrac{1}{12}$$
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$$\dfrac{1}{8}$$

If $$f(x+y)=2f(x).f(y)$$ for all $$x,y$$, where $$f'(0)=3$$ and $$f'(4)=2$$ then $$f'(4)=3$$ is equal to

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6
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12
0%
4
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3

If $$y = {\log _{10}}\left( {\sin x} \right),$$ then $$\dfrac{dy}{dx}$$ equals to:

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$$\sin x\,{\log _{10}}e$$
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$$\cos x\,{\log _{10}}e$$
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$$\cot x\,{\log _{10}}e$$
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$$\cot x$$

If $$x\sqrt {1+y}+y\sqrt {1+x}=0$$, then $$\dfrac {dy}{dx}=$$

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$$-\dfrac {1}{(x+1)^{2}}$$
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$$\dfrac {1}{(x+1)^{2}}$$
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$$-\dfrac {\sqrt {y+1}}{\sqrt {x+1}}$$
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$$\dfrac {\sqrt {1+y}}{\sqrt {1+x}}$$

If $$y = \sin x \left[ \frac { 1 } { \sin x \cdot \sin 2 x } + \frac { 1 } { \sin 2 x \sin 3 x } + \ldots\right.$$ $$+ \frac { 1 } { \sin n x \sin ( n + 1 ) x } ]$$ then $$\frac { d y } { d x } =$$

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$$\cot x - \cot ( n + 1 ) x$$
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$$( n + 1 ) \cos e c ^ { 2 } ( n + 1 ) x - \cos e c ^ { 2 } x$$
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$$\csc ^ { 2 } x - ( n + 1 ) \cos e c ^ { 2 } ( n + 1 ) x$$
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$$\cot x + \cot ( n + 1 ) x$$

Explanation

$$\begin{array}{l} y=\left[ { \frac { 1 }{ { \sin x\sin 2x } } +\frac { 1 }{ { \sin 2x\sin 3x } } +...........+\frac { 1 }{ { \sin nx\sin \left( { n+1 } \right) x } } } \right] \\ y=\left[ { \frac { { \sin x } }{ { \sin x\sin 2x } } +\frac { { \sin x } }{ { \sin 2x\sin 3x } } +...........+\frac { { \sin x } }{ { \sin nx\sin \left( { n+1 } \right) x } } } \right] \\ y=\left[ { \frac { { \sin \left( { 2x-x } \right) } }{ { \sin 2x\sin x } } +\frac { { \sin \left( { 3x-2x } \right) } }{ { \sin 3x\sin 2x } } +...........+\frac { { \sin \left( { n+1 } \right) x-nx } }{ { \sin \left( { n+1 } \right) x\sin nx } } } \right] \\ y=\left[ { \frac { { \sin \left( { 2x } \right) \cos x-\cos 2x\sin x } }{ { \sin 2x\sin x } } +\frac { { \sin \left( { 3x } \right) \cos 2x-\cos 3x\sin 2x } }{ { \sin 3x\sin 2x } } +...........+\frac { { \sin \left( { n+1 } \right) x\cos nx-\cos \left( { n+1 } \right) x\sin x } }{ { \sin \left( { n+1 } \right) x\sin nx } } } \right] \\ y=\left[ { \frac { { \sin \left( { 2x } \right) \cos x } }{ { \sin 2x\sin x } } -\frac { { \cos 2x\sin x } }{ { \sin 2x\sin x } } +\frac { { \sin \left( { 3x } \right) \cos 2x } }{ { \sin 2x\sin x } } \frac { { -\cos 3x\sin 2x } }{ { \sin 3x\sin 2x } } +...........+\frac { { \sin \left( { n+1 } \right) x\cos nx } }{ { \sin \left( { n+1 } \right) x\sin nx } } -\frac { { \cos \left( { n+1 } \right) x\sin x } }{ { \sin \left( { n+1 } \right) x\sin nx } } } \right] \\ y=\left[ { \frac { { \cos x } }{ { \sin x } } -\frac { { cos2x } }{ { \sin 2x } } +\frac { { cos2x } }{ { \sin 2x } } -\frac { { cos3x } }{ { \sin 3x } } +.....+\frac { { \cos nx } }{ { \sin nx } } -\frac { { \cos \left( { n+1 } \right) x } }{ { \sin \left( { n+1 } \right) x } } } \right] \\ y=\left[ { \cot x-\cot 2x+\cot 2x-\cot 3x+...\cot nx-\cot \left( { n+1 } \right) x } \right] \\ y=\left[ { \cot x-\cot \left( { n+1 } \right) x } \right] \\ \frac { { dy } }{ { dx } } =-\cos e{ c^{ 2 } }x-\left( { -\cos e{ c^{ 2 } }\left( { n+1 } \right) x } \right) \left( { n+1 } \right) \\ \frac { { dy } }{ { dx } } =\left( { n+1 } \right) \cos e{ c^{ 2 } }\left( { n+1 } \right) x-\cos e{ c^{ 2 } }x \end{array}$$

If $$(\cos x)^{y}=(\sin y)^{x}$$, then $$\dfrac{dy}{dx}=$$

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$$\dfrac{\log (\sin y)+y \tan x}{\log (\cos x)- x \cot y}$$
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$$\dfrac{\log (\sin y)-y \tan x}{\log (\cos x)+ x \cot y}$$
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$$\dfrac{\log (\sin y)}{\log (\cos x)}$$
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$$\dfrac{\log (\cos x)}{\log (\sin y)}$$

Let y be an implicit function of $$x$$ defined by $$x^{2x}-2x^x\cot\:y-1=0$$. Then $$y'\left(1\right)$$ equals

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$$-1$$
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$$1$$
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$$\log\:2$$
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$$-\log\:2$$

If $$y=(x+\sqrt{x^{2}+a^{2}})^{n}$$ then $$\dfrac{dy}{dx}=$$

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$$y$$
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$$ny$$
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$$\dfrac{ny}{\sqrt{x^{2}+a^{2}}}$$
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$$\dfrac{y}{\sqrt{x^{2}+a^{2}}}$$

If $$x^m\cdot y^n=\left(x+y\right)^{m+n}$$, then $$\dfrac{dy}{dx}$$ is ?

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$$\dfrac{y}{x}$$
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$$\dfrac{x+y}{xy}$$
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xy
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$$\dfrac{x}{y}$$

If $$2^{x}-2^{y}=2^{x+y}$$ then $$\dfrac{dy}{dx}=$$

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$$2^{y-x}$$
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$$2^{y/x}$$
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$$-2^{y/x}$$
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$$2^{x/y}$$

If $$y = \exp \left\{ {{{\sin }^2}x + {{\sin }^4}x + {{\sin }^6}x + ....} \right\}$$ then $$\frac {dy}{dx}=$$

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$${e^{{{\tan }^2}x}}$$
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$${e^{{{\tan }^2}x}}{\sec ^2}x$$
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$$2{e^{{{\tan }^2}x}}\tan x{\sec ^2}x$$
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none

If $$y = {x^2} + \dfrac{1}{{{x^2} + \frac{1}{{{x^2} + \ldots \ldots \infty }}}},$$ then $$\dfrac{{dy}}{{dx}}=$$

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$$\dfrac{{ - x{y^2}}}{{{y^2} + 1}}$$
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$$\dfrac{{ 2xy}}{{2y-x^2}}$$
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$$\dfrac{{ - {x^2}{y^2}}}{{{y^2} + 1}}$$
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$$\dfrac{{ x{y^2}}}{{{y^2} + 1}}$$

If $$x\dfrac{dy}{dx}=y(\log y-\log x +1)$$, then the solution of the equation

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$$\log\left(\dfrac{x}{y}\right)=cy$$
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$$\log\left(\dfrac{y}{x}\right)=cx$$
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$$x \log\left(\dfrac{x}{y}\right)=cy$$
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$$y \log\left(\dfrac{x}{y}\right)=cy$$

If $$y = \sec \left( {{{\tan }^{ - 1}}x} \right)$$, then $$\dfrac {dy}{dx}$$ at $$x=1$$ is equal to

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$$\dfrac {1}{\sqrt 2}$$
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$$\dfrac {1}{2}$$
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$$1$$
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$$\sqrt 2$$

If y(x) is the solution of the differential equation $$\left( x+2 \right) \dfrac { dy }{ dx } ={ x }^{ 2 }+4x-9,x\neq -2$$ and y(0)=0, then y(-4) is equal to :

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0
0%
2
0%
1
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-1

The solution of the differential equation $$\left( \dfrac { d y } { d x } \right) ^ { 2 } - 3 x \left( \dfrac { d y } { d x } \right) - 2 y = 8$$ is

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$$y = 2 x ^ { 2 } + 4$$
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$$y = 2 x ^ { 2 } - 4$$
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$$y = 2 x + 4$$
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$$y = 2 x - 4$$

A curve in the $$1^{st}$$ quadrant passes through $$(1,1)$$. Its drifferential equation is $$(y-xy^{2})dx+(x+x^{2}y^{2})dy=0$$. Hence the equation of the curve is

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$$y-\dfrac{1}{xy}=\ln y$$
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$$y-\dfrac{1}{xy}=\ln x$$
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$$y-xy=\ln y$$
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$$y-xy=\ln x$$

If $$\dfrac {dy}{dx}=(e^ {y}-x)^ {-1}$$ where $$y(0)=0$$ then $$y$$ is expressed explicity as

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$$0.5\log_{e}(1+x^{2})$$
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$$\log_{e}(1+x^{2})$$
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$$\log _{ e } \left( x+\sqrt { 1+{ x }^{ 2 } } \right) $$
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$$\\ \log _{ e } \left( x+\sqrt { 1-{ x }^{ 2 } } \right) $$

CBSE Questions for Class 11 Commerce Applied Mathematics Differentiation Quiz 11 - MCQExams.com

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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

CBSE Questions for Class 11 Commerce Applied Mathematics Differentiation Quiz 11 - MCQExams.com

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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

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