CBSE Questions for Class 11 Commerce Applied Mathematics Differentiation Quiz 10 - MCQExams.com

If $$y = {\left( {\sin \,x} \right)^x}$$, then $$\dfrac{{dy}}{{dx}} = $$
  • $$(\sin x)^x(\ln (\sin x)+x\cot x)$$
  • $$(\ln (\sin x)+x\cot x)$$
  • $$(\sin x)^x(\ln (\sin x)+x\tan x)$$
  • $$(\sin x)^x(\ln (\sin x)-\cot x)$$
Solve:
If $$y=\log x^x,$$ then $$\dfrac{dy}{dx}=$$
  • $$1$$
  • $$\log x$$
  • $$\log (ex)$$
  • None of these
State True or False:
If $$y\, = \,x\sqrt {{a^2}\, + \,{x^2}\,} \, + \,{a^2}\,\log \left( {x\, + \,\sqrt {{a^2}\, + \,{x^2}} } \right)\,\,then\,\,\dfrac{{dy}}{{dx}}\, = \,2\sqrt {{a^2}\, + \,{x^2}} $$.
  • True
  • False
$$\dfrac{d}{dx}\displaystyle\int\limits_{f(x)}^{g(x)}h(t)dt=$$
  • $$g'(x)h(g(x))$$
  • $$h(g(x))-h(f(x))$$
  • $$h(g(x)).g'(x)-h(f(x)).f'(x)$$
  • none of these
The differential equation of all parabolas having their axis of symmetry coinciding with the axis of X is?
  • $$y\dfrac{d^2y}{dx^2}+\left(\dfrac{dy}{dx}\right)^2=0$$
  • $$x\dfrac{d^2x}{dy^2}+\left(\dfrac{dx}{dy}\right)^2=0$$
  • $$y\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}=0$$
  • None of these
If $$y= \log_e(x+\log_e(x+ ....)),$$ then $$\dfrac{dy}{dx}$$ at $$(x= e^2-2, y= \sqrt2)$$ is
  • $$\dfrac{1}{e^{\sqrt2}-1}$$
  • $$\dfrac{\log2}{2\sqrt2(e^2-1)}$$
  • $$\dfrac{\sqrt2\log\dfrac{e}{2}}{(e^2-1)}$$
  • None of these
Find $$\dfrac {dy}{dx}$$ for $$y{e^{{x^2}}} + \tan x + \log (\sin x) = 0$$
  • None of these
  • $$ - \left( {\dfrac{{y{e^{{x^2}}}.2x - {{\sec }^2}x + \cot x}}{{{e^{{x^2}}}}}} \right)$$
  • $$ - \left( {\dfrac{{y{e^{{x^2}}}.2x + {{\sec }^2}x + \cot x}}{{{e^{{x^2}}}}}} \right)$$
  • $$  \left( {\dfrac{{y{e^{{x^2}}}.2x + {{\sec }^2}x + \cot x}}{{{e^{{x^2}}}}}} \right)$$
Differentiate $$10^{x^x}+x^{x^{10}}+x^{10^x}$$ w.r.t $$x$$.
  • $$10^{x^{x}}x^{x} (\log x + 1 )+ x^{10^{x}}x^{9}\left(1+10 \log x\right)+ x^{10^{x}}10^{x}\left(\cfrac{1}{x}+ \log x\right)$$
  • $$(1+\log x)+x^{x^{10}}x^9(1+10\log x)+x^{10^x}10^x\left(\dfrac{1}{x}+\log x\right)$$
  • $$10^{x^x}(1+\log x)+x^{x^{10}}x^9(1+10\log x)+\left(\dfrac{1}{x}+\log x\right)$$
  • $$10^{x^x}(1+\log x)+(1+10\log x)+x^{10^x}10^x\left(\dfrac{1}{x}+\log x\right)$$
The shortest distance between line $$y-x=1$$ and curve $$x={y}^{2}$$ is
  • $$\dfrac {\sqrt {3}}{4}$$
  • $$\dfrac {3\sqrt {2}}{8}$$
  • $$\dfrac {8}{2\sqrt {2}}$$
  • $$\dfrac {4}{\sqrt {3}}$$
Let $$\sqrt { x+\sqrt { x+\sqrt { x+.......\infty  }  }  }$$ then $$\dfrac { dy }{ dx } =$$
  • $$\dfrac {1}{2y-1}$$
  • $$\dfrac {x}{x+2y}$$
  • $$\dfrac {1}{\sqrt {1+4x}}$$
  • $$\dfrac {y}{2x+y}$$
Let $$y=a\cos t+b\sin t$$ then $$\dfrac{d^2y}{dt^2}=$$
  • $$y$$
  • $$-y$$
  • $$2y$$
  • none of these
Let $$f(x)=\dfrac{1}{ax+b}$$ then $$f''(0)=$$
  • $$\dfrac{2a^3}{b^2}$$
  • $$\dfrac{2a^2}{b^3}$$
  • $$\dfrac{2a^3}{b^3}$$
  • none of these
If $$f(x)=\dfrac{a^x}{x^a}$$ then $$f'(a)=$$?
  • $$log a-1$$
  • $$log a-a$$
  • $$a log a-a$$
  • $$a log a+a$$
If $$y=2^{ax}$$ and $$\dfrac{dy}{dx}=log 256$$ at $$x=1$$, then the value of a is?
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
If $$y=\tan^{-1}(\sec x+\tan x)$$ then $$\dfrac{dy}{dx}=?$$
  • $$1$$
  • $$\dfrac{1}{2}$$
  • $$-1$$
  • $$0$$
If $$y=(x^{x})^{x}$$ then $$\dfrac {dy}{dx}=$$
  • $$(x^{x})^{x}(1+2\log x)$$
  • $$(x^{x})^{x}(1-2\log x)$$
  • $$x(x^{x})^{x}(1+2\log x)$$
  • $$x(x^{x})^{x}(1-2\log x)$$
If $$y=\log\left(\dfrac {1+x}{1-x}\right)^{1/4}-\dfrac {1}{2}\tan^{-1}x$$, then $$\dfrac {dy}{dx}$$ is equal to
  • $$\dfrac {x^{2}}{1-x^{4}}$$
  • $$\dfrac {2x^{2}}{1-x^{4}}$$
  • $$\dfrac {2x^{2}}{2(1-x^{4})}$$
  • $$None\ of\ these$$
If $${ x }^{ y }={ e }^{ x-y }$$ then
$$ \frac { dy }{ dx } =\frac { logx }{ (1-logx)^{ 2 } } $$.
  • True
  • False
If $$ax^{2}+2hxy+by^{2}=1$$ then $$\dfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } $$ is equal to
  • $$\dfrac { { ab-h }^{ 2 } }{ \left( hx+by \right) ^{ 2 } } $$
  • $$\dfrac { { h }^{ 2 }-ab }{ \left( hx+by \right) ^{ 2 } } $$
  • $$\dfrac { { h }^{ 2 }+ab }{ \left( hx+by \right) ^{ 2 } } $$
  • $$\dfrac { { h }^{ 2 }-ab }{ \left( hy+by \right) ^{ 2 } } $$
If $$f(x) = |x^2 - 5x + 6|$$, then $$f'(x)$$ equals
  • $$2x - 5$$ for $$2 < x < 3$$
  • $$5 - 2x$$ for $$2 < x <3$$
  • $$2x - 5$$ for $$x > 2$$
  • $$5 - 2x$$ for $$x < 3$$
If $$y=\ x^{2}\ sin\ x ,\ then\ \dfrac{dy}{dx}$$ will be 
  • $$x ^{2}\ cos\ x \ +\ 2x \ sin\ x $$
  • $$2x \ sin\ x $$
  • $$x ^{2}\ cos\ x $$
  • $$2x \ cos\ x $$
The point(s) on the curve $${y^3} + 3{x^2} = 12y$$ where the tangent is vertical, is (are)
  • $$\left( { \pm \frac{4}{{\sqrt 3 \,}},\, - 2} \right)$$
  • $$\left( { \pm \frac{{\sqrt {11} }}{{3\,}},\,1} \right)$$
  • $$\left( {0,\,0} \right)$$
  • $$\left( { \pm \frac{4}{{\sqrt 3 \,}},\,2} \right)$$
If $$f(x)=\sqrt {(x+2\sqrt {2x-4})}+\sqrt {(x-2\sqrt {2x-4})}$$, then find the value of $$72\ f'(66)$$
  • $$8$$
  • $$9$$
  • $$11$$
  • $$22$$
If $$x^p.y^q=(x+y)^{p+q}$$ then $$\dfrac{dy}{dx}$$=?
  • $$\dfrac{y}{x}$$
  • $$-\dfrac{y}{x}$$
  • $$\dfrac{x}{y}$$
  • $$-\dfrac{x}{y}$$
If $$y=\sqrt { \tan { x+\sqrt { \tan { x+\sqrt { \tan { x+.....\infty  }  }  }  }  }  }$$    then $$\dfrac { dy }{ dx } =$$
  • $$\dfrac { \cos { ^{ 2 }x +1} }{ 2y}$$
  • $$\dfrac { \sec { ^{ 2 }x+1 } }{ 2y }$$
  • $$\dfrac { \tan { x } +1}{ 2y }$$
  • $$\dfrac { \cot { x } +1}{ 2y}$$
The line $$\dfrac{x}{a}+\dfrac{y}{b}=2$$ tangent to $$\left ( \dfrac{x}{a} \right )^{n}\left ( \dfrac{y}{b} \right )^{n}=$$at (a,b) then $$\epsilon $$?
  • Z
  • R-Z
  • N
  • R-{o}
If $$y=|\cos x|+|\sin x|$$, then $$\dfrac {dy}{dx}$$ at $$x=\dfrac {2\pi}{3}$$  is
  • $$\dfrac {1-\sqrt {3}}{2}$$
  • $$0$$
  • $$\dfrac {\sqrt {3}-1}{2}$$
  • $$\dfrac {\sqrt {3}+1}{2}$$
If $$x^{m}.y^{n}=(x+y)^{m+n}$$ then $$\dfrac {dy}{dx}=$$
  • $$\dfrac {y}{x}$$
  • $$-\dfrac {y}{x}$$
  • $$\dfrac {my}{x}$$
  • $$\dfrac {ny}{x}$$
If $$x^4 + 7x^2y^2 + 9y^4 = 24 xy^3 $$, then $$\dfrac{dy}{dx} = $$
  • $$\dfrac{x}{y}$$
  • $$\dfrac{y}{x}$$
  • $$- \dfrac{x}{y}$$
  • $$-\dfrac{y}{x}$$
$$if\,x\sqrt {1 + y}  + y\sqrt {1 + x}  = 0,\,then\,\dfrac{{dy}}{{dx}}is\,equal\,to\,$$
  • $$\dfrac{1}{{{{(1 + x)}^2}}}$$
  • $$ - \,\dfrac{1}{{{{(1 + x)}^2}}}$$
  • $$\,\,\dfrac{1}{{(1 + {x^2})}}\,\,$$
  • $$\dfrac{1}{{(1 + x)}}$$
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers