CBSE Questions for Class 11 Commerce Applied Mathematics Differentiation Quiz 9 - MCQExams.com

If $$y = 4x - 5$$ is a tangent to the curve $$y^{2} = px^{3} + q$$ at $$(2, 3)$$, then $$(p + q)$$ is equal to
  • $$-5$$
  • $$5$$
  • $$-9$$
  • $$9$$
  • $$0$$
If $$f(x)=\left| \log { \left| x \right|  }  \right| $$, then
  • $$f(x)$$ is continuous and differentiable for all $$x$$ in its domain
  • $$f(x)$$ is continuous for all $$x$$ in its domain but not differentiable at $$x=\pm 1$$
  • $$f(x)$$ is neither continuous nor differentiable at $$x=\pm 1$$
  • None of the above
If $$\sqrt{x} +\sqrt{y} = 10$$, find $$\dfrac{dy}{dx}$$  at $$y = 4$$.
  • $$4$$
  • $$-3$$
  • $$-4$$
  • $$3$$
If $$xe^{xy} + ye^{-xy} = \sin^{2}x$$, then $$\dfrac {dy}{dx}$$ at $$x = 0$$ is
  • $$2y^{2} - 1$$
  • $$2y$$
  • $$y^{2} - y$$
  • $$y^{2} + 1$$
  • $$y^{2} - 1$$
If $$ x^2 + 2xy + 2y^2 = 1, $$ then $$ \dfrac {dy}{dx} $$ at the point where $$y=1$$ is equal to :
  • $$1$$
  • $$2$$
  • $$-1$$
  • $$-2$$
  • $$0$$
If $${ y }^{ x }-{ x }^{ y }=1$$, then the value of $$\cfrac { dy }{ dx } $$ at $$x=1$$ is
  • $$2\left( 1-\log { 2 } \right) $$
  • $$2\left( 1+\log { 2 } \right) $$
  • $$2-\log { 2 } $$
  • $$2+\log { 2 } $$
If $$ y^x = 2^x , $$ then $$ \dfrac {dy}{dx} $$ is equal to :
  • $$ \dfrac {y}{x} \log \left( \dfrac {2}{y} \right) $$
  • $$ \dfrac {x}{y} \log \left( \dfrac {2}{y} \right) $$
  • $$ \dfrac {y}{x} \log \left( \dfrac {y}{2} \right) $$
  • $$ \dfrac {x}{y} \log \left( \dfrac {y}{2} \right) $$
  • $$ \dfrac {y}{x} \log \left( 2y \right) $$
If $$y = x - x^{2}$$, then the derivative of $$y^{2} w.r.t. x^{2}$$ is
  • $$2x^{2} + 3x - 1$$
  • $$2x^{2} - 3x + 1$$
  • $$2x^{2} + 3x + 1$$
  • None of these
If $$(f(x))^{g(y)} = e^{f(x) - g(y)}$$ then $$\dfrac {dy}{dx} =$$.
  • $$\dfrac {f^{1}(x)\log f(x)}{g^{1}(y) (1 + \log f(x))^{2}}$$
  • $$\dfrac {f^{1}(x)\log f(x)}{g^{1}(y) (1 + \log f(x))^{3}}$$
  • $$\dfrac {f^{1}(x).\log f(x)}{g^{-1}(y) (1 - \log f(x))^{2}}$$
  • $$\dfrac {f^{1}(x)\log f(x)}{g(y) (1 + \log f(x))^{2}}$$
Let $$f$$ and $$g$$ be differential functions satisfying $$ g' (a) =2 , g (a) b $$ and $$ fog = I $$ (identify function) then $$ f'(b) = $$ :
  • $$1/2$$
  • $$2$$
  • $$2/3$$
  • None of these
$$\dfrac {d}{dx}\left (\sqrt {3} \sin \left (2x + \dfrac {\pi}{3}\right ) + \cos \left (2x + \dfrac {\pi}{3}\right )\right ) =$$ _________.
  • $$4\cos 2x$$
  • $$-4\sin 2x$$
  • $$4\sin 2x$$
  • $$-4\cos 2x$$
If $$|x| < 1$$, then $$\dfrac{d}{dx}\left[1+\dfrac{p}{q}x+\dfrac{p(p+q)}{2!}\left(\dfrac{x}{q}\right)^2+\dfrac{p(p+q)(p+2q)}{3!}\left(\dfrac{x}{q}\right)^3....\infty\right]=$$
  • $$\dfrac{p}{q(1-x)^{\frac{p}{q}+1}}$$
  • $$\dfrac{p}{q(1-x)^{\frac{p}{q}}}$$
  • $$(1-x)^{-pq-1}$$
  • $$(1-x)^{pq+1}$$
If $$y = Tan^{-1} \left (\dfrac {\log (e/x^{2})}{\log ex^{2}}\right ) + Tan^{-1} \left (\dfrac {3 + 2\log x}{1 - 6\log x}\right )$$ then $$\left (\dfrac {dy}{dx}\right )_{x = 2} + \left (\dfrac {dy}{dx}\right )_{x = 3}$$.
  • $$-6$$
  • $$2$$
  • $$0$$
  • $$-2$$
Let $$\int _{ 0 }^{ x }{ \left( \cfrac { bt\cos { 4t } -a\sin { 4t }  }{ { t }^{ 2 } }  \right)  } dt=\cfrac { a\sin { 4x }  }{ x } $$ then $$a$$ and $$b$$ are given by
  • $$a=\cfrac { 1 }{ 4 } ,b=1$$
  • $$a=2,b=2$$
  • $$a=-1,b=4$$
  • $$a=2,b=4$$
If $$8f(x) + 6f\left( {{1 \over x}} \right) = x + 5$$ and $$y = {x^2}f(x)$$ ,then $${{dy} \over {dx}}$$ at x=-1 is equal to
  • 0
  • $${1 \over {14}}$$
  • $$ - {1 \over {14}}$$
  • None of these
If $$f:\mathrm{R}\to\mathrm{R}$$ is a differentiable function such that $$f'(x)\gt 2f(x)\forall x\in \mathrm{R}$$ and $$f(0)=1$$, then 
  • $$f(x)$$ is increasing in $$(0,\infty)$$
  • $$f(x)$$ is decreasing in $$(0,\infty)$$
  • $$f(x)\gt e^{2x} $$ in $$(0,\infty)$$
  • $$f(x)\lt e^{2x} $$ in $$(0,\infty)$$
If y=$$A\sin (\omega t - kx)$$, then the value of $${{dy} \over {dx}}$$ is
  • $$A\cos (\omega t - kx)$$
  • $$ - A\omega \cos (\omega t - kx)$$
  • $$Ak\cos (\omega t - kx)$$
  • $$ - Ak\cos (\omega t - kx)$$
$$\frac{d^n}{dx^n}[log(ax+b)]$$ is equal to:
  • $$\frac{(-1)^n n! a^n}{(ax+b)^{n+1}}$$
  • $$\frac{(-1)^{n-1} {(n-1)}! a^n}{(ax+b)^{n+1}}$$
  • $$\frac{(-1)^{n+1} ({n+1)}! a^{n-1}}{(ax+b)^{n+1}}$$
  • $$\frac{(-1)^{n-1} {(n-1)}! a^n}{(ax+b)^n}$$
Derivative of $$log_e(log_e|\sin x|) $$with respect to $$x$$ at $$x=\dfrac{\pi}{6}$$ is
  • $$-\dfrac{\sqrt{3}}{log_e2}$$
  • $$\dfrac{\sqrt{3}}{log_e2}$$
  • $$-\dfrac{\sqrt{3}}{2\log2}$$
  • does not exist
Statement I: The function f(x) in the figure is differentiable at x = a
Statement II: The function f(x) continuous at x = a

1019713_fa884f00f0bf444a8a92598dbf0fe684.png
  • Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I.
  • Both Statement I and Statement II are true and the Statement II is not the correct explanation of the Statement I.
  • Statement I is true but Statement II is false
  • Statement I is false but Statement II is true.
If $$y=x^x$$ then  $$\dfrac{d^2y}{dx^2}-\dfrac{1}{y}\left(\dfrac{dy}{dx}\right)^2-\dfrac{y}{x}=0$$
  • True
  • False
If $$e^y(x + 1) = 1$$, then $$\dfrac{d^2y}{dx^2}$$ is equal to
  • $$y$$
  • $$\dfrac{dy}{dx}$$
  • $$-y$$
  • $$\left(\dfrac{dy}{dx}\right)^2$$
Given $$y=\dfrac {3}{x}, \dfrac {dy}{dx}=$$
  • $$3$$
  • $$\dfrac {3}{x^{2}}$$
  • $$\dfrac {-3}{x^{2}}$$
  • $$3x$$

State True or False.

If $$\dfrac{{{e^y}}}{{{e^x}}} = xy$$, then $$y' = \dfrac{{2 -
\log x}}{{{{\left( {1 - \log x} \right)}^2}}}$$
  • True
  • False
If $$ f(x) = \bigg[ \frac {a+x}{1+x} \bigg]^{a+1+2x} $$ then $$ {a^{a+1}} \bigg [ 2 \ log \ a + {\frac {1-a ^2}{a}} \bigg]$$ is
  • $$ f^\prime (1) $$
  • $$ f^\prime (0) $$
  • $$ f^\prime (2) $$
  • $$ f^{\prime \prime} $$
Find $$\dfrac{dy}{dx}$$ of the function given:
$$xy = e^{(x-y)}$$
  • $$\dfrac{e^{x-y}+y}{x-e^{x-y}}$$
  • $$\dfrac{e^{x-y}+x}{e^{x-y}-y}$$
  • $$\dfrac{e^{x-y}-y}{x+e^{x-y}}$$
  • $$\dfrac{e^{x-y}-x}{e^{x-y}+y}$$
$$\dfrac{d}{{dx}}\left( {{{\sec }^2}x+{{{\mathop{\rm cosec}\nolimits} }^2}x} \right) = $$
  • $$ - 4\sec x \cdot \tan x \cdot \cos ec\,x \cdot \cot x$$
  • $$4\sec x \cdot \,\cos ec\,x$$
  • $$2\sec \,x \cdot \,\tan x - 2\cos ec\,x \cdot \cot \,x$$
  • $$2{\sec ^2} \cdot \tan x - 2{{\mathop{\rm cosec}\nolimits} ^2}x \cdot \cot x$$
Function f(x)=$$\left| {x - 2} \right| - 2\left| {x - 4} \right|\,is$$ discontinous at:
  • $$x=2,4$$
  • $$x=2$$
  • No where
  • Except $$x=2$$
Differentiate with respect to $$x$$.
$${x^{\cos x}} + \sin {x^{\tan x}}$$
  • $$x^{\cos x}\left[\dfrac {\cos x}{x}-\sin x\right]+\sin x^{\tan x}[1+\sec^2x.\log \sin x]$$
  • $$x^{\cos x}\left[\dfrac {\cos x}{x}-\sin x.\log x\right]+\sin x^{\tan x}[1+\sec^2x.\log \sin x]$$
  • $$x^{\cos x}\left[ {\cos x}-\sin x.\log x\right]+\sin x^{\tan x}[1+\sec x.\log \sin x]$$
  • None
Differentiate $${x^{\tan x}} + {{\mathop{\rm tanx}\nolimits} ^x}$$ with respect to $$x$$
  • $$x^{\tan x}(\sec^2x \log x+\dfrac{\tan x}{x})+\tan x^x(\log \tan x+\dfrac{2}{\sin 2x})$$
  • $$x^{\tan x}(\sec^2x \log \sec x+\dfrac{\tan x}{x})+\tan x^x(\log \tan x+\dfrac{2}{\sin 2x})$$
  • $$x^{\tan x}(\sec^2x \log x+\dfrac{\tan x}{x})-\tan x^x(\log \tan x+\dfrac{2}{\sin 2x})$$
  • $$x^{\tan x}(\sec^2x \log x+\dfrac{\tan x}{x})+\tan x^x(\log \tan x-\dfrac{2}{\sin 2x})$$
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers