CBSE Questions for Class 11 Commerce Applied Mathematics Differentiation Quiz 12 - MCQExams.com

The differential of $$f(x)=\sqrt{\dfrac{2-x}{2+x}}$$ at $$x=0$$ and $$\delta x=0.15$$ is
  • $$0.07$$
  • $$0.075$$
  • $$-0.075$$
  • $$0.15$$
Let $$f:[0,2]\rightarrow R$$ be a twice differentiable function such that $$f"(x)>0$$, for all $$x\in (0,2)$$ If $$\phi (x)=f(x)+f(2-x)$$, then $$\phi$$is:
  • decreasing on $$(0,2)$$
  • decreasing on $$(0,1)$$ and increasing on $$(1,2)$$
  • increasing on $$(0,2)$$
  • increasing on $$(0,1)$$ and decreasing on $$(1,2)$$
If $$f(x)=|\cos x-\sin x|$$, then $$f'\left(\dfrac{\pi}{6}\right)$$ equal to?
  • $$-\dfrac{1}{2}(1+\sqrt{3})$$
  • $$\dfrac{1}{2}(1+\sqrt{3})$$
  • $$-\dfrac{1}{2}(1-\sqrt{3})$$
  • $$\dfrac{1}{2}(1-\sqrt{3})$$
For the curve $$\sqrt{x}+\sqrt{y}=1,\ \dfrac{dy}{dx}$$ at $$(1/4,1/4)$$ is
  • $$1/2$$
  • $$1$$
  • $$-1$$
  • $$2$$
If $$y^{2}=ae^{-2x}+(2/5)(cosx-2sinx)$$  then 
$$y\dfrac{dy}{dx}+y^{2}+sinx $$   is equal to 
  • -1
  • 1
  • 0
  • none of these
If $$x+y=\sin(x+y)$$, then $$\dfrac{dy}{dx}=$$
  • $$\dfrac{1}{2}$$
  • $$0$$
  • $$-1$$
  • $$\dfrac{1}{3}$$
The solution of $$\dfrac{dy}{dx} = 1+x+y+xy$$ is
  • $$\log (1-y) = x+\dfrac{x^3}{2} + C$$
  • $$\log (1+y) = x-\dfrac{x^2}{2} + C$$
  • $$\log (1+y) = x+\dfrac{x^2}{2} + C$$
  • none of these
If  $$y ( x ):$$  Solution of a  $$D.E.$$

$$( x \log x ) \dfrac { d y } { d x } + y = 2 x \log x,$$   $$( x , 1 )$$
$$y ( e ) = ? \quad x = e$$
  • $$e$$
  • $$ 0$$
  • $$ 2$$
  • $$ 2e$$
If $$y^{2}+16=2xy$$, then which of the following is not the value of $$y'(5)$$?
  • $$-\dfrac {2}{3}$$
  • $$\dfrac {8}{3}$$
  • $$\dfrac {5}{3}$$
  • None of these
If $$xlog_e(log_ex)-x^2+y^2=4(y>0)$$, then dy/dx at $$x=e$$ is equal to:
  • $$\dfrac{e}{\sqrt{4+e^2}}$$
  • $$\dfrac{1+2e}{2\sqrt{4+e^2}}$$
  • $$\dfrac{2e-1}{2\sqrt{4+e^2}}$$
  • $$\dfrac{1+2e}{\sqrt{4+e^2}}$$
For  $$x > 1 ,$$  if  $$( 2 x ) ^ { 2 y } = 4 e ^ { 2 x - 2 y } ,$$  then   $$\left( 1 + \log _ { \mathrm { e } } 2 \mathrm { x } \right) ^ { 2 } \dfrac { \mathrm { dy } } { \mathrm { dx } }$$  is equal to :
  • $$\log _ { e } 2 x$$
  • $$\dfrac { x \log _ { e } 2 x + \log _ { e } 2 } { x }$$
  • $$x \log _ { e } 2 x$$
  • $$\dfrac { x \log _ { e } 2 x - \log _ { e } 2 } { x }$$
Let $$y={ t }^{ 10 }+1$$, and $$x={ t }^{ 8 }+1$$, then $$\dfrac { { d }^{ 2 }y }{ { dx }^{ 2 } } $$ is 
  • $$\dfrac { 5 }{ 2 } t$$
  • $$20{ t }^{ 8 }$$
  • $$\dfrac { 5 }{ 16{ t }^{ 6 } } $$
  • $$\dfrac { 15 }{ 16{ t }^{ 6 } } $$
Find $$f^{\prime} (3) $$ if $$f(x)=x^3+5x^2-3x+5$$
  • $$28$$
  • $$54$$
  • $$32$$
  • None 
If $$ y = \sin ^ { - 1 } x$$ then $$ \frac { d y } { d x } $$ is equal to 
  • $$\sec y$$
  • $$\cos x$$
  • $$\tan x$$
  • $$1$$
If $$y=e^{\sin x }$$, then find $$\dfrac{dy}{dx}$$
  • $$e^{\sin x}{\cos x}$$
  • $$e^{\sin x}$$
  • $$e^{\cos x}$$
  • $$e^{\sin x \cos x}$$
If $${ (f\left( x \right) ) }^{ g(y) }={ e }^{ f\left( x \right)-g(y) }$$ then $$\frac { dy }{ dx } $$
  • $$\frac { { f }^{ \prime }(x)\log { f } (x) }{ g(y){ (1+\log { f } (x)) }^{ 2 } } $$
  • $$\frac { { f }^{ \prime }(x)\log { f } (x) }{ { g }^{ 1 }(y){ (1+\log { f } (x)) }^{ 2 } } $$
  • $$\frac { { f }(x)\log { f } (x) }{ { g }^{ \prime }(y){ (1-\log { f } (x)) }^{ 2 } } $$
  • $$2\frac { { f }^{ \prime }(x)\log { f } (x) }{ g(y){ (1+\log { f } (x)) }^{ 2 } } $$
The derivative of $$\tan^{-1} \left (\dfrac {\sin x - \cos x}{\sin x + \cos x}\right )$$, with respect to $$\dfrac {x}{2}$$, where $$\left (x \epsilon \left (0, \dfrac {\pi}{2}\right )\right )$$ is
  • $$\dfrac {1}{2}$$
  • $$\dfrac {2}{3}$$
  • $$1$$
  • $$2$$
Differentiate the following function with respect to x.
$$x^n\tan x$$.
  • $$x^{n-1}(n \tan x+x\sec x)$$.
  • $$x^{n-1}(n \tan x+x\sec^2x)$$.
  • $$x^{n-1}(n \tan x+\sec^2x)$$.
  • $$x^{n-1}(n \tan x+x\sec^{-2}x)$$.
Differentiate the following function with respect to x.
$$x^3e^x$$.
  • $$x^2e^x(x)$$.
  • $$e^x(3+x)$$.
  • $$x^2(3+x)$$.
  • $$x^2e^x(3+x)$$.
Differentiate the following function with respect to x.
$$(2x^2+1)(3x+2)$$.
  • $$9x^2+4x+3$$.
  • $$18x^2-8x-3$$.
  • $$9x^2-4x-3$$.
  • $$18x^2+8x+3$$.
Differentiate the following function with respect to x.
$$\dfrac{x^3}{3}-2\sqrt{x}+\dfrac{5}{x^2}$$.
  • $$x^2-x^{-1/2}-5x^{-3}$$.
  • $$x^2-x^{-1/2}-10x^{-3}$$.
  • $$x^2-x^{-1/2}+5x^{-3}$$.
  • $$-x^2+x^{-1/2}+10x^{-3}$$.
Differentiate the following function with respect to x.
$$x^2e^xlog x$$.
  • $$xe^x(x log x+2 log x)$$.
  • $$xe^x(1+2 log x)$$.
  • $$xe^x(1+x log x)$$.
  • $$xe^x(1+x log x+2 log x)$$.
Differentiate the following function with respect to x.
$$3^x+x^3+3^3$$.
  • $$3^xlog 3+3x^2$$.
  • $$3^xlog 3+3x$$.
  • $$3^xlog 3+x^2$$.
  • $$xlog 3+3x^2$$.
Let $$x^k+y^k=a^k,(a,k > 0)$$ and 
$$\dfrac{dy}{dx}+\left(\dfrac{y}{x}\right)^{1/3}=0$$, then $$k$$ is :
  • $$\dfrac{1}{3}$$
  • $$\dfrac{2}{3}$$
  • $$\dfrac{4}{3}$$
  • $$\dfrac{3}{2}$$
Differentiate the following function with respect to x.
$$\sin x\cos x$$.
  • $$2\cos 2x$$.
  • $$\dfrac {\cos 2x}{2}$$.
  • $$\cos 2x$$.
  • $$\cos x$$.
If $$ y \sqrt{x^{2}+1}=\log (\sqrt{x^{2}+1}-x), $$ then $$ \left(x^{2}+1\right) \dfrac{d y}{d x}+x y+1= $$
  • 0
  • 1
  • 2
  • None of these
 Let $$ u(x) $$ and $$ v(x) $$ be differentiable functions such that $$ \dfrac{u(x)}{v(x)}=7 . $$ If $$ \dfrac{u^{\prime}(x)}{v^{\prime}(x)}=p $$ and $$ \left(\dfrac{u(x)}{v(x)}\right)^{\prime}=q, $$ then $$ \dfrac{p+q}{p-q} $$ has the value equal to
  • $$1$$
  • $$0$$
  • $$7$$
  • $$-7$$
$$ f(x)=x^{2}+x g^{\prime}(1)+g^{\prime \prime}(2) $$ and $$ g(x)=f(1) x^{2}+x f^{\prime}(x)+f^{\prime \prime}(x) $$
The value of $$ f(3) $$ is
  • 1
  • 0
  • -1
  • -2
lf $${f}'({x})={g}({x})$$ and $${g}'({x})=-{f}({x})$$ for all $$x$$ and $${f}(2)=4= {g}(2)$$, then $${f}^{2}(24)+{g}^{2}(24)$$ is
  • $$32$$
  • $$24$$
  • $$64$$
  • $$48$$
Assertion(A): Let $${ f }({ x })$$ be twice differentiable function such that $$f^{ '' }(x)=-{ f }({ x })$$ and $$f^{ ' }(x)={ g }({ x })$$. lf $${ h }({ x })=[{ f }({ x })]^{ 2 }+[{ g }({ x })]^{ 2 }$$ and $${ h }(1)=8$$, then $${ h }(2)=8$$

Reason (R): Derivative of a constant function is zero.
  • Both A and R are true R is correct reason of A
  • Both A and R are true R is not correct reason of A
  • A is true but R is false
  • A is false but R is true
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers