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CBSE Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 10 - MCQExams.com

Differentiate the following function with respect to x.
(2x23)sinx.
  • 4xsinx+(2x2+3)cosx.
  • 4xsinx+(2x23)sinx.
  • 4xsinx+(2x23)cosx.
  • 4xcosx+(2x23)cosx.
If f is differentiable at x=1 and lim
  • 0
  • 1
  • 3
  • 4
  • 5
If y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+}}}.....\infty then \dfrac{dy}{dx}=?
  • \dfrac{\sin x}{(2y-1)}
  • \dfrac{\cos x}{(y-1)}
  • \dfrac{\cos x}{(2y-1)}
  • none\ of\ these
If y=(\tan x)^{\cot x} then \dfrac{dy}{dx}=?
  • \cot x.(\tan x)^{\cot x-1}.\sec^2x
  • -(\tan x)^{\cot x}.\csc^2x
  • (\tan x)^{\cot x}.\csc^2 x(1-\log \tan x)
  • none\ of\ these
If y=\sqrt{x\sin x} then \dfrac{dy}{dx}=?
  • \dfrac{(x\cos x+\sin x)}{2\sqrt{x\sin x}}
  • \dfrac{1}{2}(x\cos x+\sin x).\sqrt{x\sin x}
  • \dfrac{1}{2\sqrt{x\sin x}}
  • none\ of\ these
If x=a(\cos\theta+\theta\sin\theta) and y=a(\sin\theta-\theta\cos\theta) then \dfrac{dy}{dx}=?
  • \cot\theta
  • \tan\theta
  • a\cot\theta
  • a\tan\theta
If x=a\sec\theta, y=b\tan\theta then \dfrac{dy}{dx}=
  • \dfrac{b}{a}\sec\theta
  • \dfrac{b}{a} \ cosec\theta
  • \dfrac{b}{a}\cot\theta
  • none\ of\ these
If y=\sqrt{\dfrac{1+\sin x}{1-\sin x}} then \dfrac{dy}{dx}=?
  • \dfrac{1}{2}\sec^2\left(\dfrac{\pi}{4}-\dfrac{x}{2}\right)
  • \dfrac{1}{2}\csc^2\left(\dfrac{\pi}{4}-\dfrac{x}{2}\right)
  • \dfrac{1}{2}\csc \left(\dfrac{\pi}{4}-\dfrac{x}{2}\right)\cot \left(\dfrac{\pi}{4}-\dfrac{x}{2}\right)
  • none\ of\ these
If \lim _{ x\rightarrow 0 }{ \cfrac { x\left( 1+a\cos { x }  \right) -b\sin { x }  }{ { x }^{ 3 } }  } =1 then
  • a=-5/2, b=-1/2
  • a=-3/2, b=-1/2
  • a=-3/2, b=-5/2
  • a=-5/2, b=-3/2
The value of \displaystyle \lim _{x \rightarrow \pi} \dfrac{1+\cos ^{3} x}{\sin ^{2} x}  is
  • 1/3
  • 2/3
  • -1/4
  • 3/2
If \displaystyle {f}'(x) = sin\,x + sin\,4x .\, cos \,x then \displaystyle {f}'(x) \left (2x^{2} + \dfrac{\pi}{2} \right ) at x = \sqrt{\dfrac{\pi}{2}} is equal to 
  • -1
  • 0
  • \displaystyle -2\sqrt{2\pi}
  • None of these
If \displaystyle sin\, y = x\, sin ( a + y) and
\displaystyle \dfrac{dy}{dx} = \dfrac{A}{ 1 + x^{2} - 2x \, cos a } then the value of A is
  • 2
  • cos\, a
  • sin\,a
  • None of these
\displaystyle \lim _{x \rightarrow 0} \dfrac{\sin x^{n}}{(\sin x)^{m}},(m<n)  is equal to
  • 1
  • 0
  • n/m
  • None of these
  The \ value \ of  \displaystyle \lim _{x \rightarrow 1}(2-x)^{\tan \dfrac{\pi x}{2}}  is
  • e^{-2 \pi}
  • e^{1 / \pi}
  • e^{2 /\pi}
  • e^{-1 / \pi}
\displaystyle \lim _{x \rightarrow 0} \dfrac{x\left(e^{x}-1\right)}{1-\cos x}  is equal to
  • 0
  • \infty
  • -2
  • 2
\displaystyle \lim _{x \to \pi / 2}\left[x \tan x-\left(\dfrac{\pi}{2}\right) \sec x\right]  is equal to 
  • 1
  • -1
  • 0
  • None \ of \ these
\displaystyle \lim _{x \rightarrow-\infty} \dfrac{x^{2} \tan \dfrac{1}{x}}{\sqrt{8 x^{2}+7 x+1}}  is equal to
  • -\dfrac{1}{2 \sqrt{2}}
  • \dfrac{1}{2 \sqrt{2}}
  • \dfrac{1}{\sqrt{2}}
  • Does not exist
 \displaystyle \lim _{x \rightarrow 0} \dfrac{x^{4}\left(\cot ^{4} x-\cot ^{2} x+1\right)}{\left(\tan ^{4} x-\tan ^{2} x+1\right)}  is equal to
  • 1
  • 0
  • 2
  • None of these
If f(x)=\dfrac{\cos x}{(1-\sin x)^{1 / 3}},  then
  • \lim _{ x\rightarrow \dfrac { \pi^- }{2 } }{ f(x)=-\infty }
  • \lim _{ x\rightarrow \dfrac { \pi^+ }{2 } }{ f(x)=\infty }
  • \lim _{ x\rightarrow \dfrac { \pi }{2 } }{ f(x)=\infty }
  • none of these
\displaystyle \lim _{x \rightarrow 0} \dfrac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^{2}}  is equal to
  • 2
  • -2
  • 1/2
  • -1/2
\displaystyle  \lim _{x \rightarrow 1} \dfrac{1+\sin \pi\left(\dfrac{3 x}{1+x^{2}}\right)}{1+\cos \pi x}  is equal to
  • 0
  • 1
  • 2
  • 4
\displaystyle \lim _{x \rightarrow 1} \dfrac{1-x^{2}}{\sin 2 \pi x} \text { is equal to }
  • \dfrac{1}{2 \pi}
  • \dfrac{-1}{\pi}
  • \dfrac{-2}{\pi}
  • None of these
Let f(x)= \sin x+ax+b, then which of the following is/are true.
  • f(x)=0 has on;ly one root which is possitive if a>1, b<0
  • f(x)=0 has on;ly one root which is negative if a>1, b<0
  • f(x)=0 has on;ly one root which is negaitive if a < -1, b<0
  • None of these
The value of \displaystyle \lim _{x \rightarrow a} \sqrt{a^{2}-x^{2}} \cot \dfrac{\pi}{2} \sqrt{\dfrac{a-x}{a+x}}  is
  • \dfrac{2 a}{\pi}
  • -\dfrac{2 a}{\pi}
  • \dfrac{4 a}{\pi}
  • -\dfrac{4 a}{\pi}
Which of the following is not true about y=f(x)?
  • It is an increasing function
  • It is a monotonic function
  • It has infinite points of inflections
  • None of these
\displaystyle \lim _{n \rightarrow \infty} \sum_{x=1}^{20} \cos ^{2 n}(x-10)  is equal to
  • 0
  • 1
  • 19
  • 20
\displaystyle  \lim _{x \rightarrow 0} \dfrac{\sin \left(x^{2}\right)}{\ln \left(\cos \left(2 x^{2}-x\right)\right)}  is equal to
  • 2
  • -2
  • 1
  • -1
Differential coefficient of \sec (\tan^{-1} x) w.r.t. x is
  • \dfrac{x}{\sqrt{1+x^2}}
  • \dfrac{x}{1+x^2}
  • x\sqrt{1+x^2}
  • \dfrac{1}{\sqrt{1+x^2}}
The value of \displaystyle \lim_{x\rightarrow \infty} \dfrac {\sin x}{x} is
  • 0
  • \infty
  • 1
  • -1
The value of \displaystyle \lim_{x\rightarrow 0} \dfrac {1 - \cos x}{x^{2}} is
  • 0
  • 1/2
  • -1/2
  • -1
0:0:1


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