MCQ Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 15

$\displaystyle\underset{x\rightarrow \dfrac{\pi}{4}}{Lt}\dfrac{\sqrt{2}-\cos x-\sin x}{(4x-\pi)^2}=?$

0%
$\dfrac{1}{16\sqrt{2}}$
0%
$\dfrac{1}{32\sqrt{2}}$
0%
$\dfrac{1}{16}$
0%
$\dfrac{1}{8}$

$\lim _{x \rightarrow 0} \frac{1-\cos ^{3} x}{x \sin 2 x}=$

0%
1 $/ 2$
0%
3 $/ 2$
0%
3 $/ 4$
0%
1 $/ 4$

The value of

$\underset { x\rightarrow 0 }{ lim } \left( \left( sinx \right) ^{ 1/x }+\left( \dfrac { 1 }{ x } \right) ^{ sinx } \right)$ equals

0%
0
0%
1
0%
$\infty$
0%
-1

$\lim _ { x \rightarrow 0 } \frac { \ln ( \sin 3 x ) } { \ln ( \sin x ) }$ is equal to

0%
0
0%
1
0%
2
0%
none of these

$\underset { x\rightarrow 0 }{ lim } \dfrac { 1 }{ { e }^{ 2 } } tan\left( \dfrac { \pi }{ 4 } +x \right) ^{ 1/x }$

0%
0
0%
1
0%
-1
0%
e

The value of

$\theta ,\quad is$

$\underset { o\rightarrow o }{ lim } \quad \frac { { cos }^{ 2 }\left\{ 1-{ cos }^{ 2 }\quad \left( 1-{ cos }^{ 2 }\quad .....\left( { cos }^{ 2 }\left\{ 1-{ cos }^{ 2 }\theta \right\} \right) \right) \right\} }{ sin\left( \frac { \pi (\sqrt { \theta +4 } -2 }{ \theta } \right) }$

0%
$\frac { \sqrt { 2 } }{ 4 }$
0%
$\sqrt { 2 }$
0%
1
0%
2

$\lim _{ x\rightarrow \infty }{ \frac { \sin { x } \sin { (\frac { \pi }{ 3 } +x) } \sin { (\frac { \pi }{ 3 } -x) } }{ x } } =$

0%
$\frac { 3 }{ 4 }$
0%
$\frac { 1 }{ 4 }$
0%
$\frac { 4 }{ 3 }$
0%
$0$

$\alpha , \beta , \ in (-\frac{\pi}{2},0)$ such that

$(sin \alpha +sin \beta ) +\frac{sin \alpha }{sin \beta} =0$ and

$(sin \alpha +sin \beta ) \frac{sin \alpha}{sin \beta }=-1$ and

$\lambda =\begin{matrix} lim \\ n\rightarrow \infty \end{matrix}\frac { 1+(2sin\quad theta\quad ){ }^{ 2n } }{ (2sin\quad \quad beta\quad ){ }^{ 2n } }$ then

0%
$2 \alpha +3 \beta = \frac{-5 \pi }{6}$
0%
$\lambda \pi +\alpha +\beta =\frac{5 \pi}{6}$
0%
$\alpha - \beta = \frac{ \pi }{3}$
0%
$\alpha + \beta = \frac{- \pi }{3}$

$\cfrac { d }{ dx } \left( \sin ^{ 5 }{ x } \sin { 5x } \right) =$

0%
$\left( \sin ^{ 4 }{ x } \sin { 5x } \right)$
0%
$5 \left( \sin ^{ 4 }{ x } \sin { 5x } \right)$
0%
$5 \left( \sin ^{ 4 }{ x } \sin { 6x } \right)$
0%
$-5 \left( \sin ^{ 4 }{ x } \sin { 6x } \right)$

$\lim _{ x\rightarrow 0 }{ \frac { { 27 }^{ x }-{ 9 }^{ x }-{ 3 }^{ x }+1 }{ \sqrt { 2 } -\sqrt { 1+\cos { x } } } = }$

0%
$0$
0%
$8\sqrt { 2 } { (\log { 3 } ) }^{ 2 }$
0%
$8{ (\log { 3 } ) }^{ 2 }$
0%
$1$

$\mathop {\lim }\limits_{h \to 0} \frac{{\sin \left( {a + 3h} \right) - 3\sin \left( {a + 2h} \right) + 3\sin \left( {a + h} \right) - \sin a}}{{{h^3}}}$ is equal to

0%
$\cos a$
0%
$- \cos a$
0%
$\sin a$
0%
$\sin a\cos a$

$L\underset { x\rightarrow \infty }{ im } \left( \sin { \sqrt { x+1 } -\sin { \sqrt { x } } } \right) =$

0%
2
0%
-2
0%
0
0%
1

$\lim _{ x\rightarrow }{ 0 } \{ (sinx-x)/{ x }^{ 3 })\}$ equals:

0%
$1/3$
0%
$-1/3$
0%
$1/6$
0%
$-1/6$

Solve

$\underset { x\rightarrow 0 }{ Lim } \frac { 8 }{ { x }^{ 8 } } \left( 1-cos\frac { { x }^{ 2 } }{ 2 } -cos\frac { { x }^{ 2 } }{ 4 } +cos\cfrac { { x }^{ 2 } }{ 2 } .cos\cfrac { { x }^{ 2 } }{ 4 } \right) =$

0%
$\cfrac { 1 }{ 16 }$
0%
$\cfrac { 1 }{ 15 }$
0%
$\cfrac { 1 }{ 32 }$
0%
$1$

$\mathop {\lim }\limits_{x \to \pi /2} \left[ {x\tan x - \left( {\frac{\pi }{2}} \right)\sec x} \right]$ is equal to

0%
1
0%
-1
0%
0
0%
None of these

$\lim _ { x \rightarrow 0 } \frac { \sin x } { x } = y$

0%
$y > 1$
0%
$y < 1$
0%
$y \geq 1$
0%
$y \leq 1$

The value of

$\mathop {{\text{Limit}}}\limits_{x \to 0} \frac{{\cos \left( {\sin x} \right) - \cos x}}{{{x^4}}}$ is equal to

0%
1/5
0%
1/6
0%
1/4
0%
1/2

$\underset { x\rightarrow 0 }{ lim } \cfrac { 8 }{ { x }^{ 8 } } \left( 1-cos\cfrac { { x }^{ 2 } }{ 2 } -cos\cfrac { { x }^{ 2 } }{ 4 } +cos\cfrac { { x }^{ 2 } }{ 2 } .cos\cfrac { { x }^{ 2 } }{ 4 } \right) =$

0%
$\cfrac { 1 }{ 16 }$
0%
$\cfrac { 1 }{ 15 }$
0%
$\cfrac { 1 }{ 32 }$
0%
$1$

$\displaystyle \lim _{ x\rightarrow 0 }{ \left[ \dfrac { 100\tan { x } .\sin { x } }{ { x }^{ 2 } } \right] }$ where

$[.]$ represents greatest integer function is

0%
$99$
0%
$100$
0%
$0$
0%
$98$

The value of

$\lim _ { x \rightarrow \dfrac { 1 } { 2 } } \dfrac { 2 \sin ^ { - 1 } x - \dfrac { \pi } { 2 } } { 1 - 2 x ^ { 2 } }$ is equal to

0%
$-1$
0%
$0$
0%
$1$
0%
$2$

The value of

$\lim _ { x \rightarrow 0 } \dfrac { \sin^3 ( \sqrt { x } ) \ln ( 1 + 3 x ) } { \left( \tan ^ { - 1 } \sqrt { x } \right) ^ { 2 } \left( e ^ { 5 ( \sqrt { x } ) } - 1 \right)x }$ is equal to

0%
$\frac { 1 } { 5 }$
0%
$\frac { 3 } { 5 }$
0%
$\frac { 2 } { 5 }$
0%
$\frac { 4 } { 5 }$

The value of

$\lim _{ x\rightarrow \frac { \pi }{ 2 } }{ \tan ^{ 2 }{ \left( \sqrt { 2\sin ^{ 2 }{ x } +3\sin { x } +4 } -\sqrt { \sin ^{ 2 }{ x } +6\sin { x } +2 } \right) } }$ is equal to

0%
0
0%
$\cfrac{1}{11}$
0%
$\cfrac{1}{12}$
0%
$\cfrac{1}{8}$

If x sin

$(\alpha +y)=siny\quad and\quad y'\quad =\quad \frac { m }{ \left( { x }^{ 2 }+ \right) nx+ } ,$ then

0%
m-n=1
0%
m+n=1
0%
${ m }^{ 2 }+{ n }^{ 2 }=1$
0%
m=n

$\mathop {\lim }\limits_{x \to \infty } \left( {\dfrac{{{x^2}\sin \left( {\dfrac{1}{x}} \right) - x}}{{1 - \left| x \right|}}} \right) =$

0%
0
0%
1
0%
-1`
0%
2

$\mathop {Lt}\limits_{x \to 1} {\left( {1 - x} \right)^{\tan \pi x}} =$

0%
$-1$
0%
$0$
0%
$1$
0%
$2$

Let

$a \in \left( 0 , \frac { \pi } { 2 } \right)$ , then the value of

$\lim _ { a \rightarrow 0 } \frac { 1 } { a ^ { 3 } } \int _ { 0 } ^ { a } \ell n (1+tan a tan x)dx$ is equal to

0%
$\frac { 1 }{ 3 }$
0%
$\frac { 1 }{ 2 }$
0%
$\frac { 1 }{ 6 }$
0%
1

Find:

$\underset { x\rightarrow 0 }{ lim } \quad \dfrac { 1-cos^{ 3 }x }{ xsin2x } =\quad$

0%
1/2
0%
3/2
0%
3/4
0%
1/4

$\underset { \rightarrow }{ Lim } \frac { 1-{ cos }^{ 2 }x }{ xsin2x }$

0%
1/2
0%
3/2
0%
3/4
0%
1/4

The value of

$\mathop {\lim }\limits_{x \to 0} \frac{{\sec 5x - \sec 3x}}{{\sec 3x - \sec x}}$

0%
-2
0%
1
0%
2
0%
-1/2

$y=\sec { \left( \tan ^{ -1 }{ x } \right) }$ then at

$x=1$ value of

$\dfrac { dy }{ dx }$ equals :

0%
$\dfrac { 1 }{ 2 }$
0%
1
0%
$\sqrt {2 }$
0%
$\dfrac { 1 }{ \sqrt {2 } }$

CBSE Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 15 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

CBSE Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 15 - MCQExams.com

0:0:4

Practice Class 11 Engineering Maths Quiz Questions and Answers

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