If $$y=e^{\sin^{2}x +\sin^{4}x + \sin ^{6}x +....+\infty} $$ , then $$\dfrac {dy}{dx} =?$$

$$2~\tan x~\sec^2x~e^{\tan^2~x}$$

MCQ Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 16

$\lim _ { x \rightarrow 0 } \int _ { 0 } ^ { x } \dfrac { \left( \tan ^ { - 1 } t \right) ^ { 2 } } { \sqrt { 1 + x ^ { 2 } } } d t$ is equal to

0%
$\pi ^ { 2 }$
0%
$\dfrac { \pi ^ { 2 } } { 2 }$
0%
$\dfrac { \pi ^ { 2 } } { 4 }$
0%
None of these

$x = 3\cos \theta - 2\cos^{3} \theta$ and

$y = 3\sin \theta - 2\sin^{3}\theta$ , then

$\dfrac {dy}{dx} =$

0%
$\sin \theta$
0%
$\cos \theta$
0%
$\tan \theta$
0%
$\cot \theta$

the value of

$\underset { x\longrightarrow \infty }{ lim } \frac { { X }^{ 4 }sin\left( \frac { 1 }{ x } \right) +{ x }^{ 3 } }{ 1+\left| x \right| ^{ 3 } }$

0%
1
0%
-1
0%
2
0%
does not exist

$y=e^{\sin^{2}x +\sin^{4}x + \sin ^{6}x +....+\infty}$ , then

$\dfrac {dy}{dx} =?$

0%
$2~\tan x~\sec^2x~e^{\tan^2~x}$
0%
$2~\sec^2x~e^{\tan^2~x}$
0%
$\sec^2x~e^{\tan^2~x}$
0%
$\tan x~\sec x~e^{\tan^2~x}$

$\underset { x\rightarrow 1 }{ lim } { \left[ cosec { \dfrac { \pi x }{ 2 } } \right] }^{ { 1 }/{ \left( 1-x \right) } }$ (where

$[.]$ represents the greatest integer function) is equal to

0%
$0$
0%
$1$
0%
$\infty$
0%
$Does \ not \ exist$

$\lim _{ x\rightarrow 0 }{ \dfrac { 1-\cos { x } }{ { { x\log { (1+x) } } } } }$ =

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

$\alpha$ and

$\beta$ be the roots of the equation

$ax^{2} + bx + c = 0$ then

$\displaystyle \lim_{x\rightarrow \dfrac {1}{\alpha}} \sqrt {\dfrac {1 - \cos^{2} (cx^{2} + bx + a)}{4(1 - \alpha x)^{2}}}$

0%
Does not exist
0%
Equals $\left |\dfrac {c}{2\alpha} \left (\dfrac {1}{\alpha} +\dfrac {1}{\beta}\right )\right |$
0%
Equals $\left |\dfrac {c}{2\alpha} \left (\dfrac {1}{\alpha} - \dfrac {1}{\beta}\right )\right |$
0%
Equals $\left |\dfrac {c}{2} \left (\dfrac {1}{\alpha} +\dfrac {1}{\beta}\right )\right |$

The value of

$\begin{matrix} lim \\ x\rightarrow \frac { 1 }{ \sqrt { 2 } } \end{matrix}\dfrac { x-cos\left( { sin }^{ -1 }x \right) }{ 1-tan\left( { sin }^{ -1 }x \right) } is$

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

$\overset {lim}{x \rightarrow \pi/2} \dfrac{\sin(x \ cos x)}{cos(x\, \ sin x)}$ is equal to

0%
$1$
0%
$\dfrac{\pi}{2}$
0%
$\dfrac{2}{\pi}$
0%
does not exist

$\underset { x\rightarrow 0 }{ lim } \dfrac { sec4x-sec2x }{ sec3x-secx } =$

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

$\cfrac { d }{ dx } \left( 3\cos { \left( \cfrac { \pi }{ 6 } +{ x }^{ 0 } \right) } -4\cos ^{ 3 }{ \left( \cfrac { \pi }{ 6 } +{ x }^{ 0 } \right) } \right) =....\quad$

0%
$\cos { \left( 3{ x }^{ 0 } \right) }$
0%
$\cfrac { \pi }{ 60 } \sin { \left( 3{ x }^{ 0 } \right) }$
0%
$\cfrac { \pi }{ 60 } \cos { \left( 3{ x }^{ 0 } \right) }$
0%
$-\cfrac { \pi }{ 60 } \sin { \left( 3{ x }^{ 0 } \right) }$

Explanation

we know that

$cos(3x)=4cos^3x-3cosx$

$\cfrac { d }{ dx } \left( -\cos { 3\left( \cfrac { \pi }{ 6 } +{ x }^{ 0 } \right) } \right)$

$=\cfrac { d }{ dx } \left( -\cos { \left( \cfrac { \pi }{ 2 } +3{ x }^{ 0 } \right) } \right)$

$=\cfrac { d }{ dx } \left( \sin { 3x\cfrac { \pi }{ 180 } } \right)$

$=\cfrac { 3\pi }{ 180 } \cos { \left( 3{ x }^{ 0 } \right) } \quad$

$=\cfrac { \pi }{ 60 } \cos { \left( 3{ x }^{ 0 } \right) }$

Value of

$L=\displaystyle\lim_{n\rightarrow \infty n}\dfrac{1}{4}\left[1.\left(\displaystyle\sum_{k=1}^{n}k\right)+2.\left(\sum_{k=1}^{n-1}k\right)+3.\left(\sum_{k=1}^{n-2}k\right)+...+n.1\right]$ is

0%
$1/24$
0%
$1/12$
0%
$1/6$
0%
$1/3$

$y=4^{log2sinx}+9^{log3cosx}$ then

$\frac{dy}{dx}$ =

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

Let

$\displaystyle x^{cos\,y} + y^{cox\,x} = 5$ , Then

0%
$at x = 0 , y =0 ,{y}' =0$
0%
$at x = 0 , y = 1 , {y}' = 0$
0%
$at x = y , y = 1 , {y}' = -1$
0%
$at x = 1 , y = 0 , {y}' = 1$

The value of

$\displaystyle \lim_{n\infty}\dfrac{1}{n^2}\left\{ sin^3\dfrac{\pi}{4n}+2sin^3\dfrac{2\pi}{4n} + ... + nsin^3\dfrac{n\pi}{4n}\right\}$ is equal to

0%
$\dfrac{\sqrt{2}}{9\pi^2}(52-15 \pi )$
0%
$\dfrac{2}{9\pi^2}(52-15n)$
0%
$\dfrac{1}{9\pi^2}(15n-15)$
0%
None of these

$\displaystyle \lim _{x \rightarrow 0} \dfrac{x^{n}-\sin x^{n}}{x-\sin ^{n} x}$ is non-zero finite, then

$n$ must be equal

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

$L=\displaystyle \lim _{x \rightarrow 0} \dfrac{\sin x+a e^{x}+b e^{-x}+c \ln (1+x)}{x^{3}}=\infty$

Equation

$a x^{2}+b x+c=0$ has

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real and equal roots
0%
complex roots
0%
unequal positive real roots
0%
unequal roots

$\displaystyle \lim _{x \rightarrow \infty} \dfrac{2+2 x+\sin 2 x}{(2 x+\sin 2 x) e^{\sin x}}$ is equal to

0%
0
0%
1
0%
-1
0%
Does not exists

$\displaystyle \lim _{x \rightarrow \pi / 2} \dfrac{\sin (x \cos x)}{\cos (x \sin x)}$ is equal to

0%
0
0%
p/2
0%
p
0%
2p

The value of

$\displaystyle \lim _{x \rightarrow 0} \dfrac{\sqrt{\dfrac{1}{2}(1-\cos 2 x)}}{x}$ is

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

Solution of the equation

$\dfrac {dy }{dx} + \dfrac {1}{x} \tan y = \dfrac {1}{x^2} \tan y \sin y$ is

0%
$2x = sin y ( x )$
0%
$2x =sin y ( 1 +cx^2)$
0%
$2x +sin y ( 1 +cx^2 )$
0%
None of these

CBSE Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 16 - 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 16 - MCQExams.com

0:0:1

Practice Class 11 Engineering Maths Quiz Questions and Answers

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