MCQ Questions for Class 11 Commerce Applied Mathematics Limits And Continuity Quiz 11

The value of

$\underset { x\rightarrow 0 }{ lim } \frac { { 27 }^{ x }-{ 9 }^{ x }{ -3 }^{ x }+1 }{ \sqrt { 5 } -\sqrt { 4+cos\quad x } }$

0%
$\sqrt { 5 } { \left( log3 \right) }^{ 2 }$
0%
$8\sqrt { 5 } log3$
0%
$16\sqrt { 5 } log3$
0%
$8\sqrt { 5 } { \left( log3 \right) }^{ 2 }$

$\lim _ { x \rightarrow 0 } \dfrac { \sin 4 x } { \tan 7 x } =$

0%
$1$
0%
$\dfrac { 4 } { 7 }$
0%
$\dfrac { 7 } { 4 }$
0%
$0$

The value of

$\underset { x\rightarrow 0 }{ lim } \frac { { 27 }^{ x }-{ 9 }^{ x }-{ 3 }^{ x }+1 }{ \sqrt { 5 } -\sqrt { 4+cosx } }$ is

0%
$\sqrt { 5 } { \left( log3 \right) }^{ 2 }$
0%
$8\sqrt { 5 } log3$
0%
$16\sqrt { 5 } log3$
0%
$8\sqrt { 5 } { \left( log3 \right) }^{ 2 }$

$\displaystyle \lim _ { x \rightarrow 0 } \dfrac { | \cos ( \sin ( 3 x ) ) | - 1 } { x ^ { 2 } }$ equals

0%
$\dfrac { - 9 } { 2 }$
0%
$\dfrac { - 3 } { 2 }$
0%
$\dfrac { 3 } { 2 }$
0%
$\dfrac { 9 } { 2 }$

$\displaystyle\lim_{x\rightarrow \dfrac{\pi}{4}}\dfrac{\cos x-\sin x}{\left(\dfrac{\pi}{4}-x\right)(\cos x+\sin x)}=?$

0%
$2$
0%
$1$
0%
$0$
0%
$3$

$\displaystyle\lim_{x\rightarrow 0}\left\{\dfrac{log_e(1+x)}{x^2}+\dfrac{x-1}{x}\right\}$ is equal to?

0%
$\dfrac{1}{2}$
0%
$-\dfrac{1}{2}$
0%
$1$
0%
None of these

Let [x] denote the greatest integer less than or equal to x. Then :

$\underset { x\rightarrow 0 }{ lim } \dfrac { tan\left( \pi { sin }^{ 2 }x \right) +\left( \left| x \right| -sin \right) \left( x\left[ x \right] \right) ^{ 2 } }{ { x }^{ 2 } } :$

0%
does not exist
0%
equal $\pi$
0%
equal 0
0%
equal $\pi$ + 1

$\underset { x\rightarrow \frac { \pi }{ 2 } }{ lim } \frac { cotx-cosx }{ { (\pi -2x) }^{ 3 } }$ equals :

0%
$\frac { 1 }{ 8 }$
0%
$\frac { 1 }{ 4 }$
0%
$\frac { 1 }{ 24 }$
0%
$\frac { 1 }{ 16 }$

$\displaystyle\lim _{ n\rightarrow \infty }{ { n }^{ 2 }\left( { x }^{ \dfrac { 1 }{ n } }-{ x }^{ \dfrac { 1 }{ n+1 } } \right) ,x>0 }$ is equal to

0%
$0$
0%
$e^{x}$
0%
$log_ex$
0%
$None\ of\ these$

$\displaystyle \lim _{ x\rightarrow 0 }[1+ax+bx^{2}]^{(2/x)}=e^{3}$ , then

0%
$a=3,\ b=0$
0%
$a=\dfrac{3}{2},\ b\neq1$
0%
$a=\dfrac{3}{2},\ b=R$
0%
$a=2,\ b=3$

If [.] deotes the greatest integer function then

$\begin{matrix} lim \\ x\rightarrow \pi /2 \end{matrix}\left[ \frac { x-\frac { \pi }{ 2 } }{ cosx } \right]$ is equal to

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

$\begin{matrix} lim\quad \\ x\rightarrow 0 \end{matrix}\dfrac { x\left( 1+acosx \right) -bsinx }{ { x }^{ 3 } } =1$ then value of a + b

0%
-4
0%
-6
0%
1
0%
None of these

$\displaystyle x\xrightarrow { lim } a\left(\sin\frac{x-a}{2}\tan\frac{\pi x}{2a} \right)$

0%
$\displaystyle a/\pi$
0%
$-\displaystyle a/\pi$
0%
$\displaystyle \pi/a$
0%
$-\displaystyle \pi/a$

Value of

$\underset { x\rightarrow 0 }{ lim } \dfrac { \sqrt [ 3 ]{ 1+\tan { x } } -\sqrt [ 3 ]{ 1-\tan { x } } }{ x }$ is

0%
$\dfrac { 1 }{ 2 }$
0%
$-\dfrac { 2 }{ 3 }$
0%
$\dfrac { 1 }{ 3 }$
0%
$0$

Value of

$\underset { x\rightarrow \dfrac { \pi }{ 2 } }{ lim } \tan { x } .\ell nsin{ x }$ is

0%
0
0%
$\dfrac { 1 }{ 2 }$
0%
$\dfrac { 3 }{ 4 }$
0%
None of these

The value of

$\displaystyle \lim_{x \rightarrow 0} (\sin x)^{\dfrac{1}{x}}+(1+x)^{(\sin x)})=0$ , where

$x > 0$ , is :

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

The value of

$\begin{matrix} lim \\ x\rightarrow 0 \end{matrix}$

$[\frac{x}{sinx}],$ where [.] represents the greatest inter function , is

0%
$1$
0%
$0$
0%
$-1$ `
0%
none of these

$\underset { x\rightarrow 0 }{ lim } \left( \dfrac { 1+tanx }{ 1+sinx } \right) ^{ cosecx }$ is equal to

0%
e
0%
$\dfrac { 1 }{ e }$
0%
1
0%
None of these

The value of

$\displaystyle \lim_{x\rightarrow 0}\left(\dfrac {1}{x^{2}}-\cot x\right)$ equals

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

$\underset { \theta \longrightarrow 0 }{ Lt } \dfrac { 3tan\theta -tan3\theta }{ { 2\theta }^{ 3 } } =$

0%
-4
0%
1/4`
0%
3/4
0%
4

$\underset { x\rightarrow 0 }{ Lt\quad } \frac { sec\quad x-1 }{ { \left( sec\quad x+\quad 1 \right) }^{ 2 } } =$

0%
1/8
0%
11/4
0%
3.2
0%
2

$\underset { x\rightarrow 0 }{ Lt } (1+sin\quad x)^{ cot\quad x }=$

0%
e
0%
$e^{ 2 }$
0%
$e^{ 3 }$
0%
$e^{ 4 }$

For

$a > 1$ then

$\displaystyle\lim_{x\rightarrow \infty}\dfrac{a^x-a^{-x}}{a^x+a^{-x}}=?$

0%
$1$
0%
$1/2$
0%
$1/3$
0%
$1/15$

The value of

$\lim_{h\rightarrow 0}\left\{\dfrac {1}{h.(8+h)^{1/3}-\dfrac {1}{2h}}\right\}$ equals

0%
$0$
0%
$\dfrac {-4}{3}$
0%
$\dfrac {-16}{3}$
0%
$\dfrac {-1}{48}$

$\underset { x\rightarrow 0 }{ lim } { \left( cosecx \right) }^{ \dfrac { 1 }{ logx } }$ is equal to

0%
$0$
0%
$1$
0%
$\dfrac { 1 }{ e }$
0%
None of these

$\underset { h\rightarrow 0 }{ lim } \quad \frac { (2+h)cos(2+h)-2cos2 }{ h } =$

0%
cos2-2sin2
0%
cos2+2sin2
0%
sin2-2cos2
0%
sin2+2cos2

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

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

$\lim_{x\rightarrow 1}\dfrac {1+\sin \pi\left(\dfrac {3x}{1+x^{2}}\right)}{1+\cos \pi x}$ is equal to

0%
$0$
0%
$1$
0%
$2$
0%
$4$

$lim_{x \to 0^-} \dfrac{x([x]+ \mid x \mid )sin[x]}{\mid x \mid}$ is equal to

0%
$-sin1$
0%
0
0%
1
0%
$sin1$

The value of

$\displaystyle \lim _{ x\rightarrow \infty } (|x^{2}|+x)\log{(x\cot^{-1}{x})}$ is :

0%
$\dfrac{1}{3}$
0%
$-\dfrac{1}{3}$
0%
$\dfrac{2}{3}$
0%
$-\dfrac{2}{3}$

$\displaystyle \lim _{ x\rightarrow \dfrac { \pi }{ 2 } }{ \dfrac { \sin { x } }{ \cos ^{ -1 }{ \left[ \dfrac { 1 }{ 4 } \left( 3\sin { x } -\sin { 3x } \right) \right] } } }$ , where [.] denotes greatest integer function is :

0%
$\dfrac{2}{\pi}$
0%
$1$
0%
$\dfrac{4}{\pi}$
0%
$does\ not\ exist$

$\lim _ { x \rightarrow \frac { \pi } { 2 } } \left( \frac { 1 + \cos x } { 1 - \cos x } \right) ^ { \sec x } =$

0%
e
0%
$e^2$
0%
$e^3$
0%
$e/4$

$Im _{ }{ \left( \dfrac { 1 }{ 1-\cos { \theta } +i\sin { \theta } } \right) }$ is equal to

0%
$\dfrac{1}{2}\tan\dfrac{\theta}{2}$
0%
$\dfrac{1}{2}\cot\dfrac{\theta}{2}$
0%
$-\dfrac{1}{2}\tan\dfrac{\theta}{2}$ `
0%
$-\dfrac{1}{2}\cot\dfrac{\theta}{2}$

The value of

$\lim_{x\rightarrow 0}\left(\dfrac {e^{x}+e^{-x}-2}{x^{2}}\right)^{1/x^{2}}$ equals

0%
$e^{1/2}$
0%
$e^{1/4}$
0%
$e^{1/3}$
0%
$e^{1/12}$

$\lim _ { x \rightarrow 0 } \frac { \sqrt [ 3 ] { 1 + \sin x } - \sqrt [ 3 ] { 1 - \sin x } } { x } =$

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

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

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

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

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

$\underset { x\rightarrow \infty }{ Lt } { 5 }^{ x }sin\left( \cfrac { a }{ { 5 }^{ x } } \right) =$

0%
0
0%
5
0%
log5
0%
None of these.

$L\underset { x\rightarrow 0 }{ im } \frac { \sec { 4x-\sec { 2x } } }{ \sec { 3x-\sec { x } } }=$

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

the value of

$\underset { x\rightarrow 0 }{ lim } \frac { sin\alpha X-sin\beta X }{ { e }^{ \alpha X }-{ e }^{ \beta X } }$ equals

0%
0
0%
1
0%
-1
0%
$\alpha -\beta$

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

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

$\lim _{ x\rightarrow -\infty }{ \cfrac { x^{ 4 }\sin { \cfrac { 1 }{ x } } +x^{ 2 } }{ 1+\left| x \right| ^{ 3 } } = }$

0%
1
0%
-1
0%
2
0%
-3

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

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

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

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

$\displaystyle {Lt}_{x\rightarrow 0}\dfrac{cos5x cos3x}{x(sin5x sin3x)}$ =

0%
$-4$
0%
$4$
0%
$-\dfrac{1}{4}$
0%
$\dfrac{1}{4}$

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

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

The value of

$\lim _{ x\rightarrow 0 }{ \left( { \left( \sin { x } \right) }^{ 1/x }+{ \left( \dfrac { 1 }{ x } \right) }^{ \sin { x } } \right) }$

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

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

$\underset { x\rightarrow \infty }{ Lim } (sin\sqrt { x+1 } -sin\sqrt { x } )=$

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

CBSE Questions for Class 11 Commerce Applied Mathematics Limits And Continuity Quiz 11 - MCQExams.com

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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

CBSE Questions for Class 11 Commerce Applied Mathematics Limits And Continuity Quiz 11 - MCQExams.com

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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

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