MCQ Questions for Class 11 Commerce Applied Mathematics Limits And Continuity Quiz 12

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

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

If $$ \alpha , \beta , \ in (-\frac{\pi}{2},0) $$ 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%
$$ \alpha + \beta = \frac{- \pi }{3}$$

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

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

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

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

$$\lim _{ x\rightarrow 0 }{ \frac { 1 }{ { x }^{ 8 } } [1-\cos { (\frac { { x }^{ 2 } }{ 2 } ) } ] } [1-\cos { (\frac { { x }^{ 2 } }{ 4 } ) } ]$$

0%
$$\frac { 1 }{ 8 } $$
0%
$$\frac { 1 }{ { 8 }^{ 2 } } $$
0%
$$\frac { 1 }{ { 8 }^{ 3 } } $$
0%
$$\frac { 1 }{ { 8 }^{ 4 } } $$

$$ \lim _{x \rightarrow a}\left(2-\frac{a}{x}\right)^{\tan \left(\frac{\pi x}{2 a}\right)} $$

0%
$$

e^{-\frac{a}{\pi}}

$$
0%
$$

e^{-\frac{2 a}{\pi}}

$$
0%
$$

e^{-\frac{2}{x}}

$$
0%
1

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%
$$1$$

If $$f\left( x \right) =\sqrt { 1-\sqrt { 1-{ x }^{ 2 } } } $$, then $$f(x)$$ is

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continuous on$$[-1,1]$$
0%
differentiable on $$(-1,0)\cup (0,1)$$
0%
both (a) and (b)
0%
None of the above

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

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%
$$2$$

$$f(x) = \log_{1 - 2x}(1 + 2x)$$ for $$ x \ne 0$$
$$= k$$ for $$x = 0$$
is continuous at $$x = 0$$, find $$k.$$

0%
$$1$$
0%
$$-1$$
0%
$$0$$
0%
$$\frac{1}{2}$$

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%
$$\cfrac{1}{8}$$

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

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

$$ \lim _{x \rightarrow 0}\left(\frac{e^{x}+e^{-x}-2}{x^{2}}\right)^{1 / x^{2}} $$

0%
$$

e^{1 / 2}

$$
0%
$$

e^{1 / 4}

$$
0%
$$

e^{1 / 3}

$$
0%
$$

e^{1 / 12}

$$

The value of $$\displaystyle \lim _{ x\rightarrow 0 }\log_{\cos{2x}}{\cos{x}}+\log_{\cos{2x}}{\cos{2x}}$$ equals

0%
$$\dfrac{5}{4}$$
0%
$$\dfrac{17}{4}$$
0%
$$\dfrac{13}{16}$$
0%
$$\dfrac{29}{10}$$

$$\begin{matrix} lim \\ x\rightarrow 0 \end{matrix}(cos\quad +\quad sinx{ ) }^{ 1/x }$$ is equal to

0%
e
0%
$${ e }^{ 2 }$$
0%
$${ e }^{ -1 }$$
0%
1

$$\lim _{ x\rightarrow 0 }{ \frac { \sin { [\cos { x } ] } }{ 1+[\cos { x } ] } } $$ is (where [] is G.I.F)

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

$$\underset { x\rightarrow a }{ lim } \left( \sin { \dfrac { x-a }{ 2 } \tan { \dfrac { \pi x }{ 2a } } } \right)$$

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

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

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

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

$$\lim_{x\rightarrow 0}\frac{1-cos^{3}x}{x sib x cos x }$$ is equal to

0%
2/5
0%
3/5
0%
3/2
0%
3/4

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 }

$$

$$\underset {x\rightarrow 0}{Lim} \frac {sin x}{x} = y $$

0%
$$y>1$$
0%
$$y<1$$
0%
$$y\ge 1$$
0%
$$y \le 1$$

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

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

$$\begin{matrix} lim \\ x\rightarrow a \end{matrix}(2-\frac { a }{ x } ){ }^{ tan(\frac { \pi x }{ 2a } ) }$$ is equal to

0%
$$ e^{-\frac{a}{\pi}}$$
0%
$$ e^{-\frac{2a}{\pi}}$$
0%
$$ e^{-\frac{2}{\pi}}$$
0%
1

$$ \lim _{x \rightarrow0}\left(\frac{e^{x}+e^{-x}-2}{x^{2}}\right)^{1 / x^{2}} $$ is

0%
$$

e^{1 / 2}

$$
0%
$$

e^{1 / 4}

$$
0%
$$

e^{1 / 3}

$$
0%
$$

e^{1 / 12}

$$

Let x be an irrational, then $$\underset { m\rightarrow \infty }{ lim } \underset { n\rightarrow \infty }{ lim } \left\{ cos(n!\pi x) \right\} ^{ 2m }$$ equals

0%
0
0%
-1
0%
1
0%
Indeterminate

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

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

$$\displaystyle x\xrightarrow { lim } 5\quad \left(\frac{\sqrt{1-\cos(2x-10)}}{\sin (x-5)} \right) $$

0%
$$-\sqrt{2}$$
0%
$$\sqrt{2}$$
0%
does not exist
0%
none of these

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

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

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

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

$$\underset { x\rightarrow 1 }{ lim } { \left[ cosec { \dfrac { \pi x }{ 2 } } \right] }^{ { 1 }/{ \left( 1-x \right) } }$$ (where $$[.]$$ represents the greatest integer function) is equal to

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

f(X)=|x|+|x-1| is continuous at

0%
'0' only
0%
0,1 only
0%
Every where
0%
No where

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

$$\displaystyle \lim_{x\rightarrow 0}\dfrac {\sin x - x}{x^{3}}$$ is equal to

0%
$$-\dfrac {1}{6}$$
0%
$$-\dfrac {1}{3}$$
0%
$$-\dfrac {1}{2}$$
0%
$$-1$$

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

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

If $$\alpha$$ 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

$$\begin{matrix} lim \\ x\rightarrow 0 \end{matrix}\frac { xcot(4x) }{ { sin }^{ 2 }x{ cot }^{ 2 }\left( 2x \right) } $$ is equal to

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

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

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

The value of $$\underset{x\rightarrow 1}{lim}(2-x)^{tan\left(\dfrac{\pi x}{2}\right)}$$ is

0%
$$e^{-2/pi}$$
0%
$$e^{1/pi}$$
0%
$$e^{2/pi}$$
0%
$$e^{-1/pi}$$

$$\underset{x \rightarrow 1} {lim}\dfrac{x^2-1}{\sin^2x+\cos x\cos (x+2)-\cos^2(x+1)}$$ is-

0%
$$0$$
0%
$$\dfrac{1}{\cos 1}$$
0%
$$\dfrac{2}{\sin 2}$$
0%
$$\dfrac{1}{2\cos 1}$$

$$\lim_{x\rightarrow 1}\frac{1-x^{-2/3}}{1-x^{-1/3}}$$

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

$$lim_{n \to \infty}\dfrac{-3n + (-1)^n}{4n - (-1)^n}$$ is equal to

0%
$$-\dfrac{3]{4}$$
0%
o if n is even
0%
$$-\dfrac{3}{4}$$ if n is odd
0%
None of these

$$\displaystyle \lim _{x \rightarrow 1}\left(\dfrac{x^{4}+x^{2}+x+1}{x^{2}-x+1}\right)^{\dfrac{1-\cos (x+1)}{(x+1)^{2}}} $$ is equal to:

0%
1
0%
$$(2 / 3)^{1 / 2} $$
0%
$$ (3 / 2)^{1 / 2} $$
0%
$$ e^{1 / 2} $$

$$ \displaystyle \lim _{x \rightarrow 0}\left(\dfrac{1^{x}+2^{x}+3^{x}+\cdots+n^{x}}{n}\right)^{1 / x} $$ is equal to

0%
$$ (n !)^{n} $$
0%
$$ (n !)^{1 / n} $$
0%
$$ n ! $$
0%
$$ \ln (n !) $$

CBSE Questions for Class 11 Commerce Applied Mathematics Limits And Continuity Quiz 12 - 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 12 - MCQExams.com

0:0:1

Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

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