#### 11th Standard Maths Differential Calculus - Limits and Continuity English Medium Free Online Test One Mark Questions 2020 - 2021

11th Standard

Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. $lim_{x\rightarrow\infty}{sin \ x \over x}$

(a)

1

(b)

0

(c)

$\infty$

(d)

-$\infty$

2. $lim_{x\rightarrow0}{\sqrt{1-cos 2x}\over x}$

(a)

0

(b)

1

(c)

$\sqrt{2}$

(d)

does not exist

3. If f(x)=x(-1)$\left\lfloor 1\over x \right\rfloor$,$x\le0$,then the value of $lim_{x\rightarrow 0}f(x)$ is equal to

(a)

-1

(b)

0

(c)

2

(d)

4

4. Let the function f be defined by  ,then

(a)

$lim_{x \rightarrow1}f(x)=1$

(b)

$lim_{x \rightarrow1}f(x)=3$

(c)

$lim_{x \rightarrow1}f(x)=2$

(d)

$lim_{x \rightarrow1}f(x)$ does not exist

5. The value of $lim_{x \rightarrow 0}{sin x\over \sqrt{x^2}}$ is

(a)

1

(b)

-1

(c)

0

(d)

$\infty$

6. The function is not defined for x = −1. The value of f(−1) so that the function extended by this value is continuous is

(a)

${2\over3}$

(b)

-${2\over3}$

(c)

1

(d)

0

7. $\lim _{ x\rightarrow 2 }{ \frac { 2{ x }^{ 2 }+x+1 }{ x+2 } }$ is equal to

(a)

$\frac { 1 }{ 2 }$

(b)

2

(c)

$\frac { 11 }{ 4 }$

(d)

0

8. $\lim _{ x\rightarrow \infty }{ \left( \frac { 1 }{ x } +2 \right) }$is equal to

(a)

$\infty$

(b)

0

(c)

1

(d)

2

9. $\lim _{ x\rightarrow \frac { \pi }{ 2 } }{ \frac { \sin { x } }{ x } } =$

(a)

$\pi$

(b)

$\frac { \pi }{ 2 }$

(c)

$\frac { 2 }{ \pi }$

(d)

1

10. The slop of the curve $y={ x }^{ 3 }-7{ x }^{ 2 }+5x+10\quad$ at x=1 is

(a)

6

(b)

-6

(c)

5

(d)

15