#### 11th Standard Maths Differential Calculus - Limits and Continuity English Medium Free Online Test 1 Mark Questions with Answer Key 2020-2021

11th Standard

Reg.No. :
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Maths

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

Answer all the questions

10 x 1 = 10
1. $lim_{x\rightarrow {\pi/2}}{2x-\pi\over cosx}$

(a)

2

(b)

1

(c)

-2

(d)

0

2. $lim_{x \rightarrow \infty}{\sqrt{x^2-1}\over 2x+1}=$

(a)

1

(b)

0

(c)

-1

(d)

$1\over 2$

3. $lim_{x \rightarrow 3}\left\lfloor x \right\rfloor =$

(a)

2

(b)

3

(c)

does not exist

(d)

0

4. If f : $R \rightarrow R$ is defined by f(x)=$\left\lfloor x-3 \right\rfloor +|x-4|$ for $x \in R$, then$lim_{x\rightarrow 3^-}f(x)$ is equal to

(a)

-2

(b)

-1

(c)

0

(d)

1

5. $lim_{n \rightarrow \infty}({1\over n^2}+{2\over n^2}+{3\over n^2}+..+{n\over n^2})$ is

(a)

$1\over 2$

(b)

0

(c)

1

(d)

$\infty$

6. Let f :$R \rightarrow R$ be defined by            then f is

(a)

discontinuous at x = ${1\over 2}$

(b)

continuous at  x = ${1\over 2}$

(c)

continuous everywhere

(d)

discontinuous everywhere

7. $\lim _{ x\rightarrow 1 }{ \frac { { x }^{ m }-1 }{ { x }^{ n }-1 } } is$

(a)

mn

(b)

m+n

(c)

m-n

(d)

$\frac { m }{ n }$

8. $\lim _{ x\rightarrow \infty }{ \frac { 1+2+3+....+n }{ { 2n }^{ 2 }+6 } }$

(a)

2

(b)

6

(c)

$\frac { 1 }{ 4 }$

(d)

$\frac { 1 }{ 2 }$

9. The points of discontinuity of the function $\frac { { x }^{ 2 }+6x+8\quad }{ { x }^{ 2 }-5x+6\quad } is$

(a)

3,2

(b)

3,-2

(c)

-3,2

(d)

-3,-2

10. Find the odd one of the following

(a)

x2

(b)

x4

(c)

cos x

(d)

sin x