Free Printable Continuity & Differentiabiliy Class XII Quiz

1.

Which is not continuous at x=4?

a)

$f\cdot g$

b)

$\frac{f}{g}$

c)

$\frac{g}{f}$

d)

$g^2$

2.

Find the value of b for which g(x) is continuous at x=3.

a)

1

b)

-1

c)

2

d)

-2

3.

The function is continuous at x = a . True or false?

a)

True

b)

False

4.

What is the limits of the graph above when x approaching 0?

a)

0

b)

−∞

c)

Does not exist

5.

What is the limit of the function as x approaches -4 from the left?

a)

2

b)

-4

c)

-2

d)

does not exist

6.

For a function,

f\left(x\right)

to be continuous at a point

x=c

, which of the following conditions must be met:

i.

\lim_{x\rightarrow c}f\left(x\right)

must exist

ii.

f\left(c\right)

must be defined

iii.

\lim_{x\rightarrow c}f\left(x\right)=f\left(c\right)

a)

i only

b)

i and ii only

c)

iii only

d)

i, ii, and iii

7.

Find the value of k, if possible, that makes the function f continuous everywhere.

a)

3

b)

0

c)

2

d)

no such k exists

8.

Find all values of k that would make the function f(x) continuous.

a)

2

b)

3

c)

4

d)

5

9.

Is the function shown below continuous on the interval [-5, 0]?

g\left(x\right)=\frac{2}{x+3}

a)

yes

b)

no, because g(0) does not exist

c)

no, because g(-3) does not exist

d)

no, because the value of g(-3) is not equal to the limit at x = -3

10.

a)

$\frac{1}{3}$

b)

0

c)

$\frac{3}{5}$

d)

$\frac{5}{3}$

11.

a)

b)

c)

d)

12.

a)

7

b)

4

c)

3

d)

-1

13.

a)

b)

c)

d)

14.

a)

b)

c)

d)

15.

a)

1

b)

2

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

16.

a)

$3$

b)

$-3$

c)

$-5$

d)

$6$

17.

a)

continuous but not differentiable

b)

differentiable but not continuous

c)

continuous as well as differentiable

d)

none of these

18.

a)

$3$

b)

$-3$

c)

$6$

d)

$-6$

19.

a)

$1$

b)

$-1$

c)

$2$

d)

$-2$

20.

a)

$\frac{1}{2}$

b)

$\frac{1}{2\sqrt[\ ]{2}}$

c)

$\frac{1}{\sqrt[]{2}}$

d)

$\frac{1}{4\sqrt[]{2}}$

21.

a)

b)

c)

d)

22.

a)

$R$

b)

$R-\left\{\frac{1}{2}\right\}$

c)

$\left(0,\infty\right)$

d)

None of these

23.

a)

b)

c)

d)

24.

a)

$3$

b)

$-3$

c)

$0$

d)

$1$

25.

a)

$0$

b)

$1$

c)

$2$

d)

None of these

Continuity & Differentiabiliy Class XII Quiz_1(Based on Ex 5.1)

Total questions: 25

Worksheet time: 49mins

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