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This mock test of Test: Continuity for JEE helps you for every JEE entrance exam.
This contains 10 Multiple Choice Questions for JEE Test: Continuity (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Which of the following functions are not continuous.

Solution:

Here, **f(x)=[X]** could be expressed graphically as:

From the graph it is clear that the function is discontinuous.

QUESTION: 2

If f (x) = [xsinπx] { where [x] denotes greatest integer function}, then f (x) is

Solution:

**► By the definition of **[x], we have f(x)=[xsinπx]=0 for −1≤x≤1, because 0 ≤ xsin(πx) ≤1

**► **Also, f(x)=[xsinπx]=−1, for 1<x<1+h for some small appropriate h> 0, because sinπx is negative and ≥−1 for 1<x<1+h.

**► **Thus f(x) is constant and equal to 0 in the interval [−1;1] and so it is continuous and differentiable in (−1,1).

**► **In particular, f(x) is continuous at x=0

QUESTION: 3

Examine the continuity of the function

Solution:

f’(x) = (x^{2}-4)/(x-2)

= [(x-2)(x+2)]/(x-2)

= (x+2) which is continuous everywhere.

QUESTION: 4

For what values of a and b, f is a continuous function.

Solution:

QUESTION: 5

Discuss the continuity of function f(x) = |x-1| + |x+1|, x R

Solution:

f(x) = |x-1| + |x+1| , x € R

► For x ≥ 1,

f(x) = x-1 + x+1

f(x) = 2x

► For -1 ≤ x ≤ 1,

f(x) = -x + 1 + x+1

f(x) = 2

► For x ≤ -1,

f(x) = -x + 1 - x-1

f(x) = -2x

As the graph of f(x) shows, the function is continuous throughout its domain.

QUESTION: 6

Examine the continuity of function f(x) = (x-1)(x-2)

Solution:

Lim f (x) = lim (x-1)(x-2) at x tend to k

► So it get k^{2}-3k+2

► Now f (k) = k^{2 }-3k+2

► So f (x) =f (k) so continous at everywhere

QUESTION: 7

What is the point of discontinuity for signum function?

Solution:

Sgn(x)=|x|/x

► for x>0, sgn(x)=1

► for x=0, sgn(x)=0

► for x<0, sgn(x)="">

► Now see graphically or theoretically sgn(x) is discontinuous at x=0

QUESTION: 8

Function f(x) = log x + is continuous at

Solution:

[-1,1] cannot be continuous interval because log is not defined at 0

The value of x cannot be greater than 1 because then the function will become complex

(0,1) will not be considered because its continuous at 1 as well. Hence D is the correct option

QUESTION: 9

Solution:

Function is not continuous at x=0

QUESTION: 10

A real function f is said to be continuous if it is continuous at every point in …… .

Solution:

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