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Test: Continuity - JEE MCQ


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10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Continuity

Test: Continuity for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Continuity questions and answers have been prepared according to the JEE exam syllabus.The Test: Continuity MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Continuity below.
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Test: Continuity - Question 1

Detailed Solution for Test: Continuity - Question 1


= 1 x 2
= 2 ≠ f(0)
Hence, given function is not continuous at x = 0

Test: Continuity - Question 2

What is/are conditions for a function to be continuous on (a,b)?

Detailed Solution for Test: Continuity - Question 2

The three conditions required for a function f is said to be continuous on (a,b) if f is continuous at each point of (a,b), f is right continuous at x = a, f is left continuous at x = b.

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Test: Continuity - Question 3

Detailed Solution for Test: Continuity - Question 3

and

and
f(2) = 1.
Therefore , f(x) is discontinuous at x = 2

Test: Continuity - Question 4

Which of the following functions are not continuous.

Detailed Solution for Test: Continuity - Question 4

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

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

Test: Continuity - Question 5

Examine the continuity of the function  

Detailed Solution for Test: Continuity - Question 5

Set the denominator in:
equal to 0 to find where the expression is undefined.

Subtract 2 from both sides of the equation.

The domain is all values of x that make the expression defined.
Interval Notation:

Set-Builder Notation:

Since the domain is not all real numbers, f(x) is not continuous over all real numbers. 
f(x) is discontinuous at x = -2.

Test: Continuity - Question 6

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

Detailed Solution for Test: Continuity - Question 6

For continuity: LHL = RHL

At x=2,
LHL: x < 2 ⇒ f(x) = 2*a
RHL: x ≥ 2 ⇒ f(x) = 4
For continuity: LHL = RHL
⇒ 2a = 4 ⇒ a = 2

At x = 0,
LHL: x < 0 ⇒ f(x) = b
RHL: x ≥ 0 ⇒ f(x) = 0 * a
For continuity: LHL = RHL
b = 0

Test: Continuity - Question 7

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

Detailed Solution for Test: Continuity - Question 7

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.

Test: Continuity - Question 8

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

Detailed Solution for Test: Continuity - Question 8

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

► So it get    k2-3k+2

► Now f (k) = k2 -3k+2

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

Test: Continuity - Question 9

What is the point of discontinuity for signum function?

Detailed Solution for Test: Continuity - Question 9

Sgn(x) = |x|/x
► for x > 0, sgn(x) = 1
► for x = 0, sgn(x) = 0
► for x < 0, sgn(x) = -1
► Now see graphically or theoretically sgn(x) is discontinuous at x = 0

Test: Continuity - Question 10

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

Detailed Solution for Test: Continuity - Question 10
  • [-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.
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