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JEE Advanced Level Test: Continuity and Differentiability- 2 - JEE MCQ


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30 Questions MCQ Test Mathematics (Maths) Class 12 - JEE Advanced Level Test: Continuity and Differentiability- 2

JEE Advanced Level Test: Continuity and Differentiability- 2 for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The JEE Advanced Level Test: Continuity and Differentiability- 2 questions and answers have been prepared according to the JEE exam syllabus.The JEE Advanced Level Test: Continuity and Differentiability- 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Advanced Level Test: Continuity and Differentiability- 2 below.
Solutions of JEE Advanced Level Test: Continuity and Differentiability- 2 questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & JEE Advanced Level Test: Continuity and Differentiability- 2 solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt JEE Advanced Level Test: Continuity and Differentiability- 2 | 30 questions in 60 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
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JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 1

The function  is continuous at 

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 1

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 2

If the function  is continuous at x = 0 then a = 

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 2

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 3

is continuous at x = 0 then

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 3

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 4

The function  is discontinuous at the points

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 4

f (x) is discontinuous when x2 - 3|x| + 2 = 0
⇒ |x|2 - 3|x| + 2 = 0 ⇒ |x| = 1, 2

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 5

The values of a and b if f is continuous at x = 0, where 

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JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 6

 is continuous at then k = 

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JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 7

so that f(x) is continuous at then

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 7

 By L-Hospital rule

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 8

where [.] denotes greatest integer function and the function is continuous then

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 8

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 9

is continuous everywhere. Then the  equation whose roots are a and b is

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 9


JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 10

 where [x] is the greatest integer function. The function f (x) is

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JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 11

The function  is continuous at exactly two  points then the possible values of ' a ' are

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 11

f (x) is continuous when x2 - ax + 3 =2 - x
⇒ x2 - a -1 x + 1 = 0. This must have two distinct roots ⇒ Δ > 0 ⇒ (a -1)2 - 4 > 0

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 12

If the function  is continuous for every x ∈ R then

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 12

x2 + kx + 1>0 and x2 - k must not have any real root ;
∴ k2 - 4 < 0 &k < 0
⇒ k ∈ [-2, 2] and k < 0 ⇒ k ∈ [-2, 0)

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 13

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 13

|x| is not differentiable at x = 0
|x| is continuous at x = 0

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 14

The function f (x) = cos-1 (cos x) is

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 14


f (x) is continuous at x = π, - π

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 15

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 15


JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 16

then which is correct

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 16

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 17

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

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 17

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 18

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 18

Since g(x) = |x| is a continuous function and   so f is continuous function. In particular f is continuous at a = 1 and x = 4) f is clearly not differentiable at x = 4) Since g(x) = |x| is not differentiable at x = 0. Now

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 19

The set of all points where the function  is differentiable is

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 19

 is not differentiable only at x = 0

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 20

If   then derivative of f(x) at x = 0 is

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 20

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 21

If f : R → R be a differentiable function, such that f (x + 2y) = f (x) + f (2y) + 4xy for all x, y ∈ R then

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 21

f (x + 2y) = f (x) + f (2 y) + 4xy for x, y ∈ R putting x = y = 0, we get f (0) = 0

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 22

Let f be a differentiable function satisfying the condition for all 
, then f ' (x) is equal to

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 22

 replacing x and y both by 1, we get


JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 23

The function is not differentiable at

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 23

By verification f ' (2 -) ≠ f ' (2 +)
∴ f(x) is not differentiable at x = 2

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 24

then set of all points where f is differentiable is 

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 24

The function is clearly differentiable except possible at x = 2, 3

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 25

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 26

Let h(x) = min {x, x2} for  Then which of the following is correct

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 26


From the graph it is clear that h is continuous. Also h is differentiable except possible at x = 0 & 1


so h is not differentiable at 1
similarly h' (0 +)= 0 but h ' (0 - ) = 1

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 27

If f (x + y) = 2f (x) f (y) for all x, y ∈ R where f ' (0) = 3 and f (4) = 2, then f ' (4) is equal to

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 27


JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 28

If  and f ' (0) = -1, f (0) = 1, then f (2) =

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 28

Take  f (x) = ax+ b

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 29

Let f (x) be differentiable function such that and y. If 

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 29

JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 30

Let f : R → R be a function defined by f (x) = min {x + 1, |x| + 1}, Then which of the following is true?

Detailed Solution for JEE Advanced Level Test: Continuity and Differentiability- 2 - Question 30

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