All Courses
Get the App Signup / Login
Sign in Open App
JEE Exam  >  JEE Tests  >  Mathematics (Maths) Class 12  >  Test: Continuity And Differentiability - 2 - JEE MCQ

Test: Continuity And Differentiability - 2 - JEE MCQ


Test Description

25 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Continuity And Differentiability - 2

Test: Continuity And Differentiability - 2 for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Continuity And Differentiability - 2 questions and answers have been prepared according to the JEE exam syllabus.The 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 Test: Continuity And Differentiability - 2 below.
Solutions of Test: Continuity And Differentiability - 2 questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & 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 Test: Continuity And Differentiability - 2 | 25 questions in 25 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
Test: Continuity And Differentiability - 2 - Question 1
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 1

L'Hopital's rules says that the  
lim x→a f(x)/g(x)
⇒ f'(a)/g'(a)
Using this, we get  
lim x→0 (1−cosx)/x2
⇒ − sin0/2(0)
Yet as the denominator is 0, this is impossible. So we do a second limit:
lim(x→0) sinx/2x
⇒ cos0/2 = 1/2 = 0.5
So, in total lim x→0 (1−cosx)/x2
⇒ lim x→0 sinx/2x
⇒ cosx/2
⇒ cos0/2= 1/2

Test: Continuity And Differentiability - 2 - Question 2
Save

If f (x) is a polynomial of degree m (⩾1) , then which of the following is not true ?

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 2

As all the three remaining statements are true for the given function.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Continuity And Differentiability - 2 - Question 3
Save

Let f and g be differentiable functions such that fog = I, the identity function. If g’ (a) = 2 and g (a) = b, then f ‘ (b) =

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 3

f(g(x)) = x 
f'(g(x)) g'(x) = 1 
put x = a
f'(b) g'(a) = 1
2 f'(b) = 1
f'(b) = 1/2

Test: Continuity And Differentiability - 2 - Question 4
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 4


Test: Continuity And Differentiability - 2 - Question 5
Save

If f (x) =x2g(x) and g (x) is twice differentiable then f’’ (x) is equal to
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 5



Test: Continuity And Differentiability - 2 - Question 6
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 6

 

Test: Continuity And Differentiability - 2 - Question 7
Save

If f(x) = | x | ∀ x ∈ R, then
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 7


The graph of f(x) = |x|
As observed from the graph, f(x) = |x| is continuous at x = 0.
As this curve is pointed at x = 0, f(x) is not derivable at x = 0.

Test: Continuity And Differentiability - 2 - Question 8
Save

Differential coefficient of a function f (g (x)) w.r.t. the function g (x) is
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 8

Test: Continuity And Differentiability - 2 - Question 9
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 9

Given xpyq = (x+y)p+qTaking log on both sides we get:
plogx+qlogy = (p+q) log (x+y).  Differentiating both sides w.r.t. x we get , 

Test: Continuity And Differentiability - 2 - Question 10
Save

If y = aemx + be−mx, then y2 is equal to
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 10

y = aemx + be-mx ⇒ y1 = amemx + (-m)be-mx ⇒y2

= am2emx + (m2)be-mx ⇒y2 = m2 (aemx + be-mx) ⇒ y2 = m2y

Test: Continuity And Differentiability - 2 - Question 11
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 11



Test: Continuity And Differentiability - 2 - Question 12
Save

 
then   is equal to 
Test: Continuity And Differentiability - 2 - Question 13
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 13

 

Test: Continuity And Differentiability - 2 - Question 14
Save

If f(x) be any function which assumes only positive values and f’ (x) exists then f’ (x) is equal to
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 14

 

Test: Continuity And Differentiability - 2 - Question 15
Save

If y = a sin mx + b cos m x, then  is equal to
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 15

y  = a sin mx+b cos mx ⇒ y1 = am cos mx − bm sin mx
⇒ y2 = −am2sin mx−bm2cosmx ⇒ y2 = −m2(a sin mx+b cos mx)

Test: Continuity And Differentiability - 2 - Question 16
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 16

 

Test: Continuity And Differentiability - 2 - Question 17
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 17

 

Test: Continuity And Differentiability - 2 - Question 18
Save

If y = tan−1x and z = cot−1x then  is equal to
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 18

Test: Continuity And Differentiability - 2 - Question 19
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 19


Test: Continuity And Differentiability - 2 - Question 20
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 20

 

Test: Continuity And Differentiability - 2 - Question 21
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 21

 

Test: Continuity And Differentiability - 2 - Question 22
Save

If both f and g are defined in a nhd of 0 ; f(0) = 0 = g(0) and f ‘ (0) = 8 = g’ (0), then  equal to
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 22

 (by using L’Hospital Rule)

Test: Continuity And Differentiability - 2 - Question 23
Save

Detailed Solution for Test: Continuity And Differentiability - 2 - Question 23

 

Test: Continuity And Differentiability - 2 - Question 24
Save

The differential coefficient of log (| log x |) w.r.t. log x is
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 24

 

Test: Continuity And Differentiability - 2 - Question 25
Save

If f is derivable at x = a , then    is equal to
Detailed Solution for Test: Continuity And Differentiability - 2 - Question 25

 

204 videos|290 docs|139 tests
Join Course
Information about Test: Continuity And Differentiability - 2 Page
In this test you can find the Exam questions for Test: Continuity And Differentiability - 2 solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Continuity And Differentiability - 2, EduRev gives you an ample number of Online tests for practice

Top Courses for JEE

204 videos|290 docs|139 tests
Join Course
Download as PDF

Top Courses for JEE

Important Questions for Continuity And Differentiability - 2

Find all the important questions for Continuity And Differentiability - 2 at EduRev.Get fully prepared for Continuity And Differentiability - 2 with EduRev's comprehensive question bank and test resources. Our platform offers a diverse range of question papers covering various topics within the Continuity And Differentiability - 2 syllabus. Whether you need to review specific subjects or assess your overall readiness, EduRev has you covered. The questions are designed to challenge you and help you gain confidence in tackling the actual exam. Maximize your chances of success by utilizing EduRev's extensive collection of Continuity And Differentiability - 2 resources.

Continuity And Differentiability - 2 MCQs with Answers

Prepare for the Continuity And Differentiability - 2 within the JEE exam with comprehensive MCQs and answers at EduRev. Our platform offers a wide range of practice papers, question papers, and mock tests to familiarize you with the exam pattern and syllabus. Access the best books, study materials, and notes curated by toppers to enhance your preparation. Stay updated with the exam date and receive expert preparation tips and paper analysis. Visit EduRev's official website today and access a wealth of videos and coaching resources to excel in your exam.

Online Tests for Continuity And Differentiability - 2 Mathematics (Maths) Class 12

Practice with a wide array of question papers that follow the exam pattern and syllabus. Our platform offers a user-friendly interface, allowing you to track your progress and identify areas for improvement. Access detailed solutions and explanations for each test to enhance your understanding of concepts. With EduRev's Online Tests, you can build confidence, boost your performance, and ace Continuity And Differentiability - 2 with ease. Join thousands of successful students who have benefited from our trusted online resources.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup