Test Details

Differentiability

Sem 1 practice 3

Nov 21, 12:00 AM

40 minutes

Nov 30, 11:00 PM

28.0 marks

MCQ

13 questions

Mukul Sir

I teach maths for IIT(JAM), JEE (main & Advance), NDA, 10+2 & other engineering entrance exams.

Class Details

Mathematics

Class 12+JEE

Mathematics

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Question Text

Question 1 :
Let f(x)=4 and f'(x)= 4. Then <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870d2d75ed294f2c7c439c' height='51' width='179' > is given by

Question 2 :
The function f(x) <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c9a75ed294f2c7c41ca' height='41' width='89' > is -

Question 3 :
The function {tex} y = e ^ { - | x | } {/tex} is

Question 4 :
If {tex} f ( x ) = \left\{ \begin{array} { l l } { \frac { 1 - | x | } { 1 + x } , } & { x \neq - 1 } \\ { 1 , } & { x = - 1 } \end{array} , \text { } \text { } \right. {/tex}then the value of {tex}f ( [ 2 x ] ){/tex} will be (where [1 shows the greatest integer function)

Question 5 :
The function &fnof;(x) = [x]2 - [x2] (where [y] is the greatest integer less than or equal to (y), is discontinuous at -

Question 6 :
The function {tex} y = | \sin x | {/tex} is continuous for any {tex} x {/tex} but it is not differentiable at

Question 7 :
If f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870b4619f8d44d3a17f6e8' height='45' width='121' >, then fof(x) is given by

Question 8 :
Let f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c9419f8d44d3a17fb0a' height='60' width='100' > be continuous and differentiable every where. The a and b are -

Question 9 :
Let f : R → R be a function defined by f(x) = max {x, x3}. The set of all points where f(x) is NOT differentiable is

Question 10 :
For the function f(x) =<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870c93e6d3604eaa92ed59' height='92' width='84' >following are true

Question 11 :
If f is a real valued differentiable function satisfying <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870d42e6d3604eaa92ef8a' height='29' width='402' >, then f(1) equals

Question 13 :
The function $f\left( x \right) = \left\{ \begin{matrix} x^{n}\sin{\left( \frac{1}{x} \right),\ x \neq 0} \\ 0,\ \ x = 0 \\ \end{matrix} \right.\ $ is continuous and differentiable at x = 0, if

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