## MATHEMATICS DIFFERENTIABILITY QUIZ-8

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.

Q1.
If f(x)=|loge⁡x|, then

•  f'(1+)=1,f'(1-)=-1
•  f'(1-)=-1,f'(1+)=0
•  f'(1)=1,f'(1-)=0
•  None of the above
Solution

Q2.
The derivative of f(x)=|x|3 at x=0 is

•  -1
•  0
•  Does not exist
•
None of these
Solution

Q3.

•  R
•  R-{1}
•  R-{2}
•  R-{1,2}
Solution

Q4.
Let f(x+y)=f(x)f(y) for all x,y∈R. If f'(1)=2 and f(4)=4, then f'(4) equal to

•  4
•  1
•  1/2
•  8
Solution

Q5.
If f(x)=(x-x0)Ï•(x) and Ï•(x) is continuous at x=x0, then f'(x0) is equal to

•  Ï•'(x0)
•  Ï•(x0)
•  x0Ï•(x0)
•  None of these
Solution

Q6.
•  n∈(0,1]
•  n∈[1,∞)
•  n∈(1,∞)
•  n∈(-∞,0)
Solution
>

Q7.

• a=0,b=0
•  a=1,b=1
•  a=-1,b=1
•  a=1,b=-1
Solution

Q8.
Let f:R→R be a function defined byf(x)=min⁡{x+1,|x|+1}. Then, which of the following is true?
•  f(x)≥1 for all x∈R
•  f(x) is not differentiable at x=1
•  f(x) is differentiable everywhere
•  f(x) is not differentiable at x=0
Solution

Q9.

•  1
•  -1
•
•  Does not exist
Solution

Q10.
If f(x)=1/2 x-1, then on the interval [0,Ï€],

•
tan⁡[f(x)] and 1/(f(x)) are both continuous
•
tan⁡[f(x)] and 1/(f(x)) are both discontinuous
•  tan⁡[f(x)] and f-1(x) are both continuous
•  tan⁡[f(x)] s continuous but 1/(f(x)) is not
Solution

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