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DIFFERENTIABILITY QUIZ-2

Dear Readers, 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.
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Q1.  Let f(x) be an odd function. Then f'(x)
•  Is an even function
•  Is an odd function
•  May be even or odd
•  None of these
Solution
Q2.If f(x+y)=f(x)f(y) for all x,y∈R,f(5)=2,f'(0)=3. Then f'(5) equals
•  6
•  3
•  5
•  None of these
Solution
Q3.

•  Continuous and derivable at x=0
•  Neither continuous nor derivable at x=0
•  Continuous but not derivable at x=0
•  None of these
Solution

Q4.
•  Continuous at x=0
•  Not continuous at x=0
•  Both continuous and differentiable at x=0
•  Not defined at x=0
Solution
Q5.
•  0
•  1≤p<∞ x=0
•   -∞
•  p=0
Solution

Q6.

•  x
•   x except at x=0
•  x except at x=1
•  x except at x=0 and x=1
Solution
Q7.

•  2
•  3
•  4
•  None of these
Solution
Q8.
The function f(x)=(1-sin⁡x+cos⁡x)/(1+sin⁡x+cos⁡x) is not defined atx=Ï€. The value of f(Ï€), so that f(x) is continuous at x=Ï€, is
•  -1/2
•  1/2
•  -1
•  1
Solution

Q9.
If f(x)=[√2sin⁡x], where [x] represents the greatest integer function, then
•  f(x) is periodic
•  Maximum value of f(x) is 1 in the interval [-2 Ï€,2 Ï€]
•  f(x) is discontinuous at x=(n Ï€)/2+Ï€/4,n∈Z
•  f(x) is differentiable at x=n Ï€,n∈Z
Solution
Q10.
If f(x)=|x2-4x+3|, then
•   f'(1)=-1 and f'(3)=1
•  f'(1)=-1 and f'(3) does not exist
•  f'(1)=-1 does not exist and f'(3)=1
•  Both f'(1) and f'(3) do not exist
Solution

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