## MATHEMATICS DIFFERENTIABILITY QUIZ-5

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.
Let f(x+y)=f(x)+f(y) and f(x)=x2 g(x) for all x,y∈R, where g(x) is continuous function. Then, f'(x) is equal to

•  g'(x)
•  g(0)
•  g(0)+g'(x)
•  0
Solution

Q2.

•  a=loge⁡b, b=2/3
•  b=loge⁡a, a=2/3
•  a=loge⁡b, b=2
•
None of these
Solution

Q3.

•  -2
•  -4
•  -6
•  -8
Solution

Q4.

•  3
•  -3
•  e3
•  e-3
Solution

Q5.

•  Continuous but not differentiable
•  Differentiable
•  Continuous
•  None of these
Solution

Q6.
•  {1}
•  {-1}
•  {-1,1}
•  None of these
Solution
>

Q7.
Let f(x)=|x|+|x-1|, then

• f(x) is continuous at x=0, as well as at x=1
•  f(x) is continuous at x=0, but not at x=1
•  f(x) is continuous at x=1, but not at x=0
•  None of these
Solution

Q8.
The value of derivative of |x-1|+|x-3| at x=2, is
•  -2
•  0
•  2
•  Not defined
Solution

Q9.
If f(x)=Min {tan⁡x,cot⁡x}, then

•  f(x) is not differentiable at x=0,Ï€/4,5Ï€/4
•  f(x) is continuous at x=0,Ï€/2,3Ï€/2
•

•  f(x) is periodic with period Ï€/2
Solution

Q10.

•
Is continuous for all x ∈I-{0}
•
Assumes all intermediate values from f(-2) to f(2)
•  Has a maximum value equal to 3/e
•  All the above
Solution

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