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DIFFERENTIABILITY QUIZ-1

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.
.

Q1. If y=cos⁡(x-f(x)) , where fx={1,if x>0 -1, if x<0 0, if x=0 . Then, (dy/dx) x=54 is equal to
•  -1
•  0
•  -1
•  Cannot be determined
Solution
b)
Q2.If fx={(1-2sin sinx)/Ï€-4x, if x≠Ï€/4 a, if x=Ï€/4 is continuous at 4, then a is equal to
•  4
•  2
•  1
•  1/4
Solution
d)
Q3.  Let f be differentiable for allx. If f1=-2 and f'(x)≥2 for x∈[1, 6], then
•  f(6)=5
•  f(6)<5
•  f(6)<8
•  f(6)≥8
Solution

d)

Q4. If for a continuous function f, f0=f1=0, f'1=2 and yx=fexef(x), then y'(0) is equal to
•  1
•  2
•  0
•  None of these
Solution
(b)
Q5.If fx={cosx, x<1 x-2, 2>x≥1 , then f(x) is
•  Discontinuous and non-differentiable at x=-1 and x=1
•  Continuous and differentiable at x=0
•  Discontinuous at x=1/2
•  Continuous but not differentiable at x=2
Solution
c)
Q6.  Given that f(x) is a differentiable function of x and that fx. fy=fx+fy+fxy-2 and that f2=5. Then, f(3) is equal to
•  10
•   24
•  15
•  None of these
Solution
a)
Q7.

•  0
•  2
•  f(2)
•  None of these
Solution
(b)
Q8.
•  Continuous but not differentiable at x=0
•  Discontinuous at x=0
•  Continuous and differentiable at x=0
•  Not defined at x=0
Solution

(c)
Q9.
•  12
•  9
•   16
•  6
Solution
(a)
Q10.
•  -1/9
•  -2/9
•  -13
•  1/3
Solution
(b)

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