## MATHEMATICS DIFFERENTIABILITY QUIZ-7

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.

•  f is discontinuous
•  f is continuous only, if Î»=0
•  f is continuous only, whatever Î» may be
•  None of the above
Solution

Q2.
The function f(x)=a[x+1]+b[x-1], where [x] is the greatest integer function, is continuous at x=1, is

•  a+b=0
•  a=b
•  2a-b=0
•
None of these
Solution

Q3.

•  f and f' are continuous for x+1>0
•  f is continuous but f' is not so for x+1>0
•  f and f' are continuous at x=0
•  f is continuous at x=0 but f' is not so
Solution

Q4.
Letf(x)=(1-tan⁡x)/(4x-Ï€),x≠Ï€/4, x∈[0,Ï€/2]. If f(x) is continuous in [0,Ï€/2], then f(Ï€/4) is

•  1
•  1/2
•  -1/2
•  -1
Solution

Q5.

•  -2
•  2
•  1
•  -1
Solution

Q6.
Let f(x)=|x| and g(x)=|x3|, then
•  f(x) and g(x) Both are continuous at x=0
•  f(x) and g(x) Both are differentiable at x=0
•  f(x) is differentiable but g(x) is not differentiable at x=0
•  f(x) and g(x) Both are not differentiable at x=0
Solution
>

Q7.

• A=3+B,B≠3
•  A=3+B,B=3
•  A=3+B
•  None of these
Solution

Q8.
•  Everywhere continuous
•  Nowhere continuous
•  Continuous only at some points
•  Discontinuous only at some points
Solution

Q9.
Which one of the following is not true always?

•  If f(x) is not continuous at x=a, then it is not differentiable at x=a
•  If f(x) is continuous at x=a, then it is differentiable at x=a
•
If f(x) and g(x) are differentiable at x=a, then f(x)+g(x) is also differentiable at x=a
•  If a function f(x) is continuous at x=a, then lim┬(x→a)⁡f(x) exists
Solution

Q10.
Suppose a function f(x) satisfies the following conditions for all x and y: (i) f(x+y)=f(x)f(y) (ii) f(x)=1+x g(x) log⁡a, where a>1 and lim┬(x→0)⁡g(x)=1. Then, f'(x) is equal to

•
log⁡a
•
log⁡a(f(x)
•  log⁡(f(x))a
•  None of these
Solution

#### Written by: AUTHORNAME

AUTHORDESCRIPTION

## Want to know more

Please fill in the details below:

## Latest NEET Articles\$type=three\$c=3\$author=hide\$comment=hide\$rm=hide\$date=hide\$snippet=hide

Name

ltr
item
BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET & IIT JEE COACHING: DIFFERENTIABILITY QUIZ-7
DIFFERENTIABILITY QUIZ-7