Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2013 · Mathematics · Continuity and Differentiability

Consider the following statements in respect of a function f(x) :...

Consider the following statements in respect of a function f(x)f(x) : 1. f(x)f(x) is continuous at x=ax=a iff lim⁡x→af(x)\lim _{x \rightarrow a} f(x) exists. 2. If f(x)f(x) is continuous at a point, then 1f(x)\frac{1}{f(x)} is also continuous at that point. Which of the above, statements is/are correct?

Options

  1. A11 only
  2. B22 only
  3. CBoth 11 and 22
  4. DNeither 11 nor 22

Correct answer

D. Neither 11 nor 22

Step-by-step solution

The correct answer is option D.
Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

What is the derivative of (x)/(|x|) with respect to x , where x< 0 ? NDA 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f ^ ∘ g(x) , then which… NDA 2026Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If p(x)=f(x)g(x) , then which of… NDA 2026If f(x) is differentiable at x=a , then consider the following statements : I. f(x) is… NDA 2026Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but… NDA 2026Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x If the… NDA 2025For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on… NDA 2025Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2… NDA 2025Paragraph: Let f(x)=[x]^2- [x^2] . Question: Consider the following statements: A. f(x)… NDA 2024Let f(x)=|x|+1 and g(x)=[x]-1 , where [.] is the greatest integer function. Let… NDA 2024Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be continuous at x=3 . What is… NDA 2023Let f(x)=\ array cc a x(x+1)+b, & x < 1 x-1 & 1 ≤ x ≤ 2 array . If the function f(x) is… NDA 2023 Full Continuity and Differentiability list Continuity and Differentiability JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs