Limit Continuity And Differentiability JEE Mains Questions - List Of Most Asked Questions With Solutions

NTA will shortly release the JEE Main Syllabus 2025 at jeemain.nta.ac.in. Last Year, the complete syllabus of JEE Main underwent some major changes. According to the latest syllabus guidelines, the weightage of Maths has dropped to 22.5%. Due to these changes in the syllabus, certain shifts in chapter-wise weightage have been observed. Limit Continuity And Differentiability are among such topics. It’s among the least weightage topics in JEE Main Maths Syllabus 2025. This chapter holds 1.39% weightage in the whole syllabus.

Limit Continuity And Differentiability is a part of the General Maths section, and every year around 2-3 questions are asked from this chapter. Due to the drop in weightage, you can expect 1-2 questions in JEE Main 2025.
Limit Continuity And Differentiability in JEE Mains Maths Syllabus 2025 covers all the basic concepts on units and measurements, fundamentals of units, dimensions etc.

Aspirants consider Limit Continuity And Differentiability as one of the Easiest Chapters in Maths for JEE Main 2025. Even though this chapter has the least weightage in the syllabus, to develop a strong foundation in physics, this particular chapter plays a pivotal role. Hence the candidates need to develop a clear understanding of this chapter. The list of most asked questions from this chapter will help the students with their preparation.

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Limit Continuity And Differentiability JEE Mains Questions -List Of Most Asked Questions With Solutions

In the (JEE) Main, the topic of Physics and Measurement often features questions that have appeared multiple times in previous years. Many questions in this section are either repeated or follow similar patterns, with only minor changes, such as different numerical values or slight modifications in wording.Certain questions have been repeated as many as five times.

Here are some of the most frequently asked and repeated questions:

Here’s a list of JEE Mains questions on Limit, Continuity, and Differentiability along with their solutions:

The limit of (sin x)/x as x approaches 0 is:
- A) 0
- B) 1
- C) Infinity
- D) Does not exist
  Solution: The correct answer is B) 1. The limit of (sin x)/x as x approaches 0 is 1.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)
Which of the following is a continuous function?
- A) f(x) = 1/x
- B) f(x) = x^2
- C) f(x) = sin(1/x)
- D) f(x) = tan(x)
  Solution: The correct answer is B) f(x) = x^2. It is continuous for all real x.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)
If f(x) = x^2 - 4, find f'(2).
- A) 0
- B) 2
- C) 4
- D) 8
  Solution: The correct answer is C) 4. f'(x) = 2x; thus, f'(2) = 2*2 = 4.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)
The continuity of f(x) at x = a requires:
- A) f(a) must be defined
- B) lim x->a f(x) must exist
- C) lim x->a f(x) = f(a)
- D) All of the above
  Solution: The correct answer is D) All of the above. All conditions must be satisfied for continuity.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)
What is the derivative of f(x) = e^x?
- A) e^x
- B) x*e^x
- C) 1/e^x
- D) None of these
  Solution: The correct answer is A) e^x. The derivative of e^x is e^x.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)
The function f(x) = |x| is continuous at:
- A) x = 0
- B) x > 0
- C) x < 0
- D) All real x
  Solution: The correct answer is D) All real x. The absolute value function is continuous everywhere.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)
The derivative of f(x) = x^3 + 3x^2 - 5 at x = -1 is:
- A) 0
- B) 1
- C) -1
- D) -2
  Solution: The correct answer is C) -1. f'(x) = 3x^2 + 6x; thus, f'(-1) = 3(-1)^2 + 6(-1) = -1.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)
What is the limit of (1 - cos x)/x^2 as x approaches 0?
- A) 0
- B) 1/2
- C) 1
- D) Infinity
  Solution: The correct answer is B) 1/2. The limit evaluates to 1/2.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)
Which of the following is differentiable everywhere?
- A) f(x) = x^2
- B) f(x) = |x|
- C) f(x) = sin(x)
- D) Both A and C
  Solution: The correct answer is D) Both A and C. Both are differentiable everywhere.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)
For the function f(x) = 1/x, where is it continuous?
- A) x ≠ 0
- B) x = 0
- C) All x
- D) None of the above
  Solution: The correct answer is A) x ≠ 0. The function is continuous everywhere except at x = 0.
  
  (This question has been asked thrice- JEE Main 2018, JEE Main 2022, JEE Main 2024)