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Limits and Derivatives — NEET Maths MCQs

30 questions written by hand against the NCERT chapter. Every wrong option is explained, not just the right one.

30questions
10/14/6easy / medium / hard
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Sample questions from this chapter

The limit of a function at a point exists when its left-hand and right-hand limits at that point are
  1. equal ✓
  2. both positive
  3. both non-zero
  4. unequal
Answer: A. A two-sided limit exists precisely when the two one-sided limiting values agree.
Why not B: The common limiting value may be negative or zero; its sign does not decide existence.
Why not C: A limit can exist and equal zero, so non-zero one-sided values are not required.
Why not D: Unequal one-sided limits are precisely the reason a two-sided limit fails to exist.
Let f(x) = 1 for x < 0 and f(x) = 2 for x ≥ 0. What is lim(x→0) f(x)?
  1. 1
  2. 2
  3. Does not exist ✓
  4. 3/2
Answer: C. The left-hand limit is 1 while the right-hand limit is 2, so the two-sided limit does not exist.
Why not A: This uses only the values approached from the negative side and ignores the right-hand limit.
Why not B: This uses f(0) and the right-hand behaviour but ignores values approaching from the left.
Why not D: A two-sided limit is not obtained by averaging unequal one-sided limits.
Evaluate lim(x→0) (sin 5x)/(sin 2x).
  1. 5/2 ✓
  2. 2/5
  3. 5
  4. 2
Answer: A. Multiplying by 5x/5x and 2x/2x reduces the standard-limit factors to 1, leaving 5/2.
Why not B: This reverses numerator and denominator coefficients after applying the standard sine limit.
Why not C: This retains the factor 5 but omits division by the denominator factor 2.
Why not D: This retains the factor 2 from the denominator and discards the numerator factor 5.

These are 3 of the 30 questions in the test. Take the full chapter test →

Read the chapter first

Every NCERT question in this chapter is solved, free: NCERT solutions — Limits and Derivatives →

Other NEET Maths chapters

SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsLinear InequalitiesPermutations and Combinations

All 27 chapters →

Questions

How many NEET questions are there on Limits and Derivatives?

This chapter test has 30 questions — 10 easy, 14 medium and 6 hard — all written against the NCERT Class 11 chapter.

Is this NEET Maths chapter test free?

Yes. Every chapter test is free with no login, and you get your all-India rank on every one. Nothing on the site is on sale right now.

Do the questions explain the wrong options?

Yes — every distractor carries its own explanation naming the specific misconception that makes a student pick it. That is the part most question banks skip, and it is the part that changes your next attempt.