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Continuity and Differentiability — 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

A function f is continuous at x=c when
  1. lim x→c f(x)=f(c) ✓
  2. f′(c)=0
  3. f(c)=0
  4. left limit alone equals f(c)
Answer: A. At an interior point, the two-sided limit must exist and equal the function value.
Why not B: Uses the definition.
Why not C: Confuses continuity with a stationary point.
Why not D: Confuses continuity with having a zero.
For f(x)=(x²−1)/(x−1), x≠1, and f(1)=k, continuity at 1 requires k=
  1. 0
  2. 1
  3. 2 ✓
  4. −2
Answer: C. For x≠1, f=x+1, whose limit at 1 is 2; continuity therefore requires k=2.
Why not A: Substitutes before cancelling.
Why not B: Reports the cancelled factor's root value 1 instead of evaluating x+1.
Why not D: Loses the sign after cancellation.
For f(x)=|x−2|, the point of nondifferentiability is
  1. 2 ✓
  2. 0
  3. −2
  4. all x
Answer: A. The absolute-value corner occurs where x−2=0.
Why not B: Locates the shifted corner.
Why not C: Forgets the horizontal shift.
Why not D: Reverses the shift sign.

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 — Continuity and Differentiability →

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 Continuity and Differentiability?

This chapter test has 30 questions — 10 easy, 14 medium and 6 hard — all written against the NCERT Class 12 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.