NCERT Mathematics · Class XII · Chapter 5

Continuity and Differentiability

Previous Years' Objective Questions — Entrance Exam Series

Questions

1997

From

2025

Exams

BITSATJEE AdvancedJEE Main

ContinuityDifferentiabilityExponential & Logarithmic FunctionsLogarithmic DifferentiationDerivatives in Parametric FormSecond Order DerivativesRolle's & Mean Value Theorem

Check left-hand and right-hand limits for continuity at a point.

Differentiability implies continuity — not the converse.

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Logarithmic differentiation for products/powers of functions.

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Continuity and Differentiability is the calculus backbone of Class XII, tested in nearly every JEE paper. These 50 questions from 1997–2025 cover continuity checks, differentiability, logarithmic/parametric differentiation, and higher-order derivatives.

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Frequently Asked Questions

Continuity describes whether a function behaves without a break at a point, whereas differentiability concerns the existence of its derivative there. Every differentiable function is continuous, although the converse is not always true.

Continuity and Differentiability is relevant to JEE Main and JEE Advanced, with recurring problems involving limits, piecewise functions, differentiability, derivatives, Rolle's Theorem, and the Mean Value Theorem.

Continuity at \(x=a\) requires \(\lim_{x\to a}f(x)=f(a)\). For a piecewise function, the left-hand limit and right-hand limit must also agree with the function's value at that point.

The left-hand derivative and right-hand derivative must both exist and have the same value. Equivalently, \(f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}\) must exist.

Yes. Differentiability at a point guarantees continuity at that point. The reverse implication is not universally valid.

Yes. The standard example is \(f(x)=|x|\), which is continuous at \(x=0\) but fails to be differentiable there because its left-hand and right-hand derivatives are unequal.

Key areas include piecewise-function continuity, modulus-based functions, differentiability, standard limits, the chain rule, implicit and logarithmic differentiation, parametric differentiation, derivatives of inverse trigonometric functions, Rolle's Theorem, and Lagrange's Mean Value Theorem.

Yes. They are based on recurring concepts and standard question patterns relevant to JEE Main, JEE Advanced, IIT-JEE, BITSAT, Olympiads, and state engineering entrance examinations.

Begin with standard limits and fundamental derivative formulas, then practise continuity and differentiability of piecewise and modulus functions. After that, work on chain-rule, implicit, inverse-trigonometric, and Mean Value Theorem problems through timed MCQ practice.

Yes. Every question provides four answer choices, identifies the correct option, and includes a concise explanation highlighting the principal concept or calculation behind the answer.

Continuity and Differentiability

CONTINUITY AND DIFFERENTIABILITY — Learning Resources

Frequently Asked Questions

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Continuity and Differentiability

CONTINUITY AND DIFFERENTIABILITY — Learning Resources

Frequently Asked Questions

Q 01 What does the Continuity and Differentiability chapter deal with?

Q 02 Why should JEE aspirants give special attention to this chapter?

Q 03 How can I determine whether a function is continuous at \(x=a\)?

Q 04 What must be checked to establish differentiability at \(x=a\)?

Q 05 Is every differentiable function necessarily continuous?

Q 06 Can continuity exist without differentiability?

Q 07 Which areas of this chapter deserve the most MCQ practice?

Q 08 Can these MCQs support preparation for JEE Main and JEE Advanced?

Q 09 What is an effective way to prepare this chapter for competitive exams?

Q 10 Do the questions include solutions or explanations?

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