Class 12 Chapter 5 Continuity and Differentiability Previous Year Questions
Master Calculus through topic-wise previous year questions (2014-2026). These modules cover all essential board exam topics including continuity, differentiability, inverse trig, logarithmic, implicit, and parametric functions.
Start with continuity and differentiability tests, then build through chain-rule, inverse-trigonometric, logarithmic, implicit, and parametric derivatives. The topic sequence also includes second-order derivatives, helping you connect notation, domain conditions, and stepwise methods in Class 12 board solutions.
Topic-wise PYQ Practice
- 1. Continuity of Functions (Finding k, a, b)
- 2. Differentiability Proofs
- 3. Differentiation Rules
- 4. Inverse Trigonometric Derivatives
- 5. Logarithmic Differentiation
- 6. Implicit Differentiation
- 7. Parametric Differentiation
- 8. Second Order Derivatives
Step-wise marking is strictly enforced across all 2-mark, 3-mark, and 5-mark subjective questions. Always quote standard algebraic identities or theorem statements before carrying out algebraic substitutions. For matrix operations and vector cross-products, clearly tabulate intermediate matrix rows and components to guarantee full partial credit even if a minor arithmetic slip occurs in the final step.
CBSE Class 12 Chapter 5: Continuity and Differentiability Blueprint & Exam Strategy
Marks Weightage: Unit III: Calculus (Total 35 Marks across Chapters 5 through 9). Question blueprint: Usually comprises 1-2 MCQs (1 Mark), one 2-Mark or 3-Mark problem on finding constants (k, a, b) for a continuous function, and one 3-Mark or 5-Mark problem on logarithmic or second-order parametric differentiation.
Examiner Advice: For continuity at x = c, explicitly show that Left Hand Limit equals Right Hand Limit and equals f(c). When performing logarithmic differentiation for functions of form u(x)^v(x), remember to apply the product rule carefully after taking log on both sides. In second-order derivatives d^2y/dx^2 with parametric equations, do not forget the chain rule factor dt/dx.