Continuity and Differentiability CBSE Class 12 PYQs

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Continuity and Differentiability PYQs (previous year questions) for CBSE Class 12: Continuity and Differentiability (Mathematics) had 25 questions across the 50 official CBSE Class 12 papers we tagged (2016–2026), and appeared in 9 of them. Asked in 9 of 10 years. The concepts asked in the most papers: Continuity, Implicit Differentiation, Second Order Derivatives.

Year-wise question count

Asked in 9 of 10 years.

Most-asked concepts

Sorted by the number of papers a concept appeared in.

How to practise Continuity and Differentiability PYQs

1. Start with the concepts at the top of the table. They have come back the most.
2. Solve one year’s Continuity and Differentiability questions from the official PDF against the clock, then check the answer listed below.
3. Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
4. Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.

Questions by year

Each line gives the question number and paper, type, concept, our one-line summary, with a link to the official PDF.

CBSE Class 122026

• Q.21 (Mathematics (65/1/1)) · Very short answer · Continuity: Check continuity of a piecewise function at x = 3 PDF
• Q.34 (Mathematics (65/1/1)) · Long answer · Second Order Derivatives: Prove (1 - x^2)y'' - xy' + m^2 y = 0 for x = cos t, y = cos mt PDF

CBSE Class 122025

• Q.5 (Mathematics (65/1/1)) · MCQ · Differentiability: Continuity and differentiability of |x| + |x - 1| at 0 and 1 PDF
• Q.20 (Mathematics (65/1/1)) · Assertion-Reason · Continuity: A-R on value of k making a piecewise function continuous at x = 5 PDF
• Q.21 (Mathematics (65/1/1)) · Very short answer · Derivatives: Differentiate 2^(cos^2 x) with respect to cos^2 x PDF
• Q.32 (Mathematics (65/1/1)) · Long answer · Implicit Differentiation: Prove dy/dx for sqrt(1-x^2) + sqrt(1-y^2) = a(x - y) PDF

CBSE Class 122024

• Q.3 (Mathematics (65/1/1)) · MCQ · Continuity: Continuity and differentiability of a piecewise function at x = 0 PDF
• Q.13 (Mathematics (65/1/1)) · MCQ · Chain Rule: Derivative of sin(x^2) at x = sqrt(pi) PDF
• Q.21 (Mathematics (65/1/1)) · Very short answer · Differentiability: Check differentiability of x^2 |x| at x = 0 PDF
• Q.27 (Mathematics (65/1/1)) · Short answer · Implicit Differentiation: Prove dy/dx relation for sqrt(1-x^2) + sqrt(1-y^2) = a(x - y) PDF

CBSE Class 122023

• Q.13 (Mathematics (65/1/1)) · MCQ · Continuity: Value of k making a piecewise function continuous at x = 2 PDF
• Q.24 (Mathematics (65/1/1)) · Very short answer · Derivatives: Show a relation for dy/dx when y = (x + sqrt(x^2 - 1))^2 PDF

CBSE Class 122020

• Q.12 (Mathematics (65/1/1)) · Fill in the blank · Differentiability: Where the greatest integer function on (0, 2) fails to be continuous PDF
• Q.22 (Mathematics (65/1/1)) · Short answer · Parametric Differentiation: Second derivative for x = at^2, y = 2at PDF
• Q.28 (Mathematics (65/1/1)) · Long answer I · Logarithmic Differentiation: dy/dx for y = e^(x cos x) + (cos x)^x type expression PDF

CBSE Class 122019

• Q.2 (Mathematics (65/1/1)) · Very short answer · Derivative of Composition: Find derivative of fof for f(x) = x + 1 PDF
• Q.16 (Mathematics (65/1/1)) · Long answer I · Implicit Differentiation: Show dy/dx = (x+y)/(x-y) for a log and tan^-1 relation PDF
• Q.17 (Mathematics (65/1/1)) · Long answer I · Second Order Derivatives: Prove a second-order relation for y = (sin^-1 x)^2 PDF

CBSE Class 122018

• Q.7 (Mathematics (65/1)) · Short answer · Derivatives of Inverse Trig: Differentiate tan^-1((1-cos x)/sin x) with respect to x PDF
• Q.14 (Mathematics (65/1)) · Long answer I · Implicit Differentiation: Find dy/dx for (x^2 + y^2)^2 = xy PDF
• Q.15 (Mathematics (65/1)) · Long answer I · Second Order Derivatives: Prove a second-order relation for y = sin(sin x) PDF

CBSE Class 122017

• Q.2 (Mathematics (65/1)) · Very short answer · Continuity: Value of k making a piecewise function continuous at x = 3 PDF
• Q.15 (Mathematics (65/1)) · Long answer I · Logarithmic Differentiation: Find dy/dx for x^y + y^x = a^b PDF

CBSE Class 122016

• Q.9 (Mathematics (65/1/N)) · Long answer I · Continuity: Find a and b so a piecewise function is continuous at x = 0 PDF
• Q.10 (Mathematics (65/1/N)) · Long answer I · Implicit Differentiation: Prove dy/dx for x cos(a+y)=cos y and a second-order relation PDF

Other Mathematics chapters

• Relations and Functions PYQs
• Inverse Trigonometric Functions PYQs
• Matrices PYQs
• Determinants PYQs
• Application of Derivatives PYQs
• Integrals PYQs
• Application of Integrals PYQs
• Differential Equations PYQs
• Vector Algebra PYQs
• Three Dimensional Geometry PYQs
• Linear Programming PYQs
• Probability PYQs

FAQ

How many Continuity and Differentiability questions come in CBSE Class 12?

In the official papers we tagged: 2 in 2026, 4 in 2025, 4 in 2024, 2 in 2023, 3 in 2020, 3 in 2019, 3 in 2018, 2 in 2017 and 2 in 2016. Not asked in the other year. That is 25 questions in all, about 8% of Mathematics.

Which Continuity and Differentiability topics repeat in CBSE Class 12?

Asked in the most papers: Continuity, Implicit Differentiation, Second Order Derivatives. The concept table lists every one with its count.

Are these official CBSE Class 12 questions?

Yes. Every question is from an official CBSE Class 12 paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.