Continuity and Differentiability

173 CBSE Class 12 Mathematics past-year questions from 4 papers, 2023 to 2026, with answers and worked solutions.

Difficulty: 29 easy · 116 moderate · 28 hard.
Most-asked subtopics: Differentiability and the Chain Rule (45), Derivatives of Implicit and Inverse Trigonometric Functions (36), Continuity (34).
Updated 19 August 2026.

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Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as follows : $f(x) = \begin{cases} x^4 - 4x^2 + 4, & 0 \leq x < 3 \\ x^2 + 40, & x \geq 3 \end{cases}$ Based on given information, answer the following questions :
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A volleyball player serves the ball which takes a parabolic path given by the equation $h(t) = -\frac{7}{2} t^2 + \frac{13}{2} t + 1$ , where h(t) is the height of ball at any time t (in seconds), $(t \geq 0)$ .
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Direction : Question numbers 19 and 20 are Assertion (A) and Reason (R) based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and other labelled Reason (R). Select the correct answer from the options (A), (B), (C) and (D) as given below.
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Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
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#37Differentiability and the Chain Rule
Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as follows : $f(x) = \begin{cases} x^4 - 4x^2 + 4, & 0 \leq x < 3 \\ x^2 + 40, & x \geq 3 \end{cases}$ Based on given information, answer the following questions :
#38Differentiability and the Chain Rule
Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as follows : $f(x) = \begin{cases} x^4 - 4x^2 + 4, & 0 \leq x < 3 \\ x^2 + 40, & x \geq 3 \end{cases}$ Based on given information, answer the following questions :
#39Differentiability and the Chain Rule
Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as follows : $f(x) = \begin{cases} x^4 - 4x^2 + 4, & 0 \leq x < 3 \\ x^2 + 40, & x \geq 3 \end{cases}$ Based on given information, answer the following questions :
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Continuity and Differentiability

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