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Maths Continuity and Differentiability Class 12 MCQ and Assertion Questions

10 Question MCQ (including Assertion) · Class 12 · Maths · CBSE

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Chapter 5 Class 12 Continuity and Differentiability | 10 questions | about 8 minutes

Practise Continuity and Differentiability Class 12 with Teachoo's 10 Question MCQ (including Assertion) (Class 12 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

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Question 1 of 10
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Question 1 of 10
NCERT Exemplar
The number of points at which the function \(\mathrm{f}(\mathrm{x})=\frac{1}{x-[x]}\) is not continuous is
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Question 2 of 10
The function \(f(x)=[x]\) (the greatest integer function) is often used to model scenarios where values are truncated or rounded down. The discontinuity at integer values implies:
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Question 3 of 10
CBSE Board Exam 2026
If \(f(x)=\left\{\begin{array}{cc}\frac{x^2-4 x-5}{x+1}, & x \neq-1 \\ k, & x=-1\end{array}\right.\) is continuous at \(\mathrm{x}=-1\), then the value of k is :
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Question 4 of 10
NCERT Exemplar
The value of k which makes the function defined by \(f(\mathrm{x})= \left\{\begin{array}{cl}\sin \frac{1}{x}, & \text { if } x \neq 0 \\ k, & \text { if } \mathrm{x}=0\end{array}\right.\), continuous at \(\mathrm{x}=0\) is
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Question 5 of 10
CBSE Board Exam 2026
If \(\tan ^{-1} x=y\), then \(\frac{d y}{d x}\) is equal to :
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Question 6 of 10
NCERT Exemplar
The set of points where the functions \(f\) given by \(f(x)=|x-3| \cos x\) is differentiable is
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Question 7 of 10
CBSE Board Exam 2026
If \(x+y=x y\), then \(\frac{d y}{d x}\) is
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Question 8 of 10
NCERT Exemplar
The derivative of \(\cos ^{-1}\left(2 x^2-1\right)\) w.r.t. \(\cos ^{-1} x\) is
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Question 9 of 10
NCERT Exemplar
The function \(\mathrm{f}(\mathrm{x})=[\mathrm{x}]\), where \([\mathrm{x}]\) denotes the greatest integer function, is continuous at
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Question 10 of 10
NCERT Exemplar
If \(x=t^2, y=t^3\), then \(\frac{d^2 y}{d x^2}\) is
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