Teachoo Quiz

Maths Continuity and Differentiability Class 12 Case Based MCQ Questions

Case Based MCQ Quiz · Class 12 · Maths · CBSE

Preparing for CBSE

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

Practise Continuity and Differentiability Class 12 with Teachoo's Case Based MCQ Quiz (Class 12 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

Attempt time 0:00
This question 0:00
Question 1 of 10
Advertisement
Question 1 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
\(f \circ g(\mathrm{x})=\) \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 2 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
\(g \circ f(x)=\) \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 3 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
$$ \frac{d}{d x}\left(\sin ^3 x\right)= $$

\(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 4 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
$$ \frac{d}{d x}\left(\sin x^3\right) $$

\(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 5 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
\(\frac{d}{d x}(\sin 2 \mathrm{x})\) at \(\mathrm{x}=\frac{\pi}{2}\) is \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 6 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
(i) Rolle's theorem is not applicable for the function \(\mathrm{f}(\mathrm{x})=\tan \mathrm{x}\) in \([0, \pi]\) because \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 7 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
The value of c satisfying Rolle's theorem for the function \(\mathrm{g}(\mathrm{x})=\sin \mathrm{x}\) in \([0, \pi]\) is \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 8 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
The value of c satisfying Rolle's theorem for the function \(\mathrm{h}(\mathrm{x})= \cos x\) in \([0,2 \pi]\) is \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 9 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
The value of c satisfying Rolle's theorem for the function \(p(x)=\sin x+\cos x\) in \([0, \pi]\) is \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 10 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
Rolle's theorem is not applicable for the function \(f(x)=|x|\) in [-2, 2] because \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.

Frequently asked questions

Who is this Continuity and Differentiability Class 12 quiz for?

This Case Based MCQ Quiz covers Continuity and Differentiability Class 12 for Class 12 · Maths · CBSE. Practise the questions in the interactive quiz and check your answers.

Is this quiz free?

Yes. This online quiz is free to attempt. Teachoo Black is not required to take the quiz.

How many questions will I get?

The current selection contains 10 questions. The questions and count can vary with the available question bank and grouped questions.

Can I check my answers and score?

Yes. In quiz mode, check your answer to receive feedback. Submit the quiz to review your score and answers. Full Teachoo solution links are shown where available.

Will I get the same questions when I retry?

Questions can change between attempts. Teachoo uses your previous practice when available to prioritise new questions and revision; a completely new set is not guaranteed.

Practice · Continuity and Differentiability Class 12

Stuck? Keep your progress moving.