Teachoo MCQ Test

Case Based MCQ Quiz

Chapter 5 Class 12 Continuity and Differentiability | 10 questions

Timed test. Answer every question before time runs out. Correct answers and solutions appear after submission.
Time remaining 912
Question 1 of 10
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 one option. Answers are shown after the test.
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 one option. Answers are shown after the test.
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 one option. Answers are shown after the test.
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 one option. Answers are shown after the test.
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 one option. Answers are shown after the test.
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 one option. Answers are shown after the test.
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 one option. Answers are shown after the test.
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 one option. Answers are shown after the test.
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 one option. Answers are shown after the test.
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 one option. Answers are shown after the test.