Class 12th Maths Exercise 5.1 Solution

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NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.1 is covered in this article. Chapter 5 includes questions from introduction, continuity, and algebra of continuous functions and will carry a weightage of around 8-17 marks in the CBSE Term 2 Exam 2022. NCERT has provided a total of 34 problems and solutions based on the important topics.

Download PDF NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.1

NCERT Solutions for Class 12 Maths Chapter 5: Important Topics

Important topics covered in the Continuity and Differentiability chapter are:

Mean Value Theorem
Rolle’s Theorem
Limits
Euler’s Number
Quotient Rule

Also check: NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

Other Exercise Solutions of Class 12 Maths Chapter 5 Continuity and Differentiability

Exercise 5.1 Solutions	34 Questions (Short Answers)
Exercise 5.2 Solutions	10 Questions(Short Answers)
Exercise 5.3 Solutions	15 Questions ( Short Answers)
Exercise 5.4 Solutions	10 Questions (Short Answers)
Exercise 5.5 Solutions	18 Questions ( Short Answers)
Exercise 5.6 Solutions	11 Questions (Short Answers)
Exercise 5.7 Solutions	17 Questions (Short Answers)
Exercise 5.8 Solutions	6 Questions (Short Answers)
Miscellaneous Exercise Solutions	23 Questions (6 Long Answers, 17 Short Answers)

Chapter 5 Continuity and Differentiability Topics:

Exponential growth formula	Limits and Continuity	Slope of secant line formula
Continuous Function	Mean Value Theorem	Second Order Derivative
Rolle’s Theorem	Mean value theorem formula	Difference quotient formula

CBSE Class 12 Mathematics Study Guides:

NCERT Solutions for Class 12 Maths	Maths MCQs	Maths Syllabus
Maths Study Material	Trigonometry	Arithmetic
Mathematics Notes	Permutation and Combination	Algebra

CBSE CLASS XII Related Questions

1.
Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]

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2.
If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]

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3.
Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

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4.
Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.

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5.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true and Reason (R) is false.
Assertion (A) is false and Reason (R) is true.

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6.
The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

\( e^{-3} \)
\( -1 \)
\( 1 \)
\( -e^3 \)

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Class 12th Maths Exercise 5.1 Solution

Download PDF NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.1

NCERT Solutions for Class 12 Maths Chapter 5: Important Topics

Other Exercise Solutions of Class 12 Maths Chapter 5 Continuity and Differentiability

CBSE CLASS XII Related Questions

1.
Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]

2.
If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]

3.
Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

4.
Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.

5.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

6.
The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

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Class 12th Maths Exercise 5.1 Solution

Download PDF NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.1

NCERT Solutions for Class 12 Maths Chapter 5: Important Topics

Other Exercise Solutions of Class 12 Maths Chapter 5 Continuity and Differentiability

CBSE CLASS XII Related Questions

1.Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]

2. If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]

3. Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

4.Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.

5.Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \). Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

6. The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

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1.
Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]

2.
If \[ \frac{d}{dx}(F(x))=\frac{1}{e^x+1}, \] then find \(F(x)\), given that \[ F(0)=\log\left(\frac{1}{2}\right). \]

3.
Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

4.
Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.

5.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

6.
The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is: