NCERT Solutions for Class 12 Maths Chapter 5 Continuity & Differentiability Miscellaneous Exercise

Exams Prep Master

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Miscellaneous Exercise is covered in this article. This miscellaneous exercise includes questions from Continuity, Algebra of continuous functions, Differentiability, Derivatives of composite functions, Derivatives of implicit functions, Derivatives of inverse trigonometric functions, Exponential and Logarithmic Functions, Logarithmic Differentiation, Derivatives of Functions in Parametric Forms, Second Order Derivative, Mean Value Theorem.

NCERT Solutions for Class 12 Maths Chapter 5 will carry a weightage of around 8-17 marks in the CBSE Term 2 Exam 2022.
NCERT has provided a total of 23 problems and solutions based on the important topic covered in this exercise.

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

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

CBSE CLASS XII Related Questions

1.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).
View Solution
2.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:

(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).
View Solution
3.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]
View Solution
4.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]
View Solution
5.
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

(i) Find \(f'(x)\) for \(0<x>3\).
(ii) Find \(f'(4)\).
(iii)(a) Test for continuity of \(f(x)\) at \(x=3\).
OR
(iii)(b) Test for differentiability of \(f(x)\) at \(x=3\).
View Solution
6.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.
View Solution

View All

Similar Mathematics Concepts

Continuity and Differentiability of a Function: Theorem & Examples

Exponential Growth Formula with Solved Examples

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

Derivatives of Function in Parametric Form & Sample Questions

Differentiation Rules: Trigonometric & Inverse Trigonometric Function

Slope Intercept Form Formula: Conversion and Examples

Quotient: Meaning, Division, Verification, Related Terms & Examples

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.2

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.3

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exercise 5.4

CBSE CLASS XII Previous Year Papers

Mathematics

Mathematics Preparation Guides

Matrices: Types, Properties, Formulas & Examples

Relations and Functions: Explanation, Types, and Representation

Types of Matrices: Row, Column, Zero, Symmetric, Skew Symmetric

Minors and Cofactors of Determinant: Definition, Formula and Solved Examples

Operations on Matrices: Addition, Subtraction, Multiplication and Solved Examples

Determinants: Types, Properties & Examples

Types of Relations: Definition, Classification and Examples

Properties of Determinants: Explanation, Important Properties and Examples

Plane: Equation of a Plane in Three-Dimensional Space

Invertible Matrices: Theorems, Properties and Examples

Symmetric and Skew Symmetric Matrices: Definition and Properties

Types of Functions: Elements, Equations, Range, and Domain

Introduction to Three-Dimensional Geometry: Distance, Important Formulae

Angle between Two Lines: Formula, Derivation & Calculation

Binary Operations: Types, Properties and Examples

Addition of Vectors: Definition, Formula, Laws and Properties

Types of Vectors: Definition, Properties & Examples

Definite Integral: Formula, Properties, Application & Examples

Integration by Partial Fractions: Formula, Steps & Examples

Angle Between a Line and a Plane: Formulas and Solved Examples

Mathematics NCERT Solutions

NCERT Solutions For Class 12 Mathematics Chapter 13: Probability

NCERT Solutions For Class 12 Mathematics Chapter 9: Differential Equations

NCERT Solutions For Class 12 Mathematics Chapter 7 Integrals

NCERT Solutions For Class 12 Mathematics Chapter 12: Linear Programming

NCERT Solutions for Class 12 Maths Chapter 3 Matrices

NCERT Solutions For Class 12 Mathematics Chapter 6 Applications of Derivatives

NCERT Solutions For Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

You can also check

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)

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

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

NCERT Solutions for Class 12 Maths Chapter 5 Continuity & Differentiability Miscellaneous Exercise

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

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 \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).

3.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

4.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

6.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

NCERT Solutions for Class 12 Maths Chapter 5 Continuity & Differentiability Miscellaneous Exercise

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

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 \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).

3.Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

4.Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

6.A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).

3.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

4.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

6.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.