Master Class 12 Maths with our NCERT Solutions Quiz - Perfect for JEE and Engine...

NCERT Solutions for Class 12 Maths

• NCERT Solutions for Class 12 Maths provide a conceptual understanding of all topics in the CBSE Class 12 Maths syllabus.

• These solutions cover important theorems and formulae with detailed explanations.

• NCERT Solutions for Class 12 Maths help students prepare for undergraduate-level Engineering entrance exams like JEE Mains, BITSAT, VITEEE, etc. for the year 2023-2024.

• BYJU’S offers Class 12 Solutions of NCERT with step-by-step explanations of problems given in the textbooks.

• Apart from solutions, BYJU’S also provides Class 12 Maths notes, solved exemplar problems, and previous year question papers, along with worksheets as study materials for students preparing for their Class 12 board exams.

• There are 13 chapters in Class 12 Maths, and each chapter has its own exercise solutions.

• Chapter 1 covers relations and functions, types of relation, types of functions, composition of functions, invertible function, binary operations, and miscellaneous examples.

• Chapter 2 covers inverse trigonometric functions, definition, range, domain, principal value branches, graphs of inverse trigonometric functions, and elementary properties of inverse trigonometric functions.

• Chapter 3 covers matrices, definition of a matrix, types of matrices, equality of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, inverse of a matrix by elementary operations, and miscellaneous examples.

• Chapter 4 covers determinants, determinant of a square matrix, properties of determinants, minors, cofactors, adjoint and inverse of a square matrix, solving system of linear equations in two or three variables using inverse of a matrix, consistency, inconsistency, and number of solutions of a system of linear equations.

• Chapter 5 covers continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second order derivatives, Rolle’s and Lagrange’s Mean Value Theorems, and their geometric interpretations.

• Chapter 6 covers applications of derivatives, rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima and minima, and simple problems.

• Chapter 7 covers integrals, indefinite integral, integration as an inverse process of differentiation, geometrical interpretation of indefinite integral, properties of indefinite integral, comparison between differentiation and integration, methods of integration, definite integrals as a limit of a sum, fundamental theorem of calculus, and miscellaneous examples.

• Chapter 8 covers applications of integrals, finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses, area between the two above-said curves.

• Chapter 9 covers differential equations, definition, order and degree, general and particularProbability and Random Variables: Key Concepts for Class 12 Maths

• The Multiplication theorem of probability allows us to calculate the probability of two or more independent events occurring together.

• Conditional probability is the likelihood of an event occurring given that another event has already occurred.

• Events are independent if the occurrence of one event does not affect the probability of the other occurring.

• The Total Probability theorem is used to calculate the probability of an event occurring based on the probabilities of other related events.

• Bayes' theorem is used to calculate the posterior probability of an event occurring based on prior probabilities and new information.

• A random variable is a variable whose value is determined by chance or probability.

• The probability distribution of a random variable shows the probability of each possible value occurring.

• The mean of a random variable is the expected value, while the variance measures the spread of the distribution.

• Repeated independent trials are used to model situations such as coin tosses or dice rolls.

• The Binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent trials.

• Consistent practice and hard work are essential for mastering Class 12 Maths topics like probability, calculus, coordinate geometry, and trigonometry.

• NCERT Solutions provide in-depth answers to problems covered in the syllabus and can be a valuable tool for exam preparation and homework assignments.

NCERT Solutions for Class 12 Maths

• NCERT Solutions for Class 12 Maths provide a conceptual understanding of all topics in the CBSE Class 12 Maths syllabus.

• These solutions cover important theorems and formulae with detailed explanations.

• NCERT Solutions for Class 12 Maths help students prepare for undergraduate-level Engineering entrance exams like JEE Mains, BITSAT, VITEEE, etc. for the year 2023-2024.

• BYJU’S offers Class 12 Solutions of NCERT with step-by-step explanations of problems given in the textbooks.

• Apart from solutions, BYJU’S also provides Class 12 Maths notes, solved exemplar problems, and previous year question papers, along with worksheets as study materials for students preparing for their Class 12 board exams.

• There are 13 chapters in Class 12 Maths, and each chapter has its own exercise solutions.

• Chapter 1 covers relations and functions, types of relation, types of functions, composition of functions, invertible function, binary operations, and miscellaneous examples.

• Chapter 2 covers inverse trigonometric functions, definition, range, domain, principal value branches, graphs of inverse trigonometric functions, and elementary properties of inverse trigonometric functions.

• Chapter 3 covers matrices, definition of a matrix, types of matrices, equality of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, inverse of a matrix by elementary operations, and miscellaneous examples.

• Chapter 4 covers determinants, determinant of a square matrix, properties of determinants, minors, cofactors, adjoint and inverse of a square matrix, solving system of linear equations in two or three variables using inverse of a matrix, consistency, inconsistency, and number of solutions of a system of linear equations.

• Chapter 5 covers continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second order derivatives, Rolle’s and Lagrange’s Mean Value Theorems, and their geometric interpretations.

• Chapter 6 covers applications of derivatives, rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima and minima, and simple problems.

• Chapter 7 covers integrals, indefinite integral, integration as an inverse process of differentiation, geometrical interpretation of indefinite integral, properties of indefinite integral, comparison between differentiation and integration, methods of integration, definite integrals as a limit of a sum, fundamental theorem of calculus, and miscellaneous examples.

• Chapter 8 covers applications of integrals, finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses, area between the two above-said curves.

• Chapter 9 covers differential equations, definition, order and degree, general and particularProbability and Random Variables: Key Concepts for Class 12 Maths

• The Multiplication theorem of probability allows us to calculate the probability of two or more independent events occurring together.

• Conditional probability is the likelihood of an event occurring given that another event has already occurred.

• Events are independent if the occurrence of one event does not affect the probability of the other occurring.

• The Total Probability theorem is used to calculate the probability of an event occurring based on the probabilities of other related events.

• Bayes' theorem is used to calculate the posterior probability of an event occurring based on prior probabilities and new information.

• A random variable is a variable whose value is determined by chance or probability.

• The probability distribution of a random variable shows the probability of each possible value occurring.

• The mean of a random variable is the expected value, while the variance measures the spread of the distribution.

• Repeated independent trials are used to model situations such as coin tosses or dice rolls.

• The Binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent trials.

• Consistent practice and hard work are essential for mastering Class 12 Maths topics like probability, calculus, coordinate geometry, and trigonometry.

• NCERT Solutions provide in-depth answers to problems covered in the syllabus and can be a valuable tool for exam preparation and homework assignments.

NCERT Solutions for Class 12 Maths

• NCERT Solutions for Class 12 Maths provide a conceptual understanding of all topics in the CBSE Class 12 Maths syllabus.

• These solutions cover important theorems and formulae with detailed explanations.

• NCERT Solutions for Class 12 Maths help students prepare for undergraduate-level Engineering entrance exams like JEE Mains, BITSAT, VITEEE, etc. for the year 2023-2024.

• BYJU’S offers Class 12 Solutions of NCERT with step-by-step explanations of problems given in the textbooks.

• Apart from solutions, BYJU’S also provides Class 12 Maths notes, solved exemplar problems, and previous year question papers, along with worksheets as study materials for students preparing for their Class 12 board exams.

• There are 13 chapters in Class 12 Maths, and each chapter has its own exercise solutions.

• Chapter 1 covers relations and functions, types of relation, types of functions, composition of functions, invertible function, binary operations, and miscellaneous examples.

• Chapter 2 covers inverse trigonometric functions, definition, range, domain, principal value branches, graphs of inverse trigonometric functions, and elementary properties of inverse trigonometric functions.

• Chapter 3 covers matrices, definition of a matrix, types of matrices, equality of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, inverse of a matrix by elementary operations, and miscellaneous examples.

• Chapter 4 covers determinants, determinant of a square matrix, properties of determinants, minors, cofactors, adjoint and inverse of a square matrix, solving system of linear equations in two or three variables using inverse of a matrix, consistency, inconsistency, and number of solutions of a system of linear equations.

• Chapter 5 covers continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second order derivatives, Rolle’s and Lagrange’s Mean Value Theorems, and their geometric interpretations.

• Chapter 6 covers applications of derivatives, rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima and minima, and simple problems.

• Chapter 7 covers integrals, indefinite integral, integration as an inverse process of differentiation, geometrical interpretation of indefinite integral, properties of indefinite integral, comparison between differentiation and integration, methods of integration, definite integrals as a limit of a sum, fundamental theorem of calculus, and miscellaneous examples.

• Chapter 8 covers applications of integrals, finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses, area between the two above-said curves.

• Chapter 9 covers differential equations, definition, order and degree, general and particularProbability and Random Variables: Key Concepts for Class 12 Maths

• The Multiplication theorem of probability allows us to calculate the probability of two or more independent events occurring together.

• Conditional probability is the likelihood of an event occurring given that another event has already occurred.

• Events are independent if the occurrence of one event does not affect the probability of the other occurring.

• The Total Probability theorem is used to calculate the probability of an event occurring based on the probabilities of other related events.

• Bayes' theorem is used to calculate the posterior probability of an event occurring based on prior probabilities and new information.

• A random variable is a variable whose value is determined by chance or probability.

• The probability distribution of a random variable shows the probability of each possible value occurring.

• The mean of a random variable is the expected value, while the variance measures the spread of the distribution.

• Repeated independent trials are used to model situations such as coin tosses or dice rolls.

• The Binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent trials.

• Consistent practice and hard work are essential for mastering Class 12 Maths topics like probability, calculus, coordinate geometry, and trigonometry.

• NCERT Solutions provide in-depth answers to problems covered in the syllabus and can be a valuable tool for exam preparation and homework assignments.

Test your knowledge of Class 12 Maths with our NCERT Solutions quiz! This quiz covers all 13 chapters of the CBSE Class 12 Maths syllabus, including topics like calculus, probability, matrices, and more. Brush up on your understanding of important theorems and formulae with our step-by-step solutions. This quiz is perfect for students preparing for undergraduate-level Engineering entrance exams like JEE Mains, BITSAT, VITEEE, etc. for the year 2023-