MP Board Class 12th Maths Important Questions with Answers Guide Pdf Free Download गणित in both Hindi Medium and English Medium are part of MP Board Class 12th Solutions. Here we have given NCERT Madhya Pradesh Syllabus MP Board Class 12 Maths Book Question Bank Solutions Ganit Pdf.

## MP Board Class 12th Maths Important Questions in English Medium

- Chapter 1 Relations and Functions Important Questions
- Chapter 2 Inverse Trigonometric Functions Important Questions
- Chapter 3 Matrices Important Questions
- Chapter 4 Determinants Important Questions
- Chapter 5A Continuity and Differentiability Important Questions
- Chapter 5B Differentiation Important Questions
- Chapter 6 Application of Derivatives Important Questions
- Chapter 7A Integration Important Questions
- Chapter 7B Definite Integral Important Questions
- Chapter 8 Application of Integrals Important Questions
- Chapter 9 Differential Equations Important Questions
- Chapter 10 Vector Algebra Important Questions
- Chapter 11 Three Dimensional Geometry Important Questions
- Chapter 12 Linear Programming Important Questions
- Chapter 13 Probability Important Questions

## MP Board Class 12th Maths Important Questions in Hindi Medium

- Chapter 1 संबंध एवं फलन Important Questions
- Chapter 2 प्रतिलोम त्रिकोणमितीय फलन Important Questions
- Chapter 3 आव्यूह Important Questions
- Chapter 4 सारणिक Important Questions
- Chapter 5 सांतत्य तथा अवकलनीयता Important Questions
- Chapter 6 अवकलज के अनुप्रयोग Important Questions
- Chapter 7 समाकलन Important Questions
- Chapter 8 समाकलनों के अनुप्रयोग Important Questions
- Chapter 9 अवकल समीकरण Important Questions
- Chapter 10 सदिश बीजगणित Important Questions
- Chapter 11 त्रि-विमीय ज्यामिति Important Questions
- Chapter 12 रैखिक प्रोग्रामन Important Questions
- Chapter 13 प्रायिकता Important Questions

### MP Board Class 12th Maths Syllabus and Marking Scheme

Latest Syllabus and Marks Distribution Maths Class XII for the academic year 2019 – 2020 Year Examination.

Maths

Class XII

Time : 3 Hours.

Maximum Marks: 100

Unit Wise Division of Marks

Unit | Topics | Periods | Marks |

I. | Relations and Functions | 30 | 10 |

II. | Algebra | 50 | 13 |

III. | Calculus | 80 | 44 |

IV. | Vectors and Three-dimensional Geometry | 30 | 17 |

V. | Linear Programming | 20 | 06 |

VI. | Probability ‘ | 30 | 10 |

Total | 240 | 100 |

Unit I: Relations and Functions

1. Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.

2. Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Unit II: Algebra

3. Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

4. Determinants

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit III: Calculus

5. Continuity and Differentiability

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.

Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

6. Applications of Derivatives

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

7. Integrals

Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

8. Applications of the Integrals

Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

9. Differential Equations

Definition, order and degree, general and particular solutions of a differential equation.Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

dy/dx + py = q, where p and q are functions of x or constants.

dx/dy + px = q, where p and q are functions of y or constants.

Unit IV: Vectors and Three-Dimensional Geometry

10. Vectors

Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.

11. Three – dimensional Geometry

Direction cosines and direction ratios of a line joining two points.Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines.Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

Unit V: Linear Programming

12. Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit VI: Probability

13. Probability

Conditional probability, multiplication theorem on probability. independent events, total probability, Baye’s theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

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