QUESTION BANK FOR MATHEMATICS FOR CLASS XII LIST OF …

1 LIST OF MEMBERS WHO PREPAREDQUESTION BANK FOR MATHEMATICS FOR CLASS XIISl. , Jheel Khuranja(Group Leader)Delhi 31.(M. 9810233862) Sanjeev , Raj Niwas Marg,(Lecturer Maths)Delhi.(M. 9811458610) , Gandhi Nagar(Lecturer Maths)Delhi 31(M. 9818415348) Joginder , Hari Nagar(Lecturer Maths)Delhi.(M. 9953015325) Manoj , Kishan Kunj(Lecturer Maths)Delhi.(M. 9818419499) , No. 1, Roop Nagar(Lecturer Maths)Delhi-110007(M. 9899240678)2 XII MathsCLASS XIIMATHEMATICSU nitsWeightage (Marks)(i)Relations and Functions10(ii)Algebra13(iii)Calculus44( iv)Vector and Three Dimensional Geometry17(v)Linear Programming06(vi)Probability10 Total : 100 Unit I : RELATIONS AND and functions (10 Periods)Types of Relations : Reflexive, symmetric, transitive and equivalence relations.

2 One to one andonto functions , composite functions , inverse of a function. Binary Trigonometric functions (12 Periods)Definition, range, domain, principal value branches. Graphs of inverse trigonometric properties of inverse trigonometric II : (18 Periods)Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetricand skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simpleproperties of addition, multiplication and scalar multiplication. Non-commutativity of multiplicationof matrices and existence of non-zero matrices whose product is the zero matrix (restrict tosquare matrices of order 2).

3 Concept of elementary row and column operations. Invertiblematrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have realentries). (20 Periods)Determinant of a square matrix (up to 3 3 matrices), properties of determinants, minors,cofactors and applications of determinants in finding the area of a triangle. adjoint and inverseof a square matrix. Consistency, inconsistency and number of solutions of system of linear3 XII Mathsequations by examples, solving system of linear equations in two or three variables (havingunique solution) using inverse of a III : and Differentiability(18 Periods)Continuity and differentiability, derivative of composite functions , chain rule, derivatives of inversetrigonometric functions , derivative of implicit function.

4 Concept of exponential and logarithmicfunctions and their derivatives. Logarithmic differentiation. Derivative of functions expressed inparametric forms. Second order derivatives. Rolle s and Lagrange s mean Value Theorems(without proof) and their geometric of Derivatives(10 Periods)Applications of Derivatives : Rate of change, increasing/decreasing functions , tangents andnormals, approximation, maxima and minima (first derivative test motivated geometrically andsecond derivative test given as a provable tool). Sample problems (that illustrate basic principlesand understanding of the subject as well as real-life situations).

5 (20 Periods)Integration as inverse process of differentiation. Integration of a variety of functions by substitution,by partial fractions and by parts, only simple integrals of the type to be ,,,,dxdxdxdxdxx a x a a a ax bx cax bx c222222,,andpx qpx qdxdx a x dxx a dxax bx cax bx cDefinite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basicproperties of definite integrals and evaluation of definite of the Integrals(10 Periods)Application in finding the area under simple curves, especially lines, area of circles/parabolas/ellipses (in standard form only), area between the two above said curves (the region should beclearly identifiable).

6 Equations(10 Periods)Definition, order and degree, general and particular solutions of a differential equation. Formationof differential equation whose general solution is given. Solution of differential equations bymethod of separation of variables, homogeneous differential equations of first order and firstdegree. Solutions of linear differential equation of the type :, whereandare function of .dyp x y q xp xq xxdx4 XII MathsUnit IV : VECTORS AND THREE-DIMENSIONAL (12 Periods)Vectors and scalars, magnitude and direction of a vector. Direction consines/ratios of 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 bya scalar, position vector of a point dividing a line segment in a given ratio.

7 Scalar (dot) productof vectors, projection of a vector on a line. Vector (cross) product of Geometry(12 Periods)Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line,coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation ofa plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a pointfrom a V : LINEAR Programming : Introduction, definition of related terminology such as constraints, objectivefunction, optimization, different types of linear programming ( ) problems, mathematicalformulation of problems, graphical method of solution for problems in two variables, feasibleand infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to threenon-trivial constraints).

8 Unit VI : (18 Periods)Multiplication theorem on probability. Conditional probability, independent events, total probability,Baye s theorem, Random variable and its probability distribution, mean and variance of haphazardvariable. Repeated independent (Bernoulli) trials and Binomial and Trigonometric and of of Papers1096 XII Maths7 XII MathsCHAPTER 1 RELATIONS AND functions Relation R from a set A to a set B is subset of A B. A B = {(a, b) : a A, b B}. If n(A) = r, n (B) = s then n (A B) = no. of relations = 2rs is also a relation defined on set A, called the void (empty) relation.

9 R = A A is called universal relation. Reflexive Relation : Relation R defined on set A is said to be reflexive iff (a, a) R a A Symmetric Relation : Relation R defined on set A is said to be symmetric iff (a, b) R (b, a) R a, b, A Transitive Relation : Relation R defined on set A is said to be transitive if (a, b) R, (b, c) R (a, c) R a, b, c R Equivalence Relation : A relation defined on set A is said to be equivalence relation iff it isreflexive, symmetric and transitive. One-One Function : f : A B is said to be one-one if distinct elements in A has distinct imagesin B.

10 X1, x2 A x1 x2 f(x1) f(x2).OR x1, x2 A f(x1) = f(x2) x1 = x2 One-one function is also called injective function. Onto function (surjective) : A function f : A B is said to be onto iff Rf = B b B, thereexist a A f(a) = b A function which is not one-one is called many-one Maths A function which is not onto is called into. Bijective Function : A function which is both injective and surjective is called bijective. Composition of Two Function : If f : A B, g : B C are two functions , then composition off and g denoted by gof is a function from A to C give by, (gof) (x) = g (f (x)) x AClearly gof is defined if Range of f C domain of g similarly fog similarly fog can be defined.