Download CBSE Value Based Questions for CBSE Class 12 Mathematics 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.
Download CBSE Value Based Questions for CBSE Class 12 Mathematics 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).
Download CBSE Value Based Questions for CBSE Class 12 Mathematics 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.
Download CBSE Value Based Questions for CBSE Class 12 Mathematics Application 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).
Download CBSE Value Based Questions for CBSE Class 12 Mathematics 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.
Download CBSE Value Based Questions for CBSE Class 12 Mathematics Application of 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).
Download CBSE Value Based Questions for CBSE Class 12 Mathematics 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.
Download CBSE Value Based Questions for CBSE Class 12 Mathematics Vector Algebra 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.
Download CBSE Value Based Questions for CBSE Class 12 Mathematics 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.
Download CBSE Value Based Questions for CBSE Class 12 Mathematics 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).
Download CBSE Value Based Questions for CBSE Class 12 Mathematics Probability Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.
Class 12th Mathematics CBSE Value Based Questions in for free download in PDF format. The most CBSE Value Based Questions for annual examination from are given here for download. The additional questions for practice from XII class CBSE exam are collected from various sources. It includes questions asked in previous year exams, questions provided by Kendriya Vidyalaya KV schools, DoE, Delhi government school, Navodaya Vidyalaya samiti NVS and other government and private schools in India and abroad that are affiliated to CBSE, New Delhi. Class 12 Mathematics have different set of questions. The questions include 1 mark questions, 2 mark questions, 3 mark questions, 4 mark questions, 5 mark questions and other questions as per the latest CBSE curriculum for the current session.
CBSE Value Based Questions, guess papers, most expected questions and best questions from 12th Mathematics have CBSE chapter wise CBSE Value Based Questions with solution for free download in PDF format. 12th Mathematics have many topics. All these topics are included in CBSE chapter wise Value Based Questions of class 12 Mathematics.
Class XII Mathematics NCERT book, refresher books and other reference books have many CBSE Value Based Questions. These questions are repeatedly asked in exams in one or other way round. Practicing such most CBSE Value Based Questions certainly help students to get good marks in exams. The solved question papers from have all type of questions may be asked in annual exams such as VSA very short answer type questions, SA short answer type questions, LA long answer type questions, VBA value-based questions and HOTS higher order thinking skill based questions.
Chapter 1: Relations and Functions
Chapter 2: Inverse Trigonometric Functions
Chapter 3: Matrices
Chapter 4: Determinants
Chapter 5: Continuity and Differentiability
Chapter 6: Application of Derivatives
Chapter 7: Integrals
Chapter 8: Application of Integrals
Chapter 9: Differential Equations
Chapter 10: Vector Algebra
Chapter 11: Three-Dimensional Geometry
Chapter 12: Linear Programming
Chapter 13: Probability
Q.1 Three shopkeepers A, B, C are using polythene, handmade bags (prepared by prisoners), and newspaper’s envelope as carry bags. it is found that the shopkeepers A, B, C are using (20,30,40), (30,40,20,), (40,20,30) polythene , handmade bags and newspapers envelopes respectively. The shopkeepers A, B, C spent Rs.250, Rs.220 & Rs.200 on these carry bags respectively. Find the cost of each carry bags using matrices. Keeping in mind the social & environmental conditions, which shopkeeper is better? & why?
[Handmade bag = Rs.5]
Shopkeeper A is better for environmental conditions. As he is using least no of polythene.
Shopkeeper B is better for social conditions as he is using handmade bags (Prepared by prisoners).
Q.2 In a Legislative assembly election, a political party hired a public relation firm to promote its candidate in three ways; telephone, house calls and letters. The numbers of contacts of each type in three cities A, B & C are (500, 1000, and 5000), (3000, 1000, 10000) and (2000, 1500, 4000), respectively. The party paid Rs. 3700, Rs.7200, and Rs.4300 in cities A, B & C respectively. Find the costs per contact using matrix method. Keeping in mind the economic condition of the country, which way of promotion is better in your view?
Ans. Cost per Contact:
Telephone = Rs0.40
House calls = Re1.00
Letters = Rs0.50
Telephone is better as it is cheap.
Q.3 A trust fund has Rs. 30,000 is to be invested in two different types of bonds. The first bond pays 5% interest per annum which will be given to orphanage and second bond pays7% interest per annum which will be given to an N.G.O. cancer aid society. Using matrix multiplication, determine how to divide Rs 30,000 among two types of Bonds if the trust fund obtains an annual total interest of Rs. 1800. What are the values reflected in the question.
Ans. Rs.15000 each type of bond.
(ii) Helping orphans or poor people.
(iii)Awareness about diseases.
Q.4 Using matrix method solve the following system of equations
x + 2y + z = 7
x – y + z =4
x + 3y +2z = 10
If X represents the no. of persons who take food at home. Y represents the no. of parsons who take junk food in market and z represent the no. of persons who take food at hotel. Which way of taking food you prefer and way?
Ans. X = 3, Y =1, Z = 2
Food taken at home is always the best way.
Q.5 A school has to reward the students participating in co-curricular activities (Category I) and with 100% attendance (Category II) brave students (Category III) in a function. The sum of the numbers of all the three category students is 6. If we multiply the number of category III by 2 and added to the number of category I to the result, we get 7. By adding second and third category would to three times the first category we get 12. Form the matrix equation and solve it.
Ans. x + y + z = 6, x + 2z = 7, 3x + y + z = 12 where x ,y ,z represent the number of students in categories I,II,III respectively.
X=3, y=1, z=2
Participating in co-curricular activities is very important. It is very essential for all round development.
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