CBSE 12th Maths Examination - 2017

This post is to list the updated information about 12th CBSE Board Examination. We know about fiasco over Mathematics question of CBSE last year and subsequent grace marks to the tune of 15. What a student can expect this year and how can he prepare within next 90 days.We know that discussion and exchange of notes always make academics better. First let me share some information about a CBSE circular on Maths paper of 2017:

"Mumbai: After tough mathematics exams for two years, the Central Board of Secondary Education (CBSE) has toned down the difficulty level for Class XII students. The new question paper design has capped the higher order thinking skills (HOTS) questions at 10% and introduced two-mark questions to bring relief to lakhs of students.

In a circular on the board's website, the CBSE said the changed question paper design would be applicable for the board examination scheduled to be held in 2017.

The HOTS questions will now be split into three two-mark questions and one four-mark question in the 100-mark paper. Teachers in the city said there had been no specification on the inclusion of HOTS questions but it varied between 10 and 20%. "It is good that the CBSE has now defined what to expect and students can prepare themselves well. Also, splitting the HOTS into three two-mark questions (see box) will mean that students can at least attempt some of them," said Jeeja K, teacher at R N Podar School, Santacruz. The CBSE categorized 20% of the paper as easy, 60% as average and 20% as difficult. With the introduction of short answers (two-mark questions), the total number of questions has increased from 26 to 29. Teachers feel it will help students score better. "When a student doesn't know how to answer a six-mark question, he or she loses out on all the six marks. With more questions with fewer marks, they are likely to lose fewer marks. Shorter questions take lesser time to solve," said Kalpana Dwivedi, principal, St Joseph High School, Panvel.

During the board examination this March, the CBSE had drawn a lot of flak over the difficulty level of the mathematics paper. Apart from social media outrage, the issue was also discussed in Parliament. Following this, the CBSE had assured to place the issue before a committee of subject experts and take remedial measures before evaluation. " Source: Times of India, 11th August, 2016.

Syllabus of 12th Maths CBSE ( Source: http://www.cbsesyllabus.in/class-12/mathematics-class-12-syllabus) 

Mathematics Class 12 Syllabus

Course Structure

Unit	Topic	Marks
I.	Relations and Functions	10
II.	Algebra	13
III.	Calculus	44
IV.	Vectors and 3-D Geometry	17
V.	Linear Programming	6
VI.	Probability	10
	Total	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

1. 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).

2. 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

1. 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.

2. 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).

3. 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 propertiesof definite integrals and evaluation of definite integrals.

4. 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).

5. 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

1. 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.

2. 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

1. 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

1. 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.

The CBSE time table is expected in the first week of January and soon we will get to know the date sheet! 

Date sheet for class 12 exams, 2017:

Thursday, March 9, 2017
ENGLISH ELECTIVE –NCERT
ENGLISH ELECTIVE-CBSE(FUNCTIONAL ENGLISH)
ENGLISH CORE

Friday, March 10, 2017
DANCE –KATHAK
DANCE-BHARATNATYAM
DANCE –ODISSI
DANCE-KATHKALI
CREATIVE WRITING & TRANSLATION STUDIES
SINDHI OFFICE COMMUNICATION
INFORMATION STORAGE & RETRIVAL
INTEGRATED TRANSPORT OPERATION
FRONT OFFICE OPERATIONS
TRAVEL AGENCY & TOUR OPERATIONS BUSINESS (NSQF)
SALESMANSHIP-II
CAPITAL MARKET OPERATIONS
BANKING-II

Also read: CBSE exams 2017 to begin from March 9, postponed by a week due to elections

Wednesday, March 15, 2017
PHYSICS
PERSIAN
SECRETARIAL PRACTICE & ACCOUNTING
AIR CONDITIONING & REFRIGERATION – III
OPTICS –II
RADIOGRAPHY-I GENERAL
ELECTRICAL MACHINE
CLINICAL BIO-CHEMISTRY (MLT)
CHILD HEALTH NURSING
GARMENT CONSTRUCTION –II
TRADITIONAL INDIAN TEXTILE

Thursday, March 16, 2017
BUSINESS STUDIES
BASIC HORTICULTURE-II
BEAUTY & HAIR -II
OPERATION & MAINTENANCE OF COMMUNICATION DEVICES

Saturday, March 18, 2017
URDU ELECTIVE
PUNJABI
TAMIL
MANIPURI
MALAYALAM
ASSAMESE
KANNADA
URDU CORE

Monday, March 20, 2017
MATHEMATICS
FIRST AID & EMERGENCY MEDICAL CARE
CLINICAL BIO-CHEMISTRY & MICROBIOLOGY-II
MICROBIOLOGY (MLT)
HEALTH CENTRE MANAGEMENT
OPTHALMIC TECHNIQUES-II
RADIOGRAPHY-II (SPECIAL INVESTIGATION IMAGING RADIOGRAPHY)

Tuesday, March 21, 2017
SHORTHAND ENGLISH
SHORTHAND HINDI
FASHION STUDIES
AGRICULTURE
ODIA
GERMAN
RUSSIAN
ENGINEERING SCIENCE
DATABASE MANAGEMENT APPLICATION (NSQF)

Thursday, March 23, 2017
HISTORY
RETAIL SERVICES-II(NSQF)
LOGISTICE OPERATION & SUPPLY CHAIN MANAGEMENT –II
BUSINESS OPERATION & ADMINISTRATION –II
LABORATORY MEDICINES (CLINICAL PATHOLOGY HEMATOLOGY & HISTOPATHOLOGY –II (MLT)

Friday, March 24, 2017
FOOD PRODUCTION III
INTRODUCTION TO HOSPITALITY MANAGEMENT(NSQF)

Also read: CBSE Class 10th and 12th exams 2016 Datesheet

Saturday, March 25, 2017
CHEMISTRY APPLIED PHYSICS
FOOD & BEVERAGE COST & CONTROL
FLORICULTURE
COST ACCOUNTING
BIOLOGY OPTHALMIC-II
RADIATION PHYSICS

Monday, March 27, 2017
INFORMATICS PRACTICES
COMPUTER SCIENCE
ADVANCED FRONT OFFICE OPERATIONS
OLERICULTURE – II
INSURANCE –II
BASIC PATTERN DEVELOPMENT

Wednesday, March 29, 2017
ACCOUNTANCY
BAKERY-II
HOLISTIC HEALTH –II
SECURITY(NSQF)

Thursday, March 30, 2017
FOOD PRODUCTION IV

Friday, March 31, 2017
ENGINEERING GRAPHICS
HERITAGE CRAFTS
HUMAN RIGHTS & GENDER STUDIES
LIBRARY AND INFORMATION
SCIENCE
TIBETAN
JAPANESE
SPANISH
MECHANICAL ENGINEERING
MARKETING- II
TEXTILE CHEMICAL PROCESSING
WEB APPLICATION – II (NSQF)

Saturday, April 1, 2017
KNOWLEDGE TRADITIONS & PRACTICE OF INDIA
LEGAL STUDIES
GRAPHIC DESIGN
HEALTH EDUCATION, COMMUNICATION AND PUBLIC
RELATIONS & PUBLIC HEALTH
THE CREATIVE & COMMERCIAL PROCESS IN MASS MEDIA-II
PRINTED TEXTILE
TYPOGRAPHY & COMPUTER APPLICATION(ENG.)

Monday, April 3, 2017
POLITICAL SCIENCE
LABORATORY MEDICINE-II
RETAIL OPERATIONS-II(NSQF)
FINANCIAL ACCOUNTING-II

Wednesday, April 5, 2017
BIOLOGY
TAXATION-II
DERIVATIVE MARKET OPERATIONS
AIR CONDITIONING & REFRIGERATION-IV

Also read: CBSE Board exams 2017 not to be delayed due to assembly polls

Thursday, April 6, 2017
GEOGRAPHY
BIOTECHNOLOGY
LIBRARY SYSTEMS & RESOURCE MANAGEMENT

Monday, April 10, 2017
PHYSICAL EDUCATION

Wednesday, April 12, 2017
SOCIOLOGY

Monday, April 17, 2017
ECONOMICS
TROUBLE SHOOTING & MAINTENANCE OF ELECTRONIC EQUIPMENT

Tuesday, April, 18, 2017
HOME SCIENCE

Wednesday, April 19, 2017
PAINTING
GRAPHICS
SCULPTURE
APPLIED ARTS-COMMERCIAL ARTS
ELECTRICAL APPLIANCES
CONFECTIONERY

Thursday, April 20, 2017
THEATRE STUDIES
TANGKHUL

Saturday, April 22, 2017
HINDI ELECTIVE
GUJARATI
NEPALI
LIMBOO
LEPCHA
BHUTIA
HINDI CORE

Monday, April 24, 2017
PSYCHOLOGY

Tuesday, April 25, 2017
MUSIC KARANATAKA (VOCAL)
MUSIC KARANATAKA INSTRUMENTAL (MELODIC)
MUSIC HINDUSTANI VOCAL
MUSIC HINDUSTANI INSTRUMENTAL MELODIC
MUSIC HINDUSTANI INSTRUMENTAL PERCUSSION

Wednesday, April 26, 2017
MASS MEDIA STUDIES

Also read: CBSE schools to renew demand for representation in CBSE Board

Thursday, April 27, 2017
SANSKRIT ELECTIVE
BENGALI
TELUGU
MARATHI
ARABIC
FRENCH
TELUGU-TELANGANA
MIZO
SANSKRIT CORE
UNDERSTANDING THE EVOLUTION AND FORMS OF MASS MEDIA-II
AUTO ENGINEERING-II(NSQF)

Friday, April 28, 2017
NATIONAL CADET CORPS(NCC)
MULTIMEDIA & WEB TECHNOLOGY
AUTOSHOP REPAIR & PRACTICE-II NSQF
FABRIC STUDY
TYPOGRAPHY & COMPUTER APPLICATION(HINDI)

Saturday, April 29, 2017
PHILOSOPHY
ENTERPRENEURSHIP
OFFICE PROCEDURE & PRACTICES
BASIC CONCEPT OF HEALTH AND DISEASE AND MEDICAL TERMINOLOGY
FOOD SERVICE-II
GEOSPATIAL TECHNOLOGY
MIDWIFERY

Economics of Subsidies

We have been taught by capitalistic economic system that subsidy is bad for business and it is anti growth. As followers of capitalistic economic system World Bank, IMF and all economists related to the economist circle of Capitalism, agree on this. Ask any noble laureate economist except deviated characters like Joseph Stieglitz about this, they will tell you mostly about the demerits of subsidies. Of course a person like Piketty has the guts to challenge this theorization of anti subsidy ideas. Any one with fair knowledge of development economics agree that the huge inequality prevailing across the globe is obnoxious. For saying this, we do not need to quote Kaushik Basu, the Chief Economist of Wold Bank. The requirements for different states vary from each other and cannot be standardized. A big country like India with mention of socialism in its preamble can try to follow path of American capitalism but may achieve limited success. Further, the question comes on the huge subsidy provided by big multinational corporations like Uber or multinational funded venture Ola. From where does the money come? These are primarily the marketing expenses during the break even period of the business.  Is it not subsidizing prices? Can we not consider this as dumping? The only difference is; these subsidies are for capturing market and expansion of business while state subsidies are for alleviating poverty and expansion of purchasing power. The huge discount provided by brands like Pantaloons or Marks and Spencer are sometimes due to distress selling. That is again bad for companies business as well as wardrobe of customers. We end up buying something which we never required. If minimalism is becoming trendy then the future of these subsidized pricing, dumping or distress selling will also be under threat. The future is unknown but for sure the world will come out as a better living space for us under Trump, Modi or multilateral leadership of Ban Ki-Moon.   

Pablo Neruda

Pablo Neruda is a widely used name in Bengali literature. It is often used and abused and represent the intellect of typical Bengali literature enthusiasts. This Chilean writer was bestowed noble prize for literature. English translation of Pablo Neruda is mesmerizing. The enigma created by him makes you travel between 'the shadow and the soul'. Pablo writes his unforgettable piece:

If you forget me

I want you to know
one thing. 

You know how this is: 
if I look 
at the crystal moon, at the red branch 
of the slow autumn at my window, 
if I touch 
near the fire 
the impalpable ash 
or the wrinkled body of the log, 
everything carries me to you, 
as if everything that exists, 
aromas, light, metals, 
were little boats 
that sail 
toward those isles of yours that wait for me. 

Well, now, 
if little by little you stop loving me 
I shall stop loving you little by little. 

If suddenly 
you forget me 
do not look for me, 
for I shall already have forgotten you. 

If you think it long and mad, 
the wind of banners 
that passes through my life, 
and you decide 
to leave me at the shore 
of the heart where I have roots, 
remember 
that on that day, 
at that hour, 
I shall lift my arms 
and my roots will set off 
to seek another land. 

But 
if each day, 
each hour, 
you feel that you are destined for me 
with implacable sweetness, 
if each day a flower 
climbs up to your lips to seek me, 
ah my love, ah my own, 
in me all that fire is repeated, 
in me nothing is extinguished or forgotten, 
my love feeds on your love, beloved, 
and as long as you live it will be in your arms 
without leaving mine. 

The Violin Player

The Violin Player; directed by Bauddhayan Mukherjee is not exactly music into the years or mind of the viewers! It takes you through the cruelty of life. A musician achieves his ultimate at the cost of loosing his world. But still it makes him happy and contended. The film was screened recently in the Habitat film festival and the director and producer were present for a Question and Answer session. There were brilliant acting, good music and of course a lateral plot which always may not sync with our world of commercial entertainment. The low budget movie can be inspirational for many budding film makers. The effort of the director in making a good movie will be appreciated by most film lovers.

The 72 minutes movie shows the life of a not so successful violin player who was finding it difficult to meet his both ends in the city of Mumbai. Suddenly he comes across an opportunity of playing a solo. But does it fulfill his objective? Can it be taken as an achievement? Is it the birth or death of an artiste? Many questions remain though the film ends without much ambiguity about the thoughts of the director. 

There may be some irrationality in certain scenes and one or two sequences may appear a bit lengthy but finally the entire movie is threaded through the violin without any loose string. We expect more and more beautiful creations from the director in future.  

Hunger

There is enough food in the world. People try hard to shade off the extra calorie in their body, A massive world population suffer from obesity. Health drinks, junk foods and Quick Service Restaurants are popular  in most of the urban places. Still in this opulent environment, you are compelled to see many hungry faces. Malnourished, underfed children show that civilization has not reached a stage where it can at least feed its members. Why so many people go hungry when there is no dearth of food in the world? Is it not lack of civility? Is it not the callous attitude of ours? Is it not the dirtiest example of selfishness? Malnutrition reduces the learning capability of children and their future productivity. Can we see the world free from hunger in the immediate future? The answer is a big NO. As per World Bank, we will require producing 50 % more food to feed the entire World population by 2050. There are challenges of climate changes cutting down our crop yield. There are schemes like mid day meal scheme in India which is an attempt to provide at least one meal to our children. Let's work towards making the world free from hunger. There are approximately 795 million people who do not have adequate food. More over enough is always not the answer to the right food which provide adequate nutrition. !165 million children under the age of 5 are stunted due to lack of nutrition. $ 1 spent on reduction of stunting gives us a return of $ 18. Economies world wide need to work towards providing nutrition and healthcare to the children for reducing stunted children across the world. The first 1000 days from the birth is most important for a child's development. Let's ensure that no pregnant women or children go hungry in the world. Let's come out from the vicious circle of poverty.  

Let Delhi Breathe!

I have traveled to the capital of independent India innumerable times since my childhood. I love Delhi. I got an opportunity to work in Delhi last year. It is an awesome experience to be in Delhi for more than a year now. Different cities wear different looks during different seasons. Delhi is at its best during winter. Delhi's fashion is great, Delhi’s roads are great, Delhi with the patronage of Government of India is no doubt the one of the best cities to live in with various amenities including public spaces like parks, gardens and auditorium.

You need luck to enjoy a sunny Sunday in December as Delhites got on the second Sunday of the month. A metro ride from Green Park to Rajiv Chowk took me less than 20 minutes. After spending some time in Jain Book Centre, I felt like going to Daryaganj old book market. I had not been  there earlier. While travelling from Canaught Place to Daryaganj again had the feeling which I am sure about Delhi now. I do not have statistics with me but almost convinced that Delhi is the most unequal amongst the metros in India. Due to heavy rate of migration from different states of India, particularly BIMARU states, Delhi can afford ' naukar' culture very much. For ironing a shirt in Delhi's posh Uday Park, I pay Rs 4! How is the rate in Chennai or Mumbai? I guess even poor Kolkata is not cheaper! For a rikshaw ride from Daryaganj to New Delhi metro station, I had to pay Rs 20, very similar to poor Kolkata or even less. Power brokers in the country have ensured that unorganized labourers are available in serving their masters in the capital of largest democracy of the world.

Delhi has problems of pollution, problems of crime but still any one will love the beautiful greeneries of Delhi. One of the greenest city in the country is Delhi.You may come across parrots often and occasionally a peacock as well. We know Delhi's pollution level higher than any acceptable norms. A recently elected AAM AADMI Chief Minister of Delhi is trying to control the situation with his educated brain but limited powers ( muscle power as well as constitutional power). Let's pray, let Delhi breath. Let Delhi continue welcome the parrots as well as immigrants from different parts of the country!

Goonj- rays of hope

First I got to know the name of Goonj few years back when they collaborated with Pantaloon for collecting old clothing. They have been active in different parts of the country. It was great to know that Goonj founder was awarded Magsaysay for the year 2015. This would definitely boost morale of different people in various parts of the world trying to act differently for the less privileged sections of the society.

It was an experience recently to interact with the Goonj founder and listen to him. The simple man speaks with lots of conviction and confidence. A brilliant student who completed his post graduation from country's premier institute Indian Institute of Mass Communication  chose to ignore the calls from corporate sector for the sake of call from his heart.

Goonj has been successful in recycling the extra clothes in our wardrobe for the people who need it. Mr. Anshu Gupta rightly says that you cannot use the word 'donation' for sharing your old clothes but even if people do that, dignity of many can be maintained, Your old cloth can not only provide warmth to the needy people but also can save lives during winter. Goonj has also been successful in making and distributing sanitary napkins to rural women through waste clothes. 

If we have more and more people like Anshu Gupta, the face of the needy and poor in this country will lighten up.