WBCHSE New Mathematics Syllabus Semester System XI and XII

West Bengal Council of Higher Secondary Education New Mathematics Syllabus Semester System XI and XII

For session 2024 onwards.

CBSE MATHS PAPER SOLVED 2020

The Central Board of Secondary Education (CBSE) conducted the class 12 annual board exam of mathematics on 17th of March 2020. Here is the solved CBSE MATHS PAPER  2020.

The question paper of class 12 Mathematics is divided into four sections- A, B, C and D. All questions are compulsory. 

Section A carries 20 questions of 1 mark each.

Section B carries 6 questions of  2 mark each.

Section C carries 6 questions of 4 mark each.

Section D carries 4 questions of 6 mark each.

Click here to download CBSE class 12 Mathematics Question Paper

Click here to download CBSE class 12 Mathematics Question Paper Solution.

Definite Integral : Problem with a twist!

Solved Integration Problems for 10+2 Level - SN Dey

Hundreds of solved problems at 10+2 level or the final year at school from the topic of integration. The aim of the document to help students from different boards (ISC, CBSE and other State Boards) studying at Higher Secondary level to get access to wide variety of problems, that too solved! Most of the problems are from the books of SN Dey, which is the most sought after book in WBCHSE.

This should not be substituted for classroom teaching neither this documents aims to teach the theories of differentiation. Students are requested to go through the theory and the rules before looking at the problems. Any error in the document can be reported at: prime.maths@hotmail.com

Integration, Methods of Substitution, Integration by Parts, Partial Fractions, Special Integrations, Trigonometric Substitutions.

If you have any query, don't forget to comment below.

A  collection of completely solved special integrals for various entrance exams ( IIT and Indian Statistical Institute ) and boards exam (CBSE,ISC and other State Boards) at 10+2 level. 

Click below the links to download the files:

File 1 Introduction ( Basic Problems )

File 2 Special Integrals 

File 3 Method of Substitution- Set I

File 4 Method of Substitution- Set II

File 5 Method of Substitution- Set II

File 6 Problems based on Standard Integrals- Set I

File 7 Problems based on Standard Integrals- Set II 

File 8 Problems based on Standard Integrals- Set III

File 9 Problems based on Integration by Parts - Set I

File 10 Problems based on Integration by Parts - Set II

More solved problems to follow. Keep visiting this space.

Special Integration

Integration : A harder Problem

 Most of the studenst will fail to solve this particular integration problem. It is trickier but once you hit the right idea, you will be able to solve the integration problem easily.

A problem on inequality

Using simple formula to prove a strong inequality.

Pigeonhole Principle

The numbers 1 to 20 are placed in any order around a circle. Prove that the sum of some 3 consecutive numbers must be at least 32!

This problem uses the alternate form of pigeon hole principle which is as follows:
 If the average of n positive numbers is t, then at least one of the numbers is greater than or equal to t. Further, at least one of the numbers is less than or equal to t.

The proof is very simple, assume the contradiction and proceed!

#Solution https://youtu.be/GLQg6cSAbms

Sum of first 'n, natural numbers

A simple way to calculate the sum of first 'n' natural numbers witout the use of calculator. Infact the same procedure is used to calculate the sum of n terms of any A.P series. See it and try to obtain the formula yourself

Inequality

A challenging problem based on the inequality that square of a real number is always greater than equal to zero. Learn the trick and prepare yourself for more challenging problems based on the same ideology.

Divisibility of 2222^5555+5555^2222 by 7

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Model Paper

Model Paper for B.Sc Maths Hons. 1st year students from various topics like algebra,geometry and analysis  ISC Board Maths paper for the last 5 years is also available with sample papers and guess papers visit http://kolkatamaths.yolasite.com/board-papers.php ISC maths paper for 2011,2010,2009,2008,2007 and CBSE class XII Maths paper for previous year is also available.

CBSE SAMPLE PAPER

CBSE Maths Sample Paper for class XII. Special care has been taken for preparing the paper, pattern and syllabus has been strictly followed. Meant for student preparing for 2012+ board exams. Download

Something Different!

1)Let p be an odd prime and n a positive integer. In the coordinate plane, eight distinct points with integer coordinates lie on a circle with diameter of length p^n. Prove that there exists a triangle with vertices at three of the given points such that the squares of its side lengths are  integers  divisible by p^n+1


2)Show that 1+2+3+........+n divides 1^k+2^k+...........+n^k, for and odd positive integer k and for nay natural number n


3)Denote by a, b, c the lengths of the sides of a triangle. Prove that
a^2(b + c − a) + b^2(c + a − b) + c^2(a + b − c) ≤ 3abc.

4)Prove that the 8th power of any integer is of the form 17k or 17k+1 or 17k-1 where k is an integer #Maths #Number Theory

5) From ten distinct two-digit numbers, one can always choose two-disjoint nonempty subsets, so that their elemets have the same sum #Maths #IMO 1972

CBSE Maths Paper for XI

Download maths paper for XI ( CBSE ). Chapters included in this paper are Sets,Realations and Function, Trigonometry and Principle of Mathematical Induction.