Solved Problems for Indian Statistical Institute (B. Math and B. Stat), Chennai Mathematical Institute, JEE Main & Advance ( IIT ) and for Olympiads ( RMO and INMO ). Get Solved problems for boards ( CBSE and ISC Mathematics Papers) along with board papers.
Saturday, October 26, 2019
Wednesday, October 23, 2019
Sum of squares of 5 consecutive natural numbers!
Here's a difficult problem of proving that a given expression is not a perfect square. A direct approach will be a nightmare ( even not sure it can be proved) but use of a simple property of perfect squares will ease the problem. We know that any perfect squares leaves a remainder either 1 or 0 when being divided by 3 or 4. This simple result would be used to solve the problem.
Labels:
IIT,
IIT-JEE,
ISI,
perfect squares,
WBJEE
Number of solutions of the given equation
Here the equation to be solved is very simple |2x-[x]|=4. But unfortunately the traditional methods of solving will not apply! You have solved equations by methods like factorisation, vanishing method, hit and trial.... But in many equations these methods don't work or requires huge computation and guess work to solve it. Here is an equation which can be solved from the simple fact that if one side of an equation is an integer the we look to the other side only and see for what values its also an integer. This simple but powerful method can be used in many problems
Monday, October 7, 2019
A very hard integration problem! Can you solve it? ( Practice for IIT-JEE)
A very hard integration problem based on the method of substitution. It took almost an hour to figure this out! Can you solve it on your own?! This problem is well suited for students preparing for IIT-JEE.
Sunday, September 29, 2019
Inequalities
Labels:
IIT,
Inequalities,
ISI
Friday, September 27, 2019
Solved Trigonometry Problems: 10th Grade
Here is a list of few good problems at the 10th grade. Get the full solution below and if you want
more comment or mail us at maths.programming@gmail.com!
Download here
more comment or mail us at maths.programming@gmail.com!
Download here
Labels:
10th Grade,
cbse,
ICSE,
trigonometry
Sunday, September 8, 2019
Saturday, August 24, 2019
Solved Problems : Logarithm
A collection of solved problems on logarithm meant for secondary students ( 9th and 10th grade). The collection covers almost all types of problems at the level mentioned.
Download the file here: Solved Logarithm Problems
Download the file here: Solved Logarithm Problems
Friday, August 23, 2019
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.
Monday, February 18, 2019
Special Integration
Labels:
cbse,
IIT,
INTEGRATION,
ISC,
ISI,
mathematics,
maths,
Special
Sunday, February 17, 2019
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.
Labels:
cbse,
IIT,
INTEGRATION,
ISC,
ISI,
mathematics,
maths
Saturday, February 16, 2019
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
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
Labels:
cbse,
ISC,
mathematics,
maths
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.
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