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.
Indian Statistical Institute B.Math & B.Stat Solved Problems, Vinod Singh ~ Kolkata
In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace is an integral transform that converts a function of a real variable (often time) to a function of a complex variable (complex frequency). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms differential equations into algebraic equations and convolution into multiplication.
The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), which is a unilateral transform defined by
(Eq.1)
where s is a complex number frequency parameter
, with real numbers σ and ω.
An alternate notation for the Laplace transform is instead of F.
Solutions of Triangle is an important topic in the JEE Main and JEE Advanced and in class XI for CBSE and other state boards in India. This topic comprises various formulae and rules like the sine rule, cosine rule, tangent rule etc. Questions based on the application of these formulas are often asked in exams. Revising these problems will help students to remember them and easily solve other questions of similar type and also apply their learning to new problems:
Solved Problems from the Book of S.L Loney Plane Trigonometry: CLICK HERE
In relations and functions Class 11, you will learn the cartesian product of sets along with relations and functions. In our day-to-day life, we have known the term relations in a pattern such as the relation between brothers and sisters, husband and wife or teacher and student. In Maths, the term relation is used to relate the numbers, symbols, variables, sets, group of sets, etc. For example, A is a subset of B denotes the relation of A and B. A function is a kind of relation which is operated between two quantities to yield output.
In this WORKSHEET, we will provide you with the relations and functions class 11 PROBLEMS, so that it would be easier for you to learn and understand the concepts.
If you have any query please comment in the comment box.
The dates for Higher Secondary Board Examination ( HS-2021 ), West Bengal Council of Higher Secondary Education (WBCHSE) has been published by the council along with the dates of class XI examinations. The dates are given below. Please make sure these are tentative dates and are subjected to change following COVID-19 pandemic situation.
Solved problems on theorem of total probability for CBSE, ISC and other state boards in India.
Problem 1. A bag contains 3 white and 2 red balls and
another bag contains 2 white and 4 red balls. A ball is taken from the first
bag and without seeing its colour is put in the second bag. A ball is taken
from the latter. Find the probability that the ball drawn is red.
Problem 2. The ratio of the number of boys to the number of
girls in a class is 1:2. It is known that the probabilities of a girl and a boy
getting a first division are 0.25 and 0.28 respectively. Find the probability
that a student chosen at random will get first division.
Problem 3. A bag contains 3 white and 6 black balls and
another bag contains 6 white and 3 black balls. A bag is selected at random and
a ball is drawn. Find the probability that the ball drawn is of white colour.
Problem 4. Two machines A and B produce respectively 60% and
40% of the total number of items of a factory. The percentage of defective
output of these machines are respectively 2% and 5%. If an item is selected at
random, what is the probability that the item is defective?
Problem 5. There are two bags. The first bag contains 5 red
and 3 black balls and the second bag contains 3 red and 5 black balls. Two
balls are drawn at random from the first bag and are put into the second bag
without noting their colours. Then two balls are drawn from the second bag.
Find the probability that the balls drawn are one red and one black.
Problem 6. There are two bags. The first bag contains 5 red
and 3 black balls and the second bag contains 3 red and 5 black balls. Two
balls are drawn at random from the first bag and are put into the second bag
without noting their colours. Then two balls are drawn from the second bag.
Find the probability that the balls drawn are one red and one black.
Problem 7. A bag X contains 3 white and 2 black balls and
another bag Y contains 2 white and 4 black balls. A bag and a ball out of it is
picked at random. What is the probability that the ball is white?
Problem 8. An urn contains m white and n black balls. A ball
is drawn at random and is put back into the urn along with k additional balls
of the same colour as that of the ball drawn. A ball is again drawn at random.
What is the probability that the ball drawn now is white?
Problem 9. An urn contains m white and n black balls. A ball
is drawn at random and is put back into the urn along with k additional balls
of the same colour as that of the ball drawn. A ball is again drawn at random.
What is the probability that the ball drawn now is white?
Problem 10. A person has undertaken a construction job. The
probabilities are 0.65 that there will be strike, 0.80 that the construction
job will be completed on time if there is no strike, and 0.32 that the
construction job will be completed in time if there is a strike. Determine the
probability that the construction job will be completed in time.
Problem 11. A survey is carried out to find the percentage
of men who sing in the bathroom. Because some people may be too embarrassed to
admit openly to be bathroom singers, each person question is asked to roll a
die in secret and answer NO if the number shown is 1 and YES if it is 6, no
matter what the true answer is, but to tell the truth (YES or NO) if 2,3,4 or 5
comes out. Because the number shown is not revealed, it is impossible to tell
from the answer given whether the person is a bathroom singer or not. Suppose
that the probability of answering YES in this survey is found to be 2/3. What
is the probability of being a bathroom singer, then?
Each student has to select one topic from Group-A and one topic from Group-B. Two separate files must be made. (one for each group)
Date of submission and viva-voce 13th October 2023.
The cover page must clearly contain the following information:
NAME OF SCHOOL
STUDENT'S NAME,
CLASS, SECTION & ROLL NUMBER
SUBJECT
TOPIC
GROUP A or B
REGISTRATION NUMBER
The same information must also be registered on the first page of your copy.
Topic Group-A ( Choose any one of the following)
Topic Group-B ( Choose any one of the following)
IMPORTANT INSTRUCTIONS:
I. Don't print and paste images, tables or graphs from the internet. If any graph or sketch is needed, you must prepare it on your own using graph paper & pencil.
II. Give proper examples and diagrams as needed.
III. USE SEPARATE COPIES FOR DIFFERENT GROUP.
IV. USE COPIES PROVIDED BY THE SCHOOL.
V. Write on one side of the paper.
Project Writing:
Use the following structure to complete your project:
Please go through the slides one by one and solve the questions that would appear on the slides.
Solved Problems: Set Theory - 11 Science
Assessment on set theory. Answer all questions. Each question carries 1 mark and has only one correct option. Please enter a valid e-mail address. If you have any query, leave your comment in the comment box.
Class Test:
Total time: 40 mins ( 6 pm - 6:40 pm ) Full Marks: 15
Thanks for participating, those who have not given the test should clarify for the same:
TRIGONOMETRY : TRIGONOMETRICAL RATIOS SOLVED PROBLEMS FOR 10TH GRADE ( CBSE, ICSE AND OTHER STATE BOARDS). SUBSCRIBE FOR MORE SOLVED PROBLEMS WHICH WILL BE UPLOADED SOON.
Trigonometric ratios are the ratios between edges of a right triangle. These ratios are given by the following trigonometric functions of the known angle A, where a, b and c refer to the lengths of the sides in the accompanying figure:
Sine function (sin), defined as the ratio of the side opposite the angle to the hypotenuse.
Cosine function (cos), defined as the ratio of the adjacent leg (the side of the triangle joining the angle to the right angle) to the hypotenuse.
Tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.
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This is not a guess paper, every year the board provides a specimen paper for the students to help gain an insight of the structure they will be facing during their board examination. Students can expect a similar pattern while the degree of difficulty may vary.
Don't forget to comment if you have any question. Get the mock test paper for ISC 2021 Mathematics by mailing us.
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.
Solved problem form the unit Relations and Functions and Inverse trigonometric Functions at 10+2 level. Here you will find numerous solved problems covering all aspects of the chapter. Learn through the method of problem solving. Variety of problem across all major boards in India. (CBSE, ISC, WBHSE and other State Boards). If you have any query just comment in the comment box.
