Pair of linear equation s class 10 imp

 Question 1.

Draw the graph of 2x + y = 6 and 2x – y + 2 = 0. Shade the region bounded by these lines and x-axis. Find the area of the shaded region. [CBSE 2007]

Solution:

The given system of equation is
2x + y – 6 = 0 ………. (i)
2x – y + 2 = 0 ……… (ii)

 solutions for each equation of the system are:
(i) ⇒ y = 6 – 2x

Table of solutions for 2x + y – 6 = 0

Similarly 

Table of solutions for 2x – y + 2 = 0

Plotting these on the graph

These intersect at (1, 4), so this is the solution. 
In graph, area bounded by the lines and x-axis is

 ∆PAB which is shaded.

Draw PM ⊥ x-axis

PM = y-coordinate of P  (1, 4)    = 4 units

and AB = 1 + 3 = 4 units

∴ Area of shaded region

= Area of ∆PAB = 12 × AB × PM

= 12 × 4 × 4 = 8 sq. units.

Zero Tax Till 12 Lakhs

 Question comes in mind that when there is no tax till 12 

lakhs income in the latest union budget which will applicable from 1 April 25 then why 

these new tax slabs are introduced. 

Actually there is very simple 

calculation behind this. 

Government says that till the 

Income 12 lakhs these slaps will 

not be appreciate because one 

will be given rebate under 87 A. 

so ones tax will be zero. 

If one earns even Rs 1 extra 

then 12 lakhs then these slabs

will be appreciate. 

In this budget government is

giving standard deduction of 

Rs 75000 also, so we can say

that there will be zero Tax till

the income of 12,75,000.

standard deviation means 

first Rs 75000 will be deducted

from your income then you 

will get Taxable income. 

This is my understanding and

if you think that this is helpful

then Thanks , If you think that 

this is not true then you can 

make ne clear also by means

of comments. 

PROBABILITY MCQ 25 MATHS

Q1.Which of the following cannot be the probability of an event? 

(A) 0.4 (B) 4% (C) 0.04% (D) 4

Ans   D) 4

Q2.In a bag containing 24 balls, 

4 are blue, 11 are green and the rest are white. One ball is drawn at random. The probability that drawn ball is white in colour is (A) 1 / 6 B) 3 / 8 C ) 11 / 24 D) 5 / 8

Ans  B) 3 / 8

Q3.(A) Two dice are rolled together bearing numbers 

4, 6, 7, 9, 11, 12. Find the probability that the product of numbers obtained is an odd number 

Ans:

Total number of possible outcomes = 6x6=36 

For a product to be odd, 

both the numbers should be odd. Favourable outcomes are (7,7) (7,9) (7,11) (9,7) (9,9) (9, 11) (11,7) (11,9) (11,11) no. of favourable outcomes = 9 

P (product is odd) = 9/36 or 1 / 4

 

 Q 4. How many positive three digit integers have the hundredths digit 8 and unit’s digit 5? Find the probability of selecting one such number out of all three digit numbers.

Ans

Total number of three-digit numbers = 900.

First 100  last 999

 Numbers with hundredth digit 8 & and unit’s digit 5 are 805,815, 825,....,895 Number of favourable outcomes = 10

 P(selecting one such number) = 10/900 or 1/ 90

Systematic Withdrawal Plan

 What is SWP ie Systematic Withdrawal Plan? 

Answer is very common that is it is way of withdrawing money systematically. It looks easy but not very easy because many experts present this as a plan which can give you money whole life and your corpus will be intact also

Experts present this plan in very simple way that if you are getting 12℅ per annum and  withdrawing  just 10℅ of your accumulated corpus then your corpus will also increase at  rate of 2℅ per annum and you are withdrawing 10℅ of your corpus also monthly. 

I want to say that it is right but here you should take some precautions also, these are... 

First don't give any command like 10℅ withdrawal  every month because this strategy could deceive you also, the better way is  Just withdraw your money once in a year first check how much did you get the the return and withdraw 4℅ less then your return. 

Example if you have Rs 1 lakh and got 10℅ return, it means your money will be 1 lakh 10 thousand then withdraw just Rs 6000 then you are withdrawing just 6℅ of your return, in this way your corpus will be intact and grow also, 

You can withdraw  money in variable manner just follow this rule first check your return and withdraw money less then your gaining amount. 

Don't withdraw every month instead withdraw once in a year. 

This is my way of using this SWP, just analysis yourself this strategy and if you find beneficial then follow, you can take advice of your financial advisor also. 

Wealth

 

Wealth is as important as health. By wealth one can maintain once health and by one's health one can earn wealth. 

It is not right way of thinking that wealth is not very important, it is not right, but actually one should pay more  emphasis on earning more money. 

It is prime duty of everyone to be wealthy. Wealth is key to success but how one can earn wealth.

Now a days there are talented people who deserve to have  lots of wealth but everyone is not able to earn wealth.There some reasons behind this. Many a time people not felt deploy importance of wealth just they  superfluously thik of having wealth. 

One should remember wealth is important and how to earn wealth it is also a subject to understand. Some ways to earn wealth are... 

First introspect yourself that what can you do to earn wealth. 

Second shun your laziness and make a roadmap to earn wealth. 

Third follow strictly your roadmap to earn wealth. 

Fourth explore other ways also to generate active income. 

Fifth maintain your wealth, it means spend less than your earning

Remember wealth can not be generated overnight but it can be destroyed overnight if you don't follow proper strategies to maintain your wealth. 

Inflation

Inflation is there and it force everyone to increase one's own income. At present it is said around 7%0Inflation is there. It means things are costly at rate of 7% per year. If a thing can be purchased at Rs 100 then same thing will come at Rs 107 next year. 

So if you are keeping your money in bank where you are getting 7 % 0interest  then actually you are just maintaining your purchasing power but when you pay the 

tax on the interest then you are losing your purchasing power. 

Therefore investment must be

 in such options where you get more return then rate of inflation. 

Options are available to beat the inflation are , one should invest in

Mutual Funds

Share Market

Property

Gold

Bonds

FDs..... etc. 

If one does not invest for maximum return then his money will not grow and one's financial conditions will not  improve. So invest wisely to

 beat the inflation. These are

 my views, you can consult your financial advisor regarding inflation  also. 

Financial Knowledge

 

   

Financial Knowledge is essential why? 

Financial knowledge is essential because status of our life depends on financial conditions. If financial condition is sound then one's life may be better but financial conditions become good by financial knowledge. 

Financial knowledge includes many factors like

Knowledge of investing options. 

Knowledge of how to increase money. 

Knowledge of importance of money

Knowledge of how long one should be invested. 

Knowledge of different 

investing strategies. 

... are some basic things about financial knowledge. 

Financial knowledge also includes

Having  emergency fund. 

Having  term insurance

Having  medical insurance

Having wish to  enhance our skills. 

Having  clear vision about saving and  spending. 

Financial knowledge is the knowledge which must be gained by everyone. If one has

 to pay some fee for financial consultation then also one should go through this. 

By having updated financial knowledge we can improve our quality of life, because  now a days to increase income is not easy and value of the money is going down because of inflation. Only way to increase our wealth is having knowledge of finance. 

By financial knowledge one learns the art of growing money without pain and without cut of our daily essential expenses. 

This is what I think and what is my knowledge. It is up to you whether you like it or not. So use your distinct and consult of your financial advisor. 

Financial Literacy

 

Financial Literacy? 

Financial literacy means 

Understanding the importance of money

Understanding the methods of growing money

Understanding of maintaining the financial status

Understanding of increasing passive income

Understanding of increasing  active income

Understanding of new updates regarding money. 

.... all these are related to financial literacy. 

Nowadays financial literacy is very important to improve financial status. 

Ways to improve financial literacy

By taking advice of any financial advisor

By going through some financial related courses

By watching some financial channels

By going through financial you Tube channels

... so there are many ways to improve financial literacy. 

Benefits of financial literacy. 

Aim of financial literacy is to earn money. 

To grow one's own money. 

To improve our financial status. 

To lead life comfortably

To have strength to fulfil our dreams. 

To enjoy the things which are expensive. 

.... so there are n number of reasons to have financial literacy. 

Financial status

 Financial Status

Financial status is important because financial status matters a lot. If one's financial status is sound then one can lead one's life comfortably. If financial status is not sound then there is always worry about to arrange two times meals. 

But how can one improve one's financial status? The answer is easy that by working hard , but it is not that much easy. Everyone works hard but only few are able to achieve good financial status. 

Because by working hard one can earn money but to achieve sound financial status one should work smartly. One should know the art of increasing money. If one is knowledgeable enough to increase one's money, then only one can get sound, good financial status. 

To grow money rapidly one shoul know some investment techniques, like

Investment in Mutual Funds

Investment in Equity

Investment in real state

Investment in gold

Investment in start up

.... By investing properly one can generate wealth but one should know the art of increasing one's active income also. 

To increase active income one should invest in oneself because until you grow your skills, you won't learn how to grow one's active income. 

To grow one's active income one should pay attention on one's skills. Try to explore different niches to earn more. One should pay attention on new ways to earn money as well as saving the money. 

Financial Management

  

Financial management is important now a days because in lack of financial management one's life may be hazardous. At present it is seen that lower middle class is disturbed because of financial crises. It is very difficult to arrange two times meal easily. 

Job market is reducing day by day by the advent of AI now job requirements are different. By having simple education it is not easy to make money. 

It is need of the hour 

first have earning source

Second know the methods to grow the money. 

Have clear distribution of money for every goal of the life. 

Have proper financial management to achieve your goals. 

Get information about different ways to make money. 

Work on your nichle to earn money. 

By financial management  you can have more money by working less. Because traditional ways of increasing our money are not efficient. 

Now by FDs you earn less interest. 

By investing in mutual funds for less time is also not beneficial. 

By investing directly in stocks are also not beneficial. 

For investing in real states the is need of lump some amount. 

In future there is fear of inflation also,.. 

But all these problem can be solved easily by financial management. 

Under financial management one learn when and where money must be invested. 

Which investing options are lucrative. 

How long one must be infested  to get good returns. 

So financial management is very important one should learn either by free source like YouTube, Blog.. or by getting proper degrees from financial institutions. 

. 

Financial Education

 

What is need of financial education, it is the burning question of today. Now a days everyone want to earn money without work and that is possible only by financial education. 

But how one can get financial education do answer is from those who have financial education. Many a time we go to our heads of family like father, mother, uncle..... etc for getting financial education, but if they don't have any financial degrees or they don't have any finance related work then they are not very helpful. 

So better we must take financial education from any finance expert who have studded finance at any stage of life. One can go to YouTube also but always follow the rule that listen everyone but take your own decision. 

Generally it is observed one doesn't want to pay the fee for consulting with financial expert to get financial education. It is not good approach. One should pay fee and take proper financial education fom some expert. 

Financial education is not subject which is learnt once and it gets over it is the subject which needs regular Updation. Financial education effects very much from present market trends , government policies, so it is vast subject therefore one has to put much efforts to learn it. 

Financial education can be got by that person who have strong mind setup because if one is not mentally fit then he can become stressful very easily. 

Financial education is now a days very important if one becomes sound in financial education then he can lead his life tension free. 

Financial Security

 Financial security means having enough money to survive without stress. 

Financial security means enough money to survive. 

Financial security means stable earning source.

Financial security means not in stress because of money. 

Financial security means don't put your mind in calculating the budget before purchasing any thing. 

Financial security means not in worry because of money. 

Financial security means you can go through any type of medical expenses. 

Financial security means you can rest sometimes. 

Financial security means you can go on vacation. 

Financial security means you can think of you can help others without thinking much. 

These are some aspects of financial security. But big question is that how one can get financial security. 

Answer by increasing present  earning sources don't think that by only investing you can have financial security , you can have financial security in this way also but you will have wait much time because compounding works in the long run. 

If you increase your earning sources then you can get this financial security at earliest. 

For this if you have a stable job then try to search some online platforms to make money. For this online platform can be gone through. 

Make video on YouTube

write a blog

Invest your money for long time

Write a book

Talk about making money

Be confident that you will be able to have money

Have Dmat and purchase some good shares

Ultimately your every second must be used to earn money. 

Financial Freedom

 We want to state that now a days financial freedom is important. Everyone wants to lead life without any worry but obstacle is worry of money for daily use. 

If someone is not worried about money then he can lead his life peacefully. But big question is how to achieve the financial freedom. 

Keep money in the bank but in this one's money will not grow as per future need. So one can start any shop but now a days people don't want to work so he wants money without work. 

One can put his money in Mutual Fund but it depends on your right choice and right time for investment. If one is good at this then he can earn money otherwise one will finish with little growth or with loss in invested money. 

One can buy property but there is need much money to purchase property and also it is very painful to keep vigil on the property. If one's property is captured by someone then whole life may pass in the process of court. 

Financial freedom is such which depends on one's need and one's desires. One can fulfill one's need but not one's desires. So better find the ways to grow your money but find ways of different earning sources are also essential. 

Funda is  earn more, work more, keep less desires, be realistic and invest the money and try hope to earn decent interest then you can be little near to financial freedom. 

Financial planning

 We need financial planning? 

Yes it is important to have planning or work till last breadth. Today every one want easy money, money without work is required by everyone. 

But it is not so easy task now a days after working hard also enough money is not earned

Inflation is very high, jobs are rare in this scenario one should focus on investment and  take  benefits from compounding. 

Only this is the way to maintain our present lifestyle without stress. 

What is financial planning? To increase our less amount by investing is financial planning. One should find the way how one can grow his money. 

By investing in Mutual Fund

By FD

By investing in share m share market

By trading

..... Or in any other way. 

Actually choosing the right method is also an skill and every one does not have it. So first think and estimate how much money is required for you? 

Then analysis Whether you have that Or not, if not th e n take help of any financial planner. It would be beneficial. 

These are my views follow if you like. 

Stop making silly mistakes in maths

 

Now exam is near and it is common practice with everyone to commit mistakes.Generally everyone commit silly mistakes which can be judged by the examiners easily.

 Try to ignore  following errors. 

1.Students  must read the question clearly. 

Many a time it is seen that students don't read the question clearly. And get the answer incorrect. 

2.Go through the paper thoroughly,

 Generally sometime we miss the question in the paper which was easy and of  our choice. 

3.Cram some values, 

Many a time it is seem that calculation takes much time  and  in hurry sometimes mistakes are committed. So sometime to avoid such wastage of time try to learn by heart some values, so that we can check the wastage of time. 

4.Learn some new methods,

 Always practice many questions daily, and try to learn new methods, by resorting to new methods you can solve questions easily and quickly. 

5.Write clearly ,

 It is common thinking that every one thinks that in maths there is no need to write clearly. Good writing always matters. When examiner has to put his efforts to understand the writing then out of irritation he did not gives marks easily, he try to cut the marks out of frustration. 

So stop comming silly mistakes in maths and score much. 

Three Tips For Board Exam.

 

CBSE board exam is near and how one should prepare for the exam without tension, stress some ways are

1 Solve Previous Years papers

Just open the papers of previous years and solve them. Once when you start solving the previous years papers you will gain the confidence and you will come to know what types of questions actually asked in the exam. 

Previous Years Papers are the source to understand the nature of the asked questions in past and it is very useful once you understand the nature and types of questions frequently asked in the exam you will be able to solve the questions comfortably. 

2. Objective Questions

Objective questions are very important and demands much deep knowledge . Objective questions are important because they can give you full marks without any deduction. To solve the objective questions , first you should go through the Objective Questions of previous years papers. When you solve the objective problems of previous years papers then you understand the nature of the questions and Types of questions also. 

3. Have Strategies

Don't be in tension but have plan to compete the task. By planning you can achieve your goals but by worrying you can loose your mental peace better to write Strategies and work accordingly. 

At present when there is not any death of  material, then gaining good marks is not a Herculean task. 

Just go through many website which have collection of imp questions, solve them. 

Chapter Wise Test Series by RK Swami Sir CLASS 10 MATHS

How to prepare 2025 Board Exam

 2025 Board Exam

Now time is less and Board exam is very near. 

In the month of February Board Exam will commence. 

Some points to follow for your board exam

1 you know all the syllabus and you have all the material related to exam now prepare a list of expected questions first and prepare them first. 

2 prepare first easy questions

3.Eat healthy and do yoga Breathing Exercises for 20 minutes daily. 

4.sleep early and getup early

5 don't hesitate to clear your doubt from your teachers and friends. 

6.help your friends also. 

7 don't waste much time on social media. 

8.away from TV, web series for the period your exam is going on. 

9 utilize your previous years papers in good way. 

10 have confidence in your self. 

I think above suggestions will be helpful.