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.