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  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 =  1 2  × AB × PM =  1 2  × 4 × 4 = 8 sq. units.

  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....

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...

 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...

  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...

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 infl...