SIMILARITY AND PYTHAGORAS' THEOREM-TIPS

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IMPORTANT TIPS:

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CONDITIONS FOR SIMILARITY (OF TRIANGLES) - TIPS

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IMPORTANT TIPS:

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SIMILAR TRIANGLES - TIPS

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IMPORTANT TIPS:

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MEAN - TIPS

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IMPORTANT TIPS:

INCOME TAX - TIPS

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IMPORTANT TIPS:

• All governments collect taxes from the citizens of the nation.The amount received in the form of taxes is utilized to create infrastructure, provide better education and maintain public health, etc.



• Income tax is a type of DIRECT TAX.



• Income tax is collected from those citizens whose annual income exceeds certain fixed minimum amount.



• The person who pays tax is called a TAX-PAYER (an ASSESSEE).



• There are certain rules decided by the government to calculate the amount of tax to be paid by a person based on his annual income.These rules are amended as and when needed (i.e. these rules are not permanent).



• Income tax is calculated according to the rates prevailing in the year under consideration.



• Some special SAVINGS made by the person during that year are deducted from his GROSS ANNUAL INCOME before calculating TAXABLE INCOME.



• The tax amount is calculated on TAXABLE INCOME.



• Sometimes, the government charges cesses like educational cess and surcharge on the income tax to be paid by the assessee.These are additional liabilities on the tax-payer.



• For a salaried person, income tax is deducted from his salary every month and deposited to the Income-Tax Department.This is called TAX DEDUCTED AT SOURCE (T.D.S.).



• Businessman, Industrialists, Professionals and Self-employed persons pay their taxes directly to the I.T.Dept.



• Each tax payer has to file ANNUAL INCOME TAX RETURN in which he gives statements of his income, expenditure, savings, etc.



• It is compulsory for the assessee to mention his/her PAN (PERMANENT ACCOUNT NUMBER) in the income tax return filed by him/her.



• A person whose income is less than the minimum income fixed to calculate tax does not have to pay income tax.



• A person who has paid more income tax (as T.D.S. or Advanced Tax) than he should actually have paid is refunded the excess amount paid by him.



• Each ACCOUNTING YEAR starts on 1st April of the year and ends on 31st March of the next year.



• The next year is called the ASSESSMENT YEAR for the previous accounting year. Thus, for the accounting year 2004 - 2005 (i.e. 1 - 4 - 2004 to 31 - 3 - 2005),the assessment year is 2005 - 2006.



• Rates of Income Tax for the financial year(accounting year) 2005 - 2006 are:

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  [Here, I.T. = INCOME TAX.The surcharge is calculated on I.T. Thus, if calculated tax is Rs.5000 and surcharge is 10% then it amounts to 10% of 5000 or Rs.500.Similarly, Educational Cess is calculated as 2% of the total of I.T. and surcharge.]


• For any taxpayer(who is not a woman/senior citizen), the gross income upto Rs.100000/- is free from incone tax.



• For a woman taxpayer(who is not a senior citizen),the gross income upto Rs.135000/- is free from income tax.



• For senior citizens (persons above 65 years of age),the gross income upto Rs.185000/- is free from income tax.



• Savings amount upto Rs.100000/- under section 80C is exempted from tax.Such savings include:LIC(Life Insurance Corporation)Premiums, PPF(Public Provident Fund),GPF(General Provident Fund),PLI(Postal Life Insurance),Certain Government Bonds(RBI Bonds,National Savings Certificate-NSC,Kisan Vikas Patra-KVP,etc).



• Housing loan interest upto Rs.150000/- is exempted from total income under section 80D.Housing loan principal is exempt under section 80C within the limit of Rs.100000/-.



• Mediclaim premium upto Rs.10000/- is exempted under section 80D.



• DO NOT APPLY ANY OTHER INCOME TAX RULE WHICH HAS NOT BEEN MENTIONED IN THE TEXT BOOK.INCOME TAX RULES KEEP ON CHANGING YEAR BY YEAR.IT IS NOT POSSIBLE TO MENTION ALL RULES IN THE BOOK.THE PURPOSE OF THE CHAPTER IS TO GIVE YOU A PRELIMINARY IDEA OF CALCULATING TAX.

INSTALMENTS-TIPS

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IMPORTANT TIPS

• INSTALMENT PURCHASE SCHEME is a contract between the buyer and the seller by which buyer makes part payment of the price of the commodity (called DOWN PAYMENT) at the time of purchase to the seller and agrees to pay remaining amount in fixed instalments and, in return, the seller gives that commodity to the buyer.



• CASH PRICE : The amount in full (Selling Price) to be paid at the time of purchase is called CASH PRICE of the commodity.



• DOWN PAYMENT : If the buyer does not pay the full price (selling price) of the commodity and prefers to buy it under instalment scheme, then the part payment made by him at the time of purchase is called DOWN PAYMENT.
  
  For example: Cash price of a TV is Rs. 15000/- and the buyer pays Rs. 5000/- at the time of purchase, then Rs. 5000/- is called DOWN PAYMENT.



• RATE OF INTEREST : If a commodity is purchased under instalment scheme, the buyer has to pay some extra amount as interest on the unpaid amount which is calculated at some rate called RATE OF INTEREST.



• INSTALMENT : An amount paid regularly after definite time period (till the total dues,i.e.principal + interest, are paid in full) by the buyer to the seller is called INSTALMENT.



• For calculating simple interest we use the following formula:
  
  I = PRN/100
  
  where I = simple interest, P = principal amount, R = rate of interest( % ) and N = number of years (time period in years).



• For calculating the rate of interest we use:
  
  R = (I x 100)/PN.

ARITHMETIC PROGRESSION-TIPS

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IMPORTANT TIPS

• Observe the following sets of numbers carefully:
  
  
  
  
  1. 1, 2, 3, 4, 5, ...
  2. 2, 4, 6, 8, 10, ...
  3. 1, 4, 9, 16, 25, ...
  4. 1, 11, 111, 1111, 11111, ...
  5. 1, 1/2, 1/3, 1/4, 1/5, ...
  
  
  
  
  Here, in each set, we find numbers arranged in some order and there is an obvious (definite) rule by which we can obtain the next number and as many subsequent numbers as we wish to find.
  
  Such sets are called SEQUENCES ( PROGRESSION ) and each number of the set is called a TERM of the sequence.



• A sequence refers to an ordered set of numbers in which each number (term) can be obtained by a definite rule.



• The rule by which a sequence is formed may be written as a formula for n^th term of the series but all sequences need not have a formula.



• The n^th term of 1, 2, 3, 4, 5, ... is n.



• The n^th term of 1, 4, 9, 16, 25, ... is n².



• The n^th term of 3, 4, 7, 12, 19, ... is (n - 1)² + 3.



• 2, 3, 5, 7, 11, 13, ... is the progression of prime numbers.



• The n^th term of a progression is denoted by either a_n or T_n



• If a progression starts with a definite real number and if any successive term is obtained by adding a constant nonzero real number to the previous term, then the progression is called an ARITHMETIC PROGRESSION (written in short as A.P.)



• Sequences (a) and (b) in the examples given in the beginning are examples of Arithmetic progression whereas sequences (c), (d) and (e) are progressions but they are not Arithmetic progressions.



• The difference between any two consecutive terms of an A.P. is a nonzero constant. This difference is called the COMMON DIFFERENCE.



• The general form of an A.P. whose first term is a (a ∈ R) and the common difference is d (d≠ 0) is:
  
  a, a + d, a + 2d, a + 3d, ...



• The n^th term (T_n) of an A.P. is
  
  T_n = a + (n - 1)d



• The sum of the first n terms of an A.P. is given by
  
  S_n = (n/2)(a + l)
  
  where a = first term of the A.P. and l = last term of the A.P.
  
  Since l = T_n = a + (n - 1)d,
  
  S_n = n/2 [ 2a + (n - 1)d]



• T_n - T_n-1 = d



• S_n - S_n-1 = T_n



• T_m - T_n = (m - n)d [where m>n,&m,n ∈ N].