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BASICSBASICSDr. T.K. Jain.Dr. T.K. Jain.

AFTERSCHOOOLAFTERSCHOOOLM: 9414430763M: 9414430763

tkjainbkn@yahoo.co.intkjainbkn@yahoo.co.in

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WHAT IS AP? Arithmetic Progression is called AP For example: 101,103,105,107 The difference in each case is 2. The difference is same

Starting term is called A. Difference is called D. In this case , A= 101, D = 2. Tn = (7th term) = A+(n-1)D = 101+(6*2) = 113. Sn = (sum of 4 terms) = N/2(2a+(n-1)d)

Sn = N/2 (first term+last term)

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What is GP? Geometric Progression. Here ratio is fixed for example

2,4,8,16,32,64 .. So. On Here also we have a starting term = A = 2 Ratio can be identified by dividing second

term by first term. = 4/2 =2

Tn= A*R^(n-1) Sn = A (R^n -1)/ (R-1)

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What is HP? Harmonic Progression It is just opposite of AP.

Example:1/2, , 1/6, 1/8, 1/10

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What are AM,GM, & HM? Arithmetic mean, Geometric Meanand Harmonic Mean.

AM will be heighest among these.

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Calculate AM,GM,HM of

2&4, which is lowest? AM = (2+4)/2 = 3 GM = (2*4)^1/2 =2.83

HM = (1/2 +1/4 ) = * 6/8 = = 3/8 now reverse it = 8/3 =2.66.

So HM is lowest.

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What is the average speed ofMukesh, who goes to college at the

speed of 20 but returns back atthe speed of 30 km p.h.?

Is it 25? No it isnt 25. We have to calculate HM not AM. (1/20+1/30) = (50/600) = 25/600= now reverse

it : 600/25 = 24ans.. For speed calculations, use HM.

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Some amount is Rs. 10035 after 6years, but Rs. 4460 now, what is it

after 3 years (compound interestis followed)?

Is it 7247.5 (simple mean) ?

No it isnt AM. We have to calculate GM here : (4460*10035)^1/2 =44756100^1/2 Square root of 44756100 = 6690. ans.

In compound interest questions, calculate GM.

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How did we calculate square

root of 44756100? Take factorization of 44756100 and

get all the factors.

List down all the factors and take afactor once which has come twice multiply it and get the answer.

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ow to ca cu ate squareroot of 44756100

alternative method? Let us take pairs of two numbers from last the first pair is 44, II 75,III 61 IV- 00.

44 can be divided by square of 6. remainder is 8 Now we will bring next pair 75 so we have 875. Since we had divided by 6, double it so 6+6 =12.

Now 12 with 5 will give us 125*5=625 which is very less. 127*7 = 889 which is very high so we have to get middle number., nowwe have 875, divide it by (6+6) = 126*6= 756, remainder = 119, +61, we have11961.

Remember to add last digit 126+6 = 132 (rule). Now we will divide by 126+6 = 1329*9= 11961 so remainder is zero. But 00

is still left, so we will divide by 13380*0 = to get 000000. All thenumber which we have used in dividing, have to be put together - the

final answer is 6690. Ans.

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Which is bigger : or

1/3 ? Step 1.: find LCM of 2 and 3 Multiply 2*3 = 6

Step 2: multiply 6 to both thenumbers: *6 = 3

1/3*6 = 2.

Which is bigger = 3 so is bigger.

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Which is bigger 11/852

or 19/1491. ? Step 1.: find LCM of 852 and 1491. LCM is 5964.

Step 2: multiply 5964 to both thenumbers. Firs number becomes 77, Second

number becomes 76, naturally firstnumber is bigger. Ans.

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How did I get LCM of

852 and 1491 LCM = least cost multiple HCF = Heightest common factor

To calculate LCM, I have multipliedthese numbers and divided them bytheir HCF.

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How did I get HCF of

852 and 1491 HCF = heightest common factor There are two ways first factorize them

- and find common factors. Second faster divide 1491 by 852, you

get 639 as remainder. No divide 852 by639 you get 213 as remainder. Nowdivide 639 by 213, remainder is Zero -therefore 213 is HCF.

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How many factors are

possible in 4? 2*2*1

So total number of factors are two 1 and 2. two comes twice and 1comes once.

t t

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ow many actors are t ereis 12, how many sub factors

can you make? 2*2*3*1= there are three factors 1,2,3 -2 comes twice.

The main factors are 2 & 3.

To find how many subfactors can we make we use the formulae: n stands fornumber of a factor.

(n+1)(n+1) -1

(2+1)(1+1) -1 =5 Ans. Check it: 12,2,3,4,6

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How many subfactors are

possible in 192? Factors are: 2*2*2*2*2*2*3. (6+1)(1+1)-1

=13 ans. Check

it:,2,3,6,4,8,12,16,24,32,48,64,96,192

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How many factors are there in 24 andhow many sub factors can you make out

of it? =2*2*2*3 To find how many subfactors can we

make we use the formulae: (n+1)(n+1) -1 (3+1)(1+1) -1

=7 Ans. Check it :24,2,3,4,6,8,12,

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What is the average of

first 25 prime numbers? Prime number has no other factor thanitself. The first prime number is 2.

First 25 prime numbers are2,3,5,7,11,13,17,19,23,29,31,37,41,47,53,59,61,67,71,73,79,83,89,97.

We will find their AM. add them anddivide the total by 25 = 1017/25 = 40.68ans.

i i t t

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ic is sma est naturanumber and smallest whole

number? Smallest natural number is 1 Smallest whole number is 0

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Is 571 a prime number? Square root of 571 is approx. 24. So divide 571 by all prime numbers

till 24. We will try by2,3,5,7,11,13,17,19,23

But it is not divisible by any of these

numbers, so 571 is a prime number.

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Test of divisibility of

8,9,11? To find divisibility by 9 or its sub factor 3 wehave to add all the digits and divide the total by 9if it is divisible it is divisible by 9. for example= 4470444 =is divisible (total = 27)

For 8, look at last three digits (for four look atlast 2 digits and for 2 look at the last digit) ifthat is divisible - the number is divisible.(in theabove figure 444 is not divisible by 8 so thenumber is not divisible)

For 11, take alternate digits if the difference intotal of alternate digits is divisible by 11 (or itmay be zero), the number is divisible by 11. (19-8) so above number is divisible by 11.

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