 ## Number Theory -Sheet-1

In this forum, please discuss the questions appearing in the QA class sheets :especially the practice and the DS questions at the end of the sheet.

### Number Theory -Sheet-1

This sheet is used as a classroom teaching material for Number Theory Session -2

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### Re: Number Theory -Sheet-1

sir i am not able to solve questions 4,7,5 from number theory.
tpsriram

Posts: 39
Joined: Wed Feb 27, 2013 8:43 am

### Re: Number Theory -Sheet-1

good morning ,

sir i have doubts in PRACTICE QUESTIONS of AVERAGE lesson and questions number are as follows:
2,12,15,30
tpsriram

Posts: 39
Joined: Wed Feb 27, 2013 8:43 am

### Re: Number Theory -Sheet-1

sir i solved RDCS-02Big GrinI-01 sheet completely and i got doubts in following questions:44, 51 to 55 . and secondly for question 38(B) i am getting 16.7 but in key it is given 17 and also in 39(A) i am getting 21.4 but in key it is 21 . thank you
tpsriram

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### Re: Number Theory -Sheet-1

please post this question in the correct forum. Please follow the forum discipline for better response.

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### Re: Number Theory -Sheet-1

-QUESTION- 8, 9 , 15(e) , 16 (d,e,f,g )-- IS THERE ANY FORMULA?

Q 20 -- I SOLVED IN THE FOLLOWING WAY--

a) 172 *173*179*171 divided by 17

....remainder of each of the 4 numbers if divided by 17 will be--
2,3,9,1
..... multiplying them -54
....... 54 now divided by 17 -- 3 will be remainder

b) 143^15 divided by 12
since one 143 will be alone as 14 wil be in 7 pairs
143 divided by 12 will give 11 the remainder,

c) 175^50 divided by 32

since all will be in in 25 pairs ,
175/32, remainder= 15
15*15 = 225,,, divided by 32,,,remainder is 1 ,,answer-1

is the correct approach ?

in practice questions- 8,9,18,21,23
Anantdeep

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### Re: Number Theory -Sheet-1

Q8 Evaluate (51 + 52 + 53 ..... 100)

Solution :

The above question can be used by adding the numbers from 1 to 50 and then subtracting them -

=> ( 1+2+3 ....50+ 51+52+...100) -( 1+2+3+4 ...50)

We know that - the sum of first "n" natural numbers = n(n+1)/2

applying the above formula twice for the above two brackets we get

5050 -1275 =3775

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### Re: Number Theory -Sheet-1

Q9-

For this question simply evaluate the brackets and see what happpens

(1-1/3) =2/3
1-1/4) =3/4

thus we get 2/3 * 3/4* 4/5 .........(n-1)/n

all the numerators and the denominators get cancelled out barring 2 and n which gives the answer as 2/n

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### Re: Number Theory -Sheet-1

Q 15 (E)
(e) Find the no. of zero’s in 250!

Solution

The above question simply means that you need to calculate the highest powerr of 10 which divides 250!.

10 =5X2 ... THERE fore find the highest power of 5 which divides 250 !

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### Re: Number Theory -Sheet-1

16 -D,E,F,G - are straight formula based questions - check the chapter on number theory in the Maths basic reference book, for these formulas 