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A thin wire 40 meters long is cut into two pieces.one piece is used to form a circle with radius r and the other is used to form a square.no wire is left over.which of the following represents a total area,in square meters,of the square and circular regions in tyerms of r?

Pi r^2

Pi r^2+10

Pi r^2+1/4pi^2 r^2

Pir^2+(40-2pi r)^2

Pi r^2+(10-1/2pi r)^2

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it should be 13.

no when divided by 5 will leave reminder as 3 and when by 3 it will leave reminder 1so it is of the form 35K+13. so 13.

pls explain the bold part......

sorry typo. it is of the form 15K+13

see it is 5k+3 type as when it divided by 5 it will leave reminder 3, now 5k+3 should leave reminder 1 when divided by 3, so divide 5k+3 by 3 it will have reminder as 2K. now 2k should leave reminder 1 so smallest possible value of K is 2, and smallest no. is 5K+3 which is 13. so no. is of the form 15K (LCM of 5 & 3)+13

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no when divided by 5 will leave reminder as 3 and when by 3 it will leave reminder 1so it is of the form 35K+13. so 13.

pls explain the bold part......

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17 nov D Day Saysremainder when 7^15 divided by 15 ????

it should be 13.

no when divided by 5 will leave reminder as 3 and when by 3 it will leave reminder 1 so it is of the form 15K+13. so 13.

@ nachiketbhai CAT kaisi rahi

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Nachiket Deshmukh
@ThinkAce
11,961

plz explain why the bold steps give different result or why in former m=8

See.. when we have 9*2*2; we have powers as (8, 1, 1)

But, power 8 can be taken from y or z. And other two will give (1, 1) as power. So, total 2 cases; one when y gives 8 and one when z gives 8.

When we have 4*3*3; powers are (3, 2, 2). Anyone can be 3 or 2.

So, we can have any one of x or y or z as power 3 and other 2 can take power 2. So, 3 cases. It is like 3 digit numbers with 2 digits being same.

When we have 6*3*2; powers are (5, 2, 1).

So, we have 3! ways.

It is like a digit number from 3 distinct digits.

Hope it is clear now..

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d b
@fedbite
344

Is your question solved? You snipped it before I could clarify..

Which bold step? I think you missed making it bold.. Please clarify..

My take is 13

Euler's number for 15 is 8

So, 7^8k will leave remainder by 15 as 1

=> 7^16 will leave remainder as 1

Let, remainder by 7^15 be 'x'.

So, 7x will leave remainder by 15 as 1 (or -14)

=> x = -2 or 13

sorry just missed a bracket now corrected it

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Nachiket Deshmukh
@ThinkAce
11,961

tarun g Sayssnipped...

Is your question solved? You snipped it before I could clarify..

fedbite Saysplz explain why the bold steps give different result or why in former m=8

Which bold step? I think you missed making it bold.. Please clarify..

17 nov D Day Saysremainder when 7^15 divided by 15 ????

My take is 13

Euler's number for 15 is 8

So, 7^8k will leave remainder by 15 as 1

=> 7^16 will leave remainder as 1

Let, remainder by 7^15 be 'x'.

So, 7x will leave remainder by 15 as 1 (or -14)

=> x = -2 or 13

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d b
@fedbite
344

My take is 18

As a, b, and c are sqaures of primes number let those prime numbers be x, y and z resp.

So, N = x^6 * y^8 * z^10

We need 36 factors. And number can involve 2 or 3 prime numbers as with only one prime number we will need p^35 which is not possible.

Case 1: (p1)^m * (p2)^n

=> (m+1)*(n+1) = 36

So, (m, n) can be: (8, 3) or (5, 5) as m, n With (8, 3) we can have y or z as m and n can be other 2. So, total 2*2 = 4 cases

With (5, 5) we just need to pick 2 out (x, y, z) => 3C2 ways = 3 ways

So, total 7 ways for case 1

Case 2: (p1)^m * (p2)^n * (p3)^o ... it is 'o' and not '0' (zero)

=> (m+1)*(n+1)*(o+1) = 36

=> 9*2*2 or 6*3*2 or 4*3*39*2*2 => m = 8 => m can be from y or z => 2 ways

6*3*2 => m = 5 => m. n. o can be from any body => 3! = 6 ways4*3*3 => m, n, o can be from anyone agian => 3!/2! = 3 ways

So, total 11 ways from case 2

In all; we have 7+11 = 18 ways

plz explain why the bold steps give different result or why in former m=8

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euler number of 15 is 8

so 7^15 mod 7 = 7^7 mod 7 = 49*49*49*7 mod 7 = 4*4*4*7 mod 7

= 1*28 mod 7 = 13

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17 nov D Day Sayssorry typo mistake its 7^15 is divided by 15..

(7^3)^5 mod 15 = (343)^5 mod 15 = (-2)^5 mod 15 = -32 mod 15 = -2 or 13..

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@jackoneill
4,258

17 nov d day Saysremainder when 7^15 divided by 15 ????

=> (7^2)^7 * 7 % 15

=> 4^7 * 7 % 15

=> (4^2)^3 * 4 * 7 % 15

=> 1 * 4 * 7 % 15

=>

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tarun g Saysquestion is incomplete. 7^15 is divided by what?

sorry typo mistake its 7^15 is divided by 15..

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17 nov D Day Saysremainder when 7^15 divideb by????

question is incomplete. 7^15 is divided by what?

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snipped...

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