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MTH202 Assignment No 02 Solution & Discussion Due Date:24-01-2017

Question: 01   Prove by contradiction that     is irrational.

 

Question# 02 (a)  Find the number of words that can be formed from the word VIRTUAL if the words end with letter  T and start with letter L. (Words need not be in the dictionary and each letter should be used once)

(b) How many 4-digit even numbers can be formed using digits 1,2,3,5 using each digit once? 

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full solution

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Aamir Shehzad thanks for sharing 

Aamir ap ny Q3. ko ksay solve kia i don't understand..
How many 4-digit even numbers can be formed using digits 1,2,3,5 using each digit once?

ap ny iska ans jo batye hai woh kasy EACH DIGIT ONCE in ur ans 1two times aya hai..
kia yeh ans theek hai..
5*3*2*1=30
is may 4 digits b hai aur ans b even hai..plzzzz koi bataye...

Solution#1
Suppose 7+11√2 is rational
Then by definition
7+11√2 = a/b
11√2 = 7-a/b
11√2 = (7b-a)/b
√2 = (7b-a)/11b
Since a and b are integers, so 7b-a and 11b and 11b≠0,
Hence √2 is a quotient of two integers 7b-a and 11b with 11b≠0
Accordingly, √2 is rational (by definition of rational).
This is contradicts the fact because √2 is rational.
Hence our supposition is false and so 7+11√2 is irrational.

Question: 01   Prove by contradiction that     is irrational.

 

Suppose is rational

Then by definition of rational

= a / b

Now

 = (a / b) – 7

 

= (a – 7b) / b

 = (a – 7b) / 11b

Since a and b are integer, so are a – 7b and 11b and 11b # 0

Hence is the quotient of a – 7b and 11b, this means is rational.

This contradict the fact that is irrational.

Hence our supposition is false and is irrational

 

 

Question# 02 (a)  Find the number of words that can be formed from the word VIRTUAL if the words end with letter  T and start with letter L. (Words need not be in the dictionary and each letter should be used once)

Answer:

 

Number of words end with T and start with L = 5! = 5x4x3x2x1 = 120

 

(b) How many 4-digit even numbers can be formed using digits 1,2,3,5 using each digit once?

Answer:

 

Number of 4 digit even numbers = 1 x 3 x 2 x 1 = 6

Guess what with reason

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Q.2(a) Solution  :7!/(7-5)!=2520

(b)    solution:  4!/(4-3)!=24 

Bhai ya to wrong nai ha

1st ma hum 1*5*4*3*2*1*1

nd 2nd ma

3*2*1*1 krn gay

MTH202 Complete Solution

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