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Your father is 50 years old now and his plan is to retire exactly at the age of 60. His goal is to create a fund that will allow him to receive Rs15,00,000 at the time of retirement so that he can start a small business. He has searched the market and is confused between the two options:
[list]
[*]Option 1: To deposit Rs.9,000 after every 6 months in banks A
[*]Option 2: To deposit Rs.2,000 after every 4 months in banks B Both banks assume payments at the end of respective months. As a business graduate, you have been asked to help him out as:
What interest rate assumption has the Bank A used in its offer?
What interest rate assumption has the Bank B used in its offer?
Which option is favorable?

Solution:-
1,500,000 = 9000 [(1+i/2)^10*2-1] 19%
1,500,000 = 2000 [(1+i/3)^10*3-1] 18%

18 % is the favourable option because we can get same
result with small amount of money. in first option
we ll pay 9000 * 20 = 180 000 and in second we ll pay 2000 * 30 = 60 000
in 10 years and the result is same 15 00 000. so second option is favourable



18 wala theek hay bcoz if u convert it compounded yearly rate then it comes
almost 53.20% and the other one comes 38.12% and moreover in 2nd case u invest
only 60000 whereas in the first option u have to invest 180000 so in second
option u will get more profit with less investment

Question No.1 Marks: 4

a) Give regular expressions of the following languages over Σ={0,1}:
1. All strings having no pair of consecutive zeros.
2. All strings having exactly two 1’s or three 1’s not more than it.

b) Show that the Regular expression ^ + 0(0+1)*+(0+1)*00(0+1)* is equivalent to ((0*1)*01*)*

Solution:
a)
1. {0,1,01,11,10,101,010,011,110…………}
2. {011,110,0110.10101.1101,01101,111,0111,…………….}
b)
Both are equivalent because they generate the same language


Question No. 2 Marks: 4

a) Give recursive definition for the language ODD, of strings defined over ∑={-,0,1,2,3,4,5,6,7,8,9},

b) Give recursive definition for the language of palindromes having odd length

Solution:
a)
step1: 1 is in odd
Step2: If x is in odd then x+2 and x-2 are also in odd.
step3: No strings except those constructed in above are allowed to be in odd

b)
Step 1: 1 is in palindrome
Step2: if x is palindrome, than s(x) Rev(S) and xx is also be palindrome whereas belongs to E*
Step3: no string except one, constructed in above, are allowed to be in Palindrome