You have three compulsory problems and one optional problem for this lab. The optional problem is for your practice and will not be graded. However, it is recommended that if you have sufficient time then you must attempt the optional problem. The optional problem is relatively tough as compared to the other three problems.

1. (30 marks) Write a program that takes a number as input and outputs the largest among 1 3 5 or 7 that divides the number. For example:

Input: 55
Output: 5

Input: 24851 (a prime number)
Output: 1

Input: 105
Output: 7

2. (40 marks) Write the program that takes the annual salary (in Lac INR) of a person as input and outputs the corresponding amount of income tax to be paid by the person (again in Lac INR). Make use of the switch statement. The income tax is computed according to the following protocol:
If salary is less than 2 Lacs, no tax is to be charged.
If it is more than 2 Lacs but less than 5 Lacs, charge 10% of tax on whatever is in excess of 2 Lacs
If it is more than 5 Lacs but less than 10 Lacs, charge 20% on whatever is in excess of 5 Lacs in addition to the tax on 5 Lacs according to the previous rule.
If it is more than 10 Lacs, charge 30% on whatever is in excess of 10 Lacs in addition to the tax on 5 Lacs according to the previous rule.

For example:
Input: 7 (in Lacs)
Output: 0.7 Lacs (3*0.1+2*0.2=0.7)

Input: 13 (in Lacs)
Output: 2.2 Lacs (3*0.1+5*0.2+3*0.3=2.2)

3. (40 marks)  Take two numbers a and b as input from the user and print the sum of the squares of all the odd numbers between a and b (including a and b). For example:

Input: a=1 b=6
Output: 35

Input: a=11 b=18
Output: 579

Optional Problem:

In a game of Black Jack the cards 2 through 10 are counted at their face
value regardless of suit, all face cards (jack, queen and king) are
counted as 10. An ace is counted as either 1 or 11 depending on the
total count of all the cards in the player's hand. The ace is counted as
11 only if the resulting total value of all cards in a player's hand
does not exceed 21, else it is counted as 1. Make use of this
information to write a program that accepts three card values as inputs
(a 1 corresponding to an ace, a 2 corresponding to a 2 and so on) and
outputs the total value of the hand appropriately. Assume that Jack,
Queen, and King are represented by input values 11, 12, 13 respectively.
Also assume that there will not be more than one instance of Ace in a
single hand.

Sample Input/Output:

Input: 2 11 13
Output: 22

Input: 2 4 1
Output: 17   (Ace counted as 11)

Input: 1 9 13 (Ace counted as 1)
Output: 20