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Show that T(x1, x2, x3, x4) = 3x1_7x2+5x4 is a linear transformation by finding the matrix for the transformation. Then find the basis for the null space of the transformation.


1)  Imagine you need to open a standard combination dial lock but don't know the combination and don't have a pair of bolt cutters. Write a program that prints all possible combinations so you can print them on a piece of paper and check off each one as you try it. Assume the numbers on the dial range from zero to thirty-six and three numbers in sequence are needed to open the lock.

         Suppose the lock isn't a very good one and any number that's no more than one away from the correct number will also work. In other words if the combination is 17-6-32 then 18-5-31 will also open the lock. Write a program that prints the minimum number of combinations you need to try to guarantee opening the lock.


Compose an Employee class with the attributes personalia(data type Person),

employeeNo, yearofAppointment, monthSalary, and taxPercent. In addition to get

methods for all the attributes, the following operations should be available :

a. Find the employee’s monthly tax.

b. Find the gross annual salary

c. Find tax savings per year. To our employees June is tax free, and in

December there’s only half the usual tax.

d. Find name (in the format last name, first name.)

e. Find age

f. Find number of years employed at the company.

g. Find out if the person has been employed for more than a given number of

years (parameter)

h. Set methods to change attributes that it makes sense to change.

i. Find out in which cases an instance of the Employee class has to

collaborate with its personalia object in order to complete these tasks.


Write a simple program that puts data into an instance of the Employee class and calls all

the methods you’ve created. Check that the results are correct


Compose an Employee class with the attributes personalia(data type Person),

employeeNo, yearofAppointment, monthSalary, and taxPercent. In addition to get

methods for all the attributes, the following operations should be available :

a. Find the employee’s monthly tax.

b. Find the gross annual salary

c. Find tax savings per year. To our employees June is tax free, and in

December there’s only half the usual tax.

d. Find name (in the format last name, first name.)

e. Find age

f. Find number of years employed at the company.

g. Find out if the person has been employed for more than a given number of

years (parameter)

h. Set methods to change attributes that it makes sense to change.

i. Find out in which cases an instance of the Employee class has to

collaborate with its personalia object in order to complete these tasks.

Draw sequence diagrams for these operations.


An online E-commerce website is using non-persistent cookies to store the sessions of its visitors. The sessions are currently stored on the user’s computer locally. The website is facing a severe issue that before placing the order if the light goes off, the user’s cart information gets lost and the user has to add products again to the cart.

You are given a task to save the information stored in a session if the user accidentally leaves the website due to any reason. You have to select one session tracking technique from the following to resolve this issue.

1.        URL Rewriting

2.        HTTP Session

Now which technique you will prefer to resolve this issue. Justify your answer with solid arguments.



A force of 60 N is supported by the bracket as shown. Determine the resultant internal loadings acting on the section through point A.

In the circle graph, what is the measure of the central angle corresponding to each item?


Use a single subscripted array to solve the following problem. Read in 20

numbers, each which is between 10 and 100, inclusive. As each number is read,

print it only if it is not a duplicate of a number already read. Provide for the

“worst” case in which all 20 numbers are different. Use the smallest possible way

to solve the problem.


.A solution prepared by adding 10g of an unknown non-volatile, non-electrolyte solute to 150 g of water. The Boiling point of the solution is elevated by 0.433 0C above the normal boiling point of the solvent. What is the molar mass of the unknown substance?



List=[1,2,2,3,4,5]


Using break or continue condition find frequency of each element in List without using any other functions like append, count or dictionaries.

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