Singular matrix

Decomposable matrix

Adjugate of a matrix

If Z = f(x,y) = xy

Find the maximum value for f(x,y) if x and y are constrained to sum to 1 (That is, x +y = 1). Solve the problem in two ways: by substitution and by using the Lagrangian multiplier method.

Solve the following differential equation

given Y(0) = 4

Let Z = f(x,y) = 3x³ -5y² -225x + 70y + 23.

(i) Find the stationary points of z.
(ii) Determine if at these points the function is at a relative maximum, relative
minimum, infixion point, or saddle point.

An individual consumer consumes two commodities X1 & X2. The utility function is 

The price of commodity one is P1 = Rs.3.00, the price of commodity two is P2 = Rs.4.00, the individual’s income per period is Rs.108. Determine the utility maximizing level of X1 & X2 and derive the demand curves for the two commodities.

Consider the following two matrices.

(i) Find the rank of ‘A’ and ‘B’
(ii) Show that (AB)^-1 = B^-1 A ^-1
(iii) Show that (A^-1)^-1= A
(iv) Show that (B^-1)^-1= B

Write a program to demonstrate use of commit and rollback methods in JDBC programming.

Write a java program to demonstrate use of Set and Map collection interfaces in problem solving.

Write a java program to create an abstract class Student. Inherit UG_Student class and PG_Student class from the Student class. Define constructors and appropriate methods to display details of students. Make necessary assumptions.

Write a program to demonstrate use of different data types and operators in Java.

Write and run the following queries for your database using SQL commands:
1. List all the customers whose pin code is “1100067”.
2. List the order id and amount of those orders which are placed in first week of the month and are of
amount more than 10,000.
3. List the customer name and contact number of those customers who have placed more than one
order in October 2023.
4. List the customer details, who has placed their orders on 10-10-2023.
5. List all the customers whose name starts with alphabet ‘A’.
10
6. Find the total price of the order id O0011 .
7. List the electronic products information in the increasing order of price.
8. Find the detail of products which have been ordered more than once.
9. ist the order details of the orders placed on 11-10-2023 and payment mode is COD.
10. List the different types (such as electronic, grocery, cloth etc.) of items available for shopping.

Implement the database design (create tables) that you have created in question 1 using a RDBMS with proper integrity constraints. Enter about 10-15 meaningful records in each of your table.

List the entities, their attributes and relationships for the description and make an ER-diagram for this e-Commerce Portal. You may use the concept of keys, aggregation, generalisation, cardinality etc. in a proper way. Design the suitable RDBMS tables for the ER-diagram created by you. The database design should include keys, foreign keys, constraints and referential integrity constraints. Your database design must be normalized up to 3rd Normal form. Make necessary assumptions wherever require.

Write a program in ‘C’ language that implements a Queue using Linked Lists. Make necessary assumptions.

Write an algorithm and program in `C’ language that accepts a Tree as input and converts it into a Binary Tree. The output of the program should be Binary Tree. Input: Tree Output: Binary Tree

What is a Doubly Linked List? How does it differ from Circularly Doubly Linked List?

What is Heap Sort? What is Merge Sort? Write the factors on the basis of which Heap Sort or Merge Sort is selected.

Explain the process of converting a Tree into a Binary Tree with an example.