There are nine questions in this assignment. Answer all the questions.

Question 1: Differentiate y w.r.t. x where
(3 marks)

Question 2: Find: (1 ½ marks)

Question 3: If f(x) = 12, if x is an integer
─7, if x is a real number which is not an integer

Find whether f is continuous at x = 9. (2 ½ marks)

Question 4: For the following function, find a point of maxima and a point of minima, if these exist

f(x) = 12x6 – 4x4 + 15x3 –1. (3 marks)

Question 5: If α, β; γ; are the roots of the equation

3x3─5x2 + 2x + 5 = 0

Find the equation whose roots are

α2 + β2 + βα , β² + γ² + γβ, γ² + α² + γα (5 marks)
Question 6: Evaluate: (2 marks)

Question 7: Find all the seventh roots of (3+4i). (1 marks)

Question 8: Find the area bounded by the x-axis, the curve y = e2x and the ordinates x = 4 and x = 7. (3 marks)

Question 9 (a): Find the equation of the line joining the points
(─7, 6, ─ 3) and (7, ─ 6, 3). (1 marks)
(b) Find the equation of the sphere, which contains the circle
x2 + y2 + z2 = 18 , 3x + 3y + 3z = 11 and passes through the origin. (3 marks)

There are six questions in this assignment. Answer all the questions. You may use illustrations and diagrams to enhance your explanations.

Question 1: What are priority Queues? How can priority queues be implemented? Explain.
(2 marks)

Question 2: Write a program in ‘C’ programming language to add two polynomials
using linked list.

(4 marks)

Question 3: Write a non-recursive function in ‘C’ programming language to reverse a doubly linked list.
(4 marks)

Question 4: Let G=(V,E) be an undirected graph. Use depth-first search to develop a
program using ‘C’ language to convert each edge in G to a directed edge such that the resulting graph is strongly connected, or determine that this is not possible

(5 marks)

Question 5: Consider a linked list with n integers. Each node of the list is numbered
from ‘1’ to ‘n’. Develop a program using ‘C’ language to split this list into 4 lists so that:

• first list contains nodes numbered 1,5, 9, 13- - -
• second list contains nodes numbered 2, 6, 10, 14- - -
• third list contains nodes numbered 3, 7, 11, 15- - -
• and fourth list contains nodes numbered 4,8, 12, 16- - -

(5 marks)

Question 6: Write a program in ‘C’ programming language to list the nodes of a binary tree in the following way: List the root, then nodes at depth 1, followed by nodes at depth 2, and so on.

(5 marks)

There are six questions in this Assignment. Answer all the questions.

Question 1:    Explain in detail all the options/items on the Menu bar and Tool bar of any Internet Browser (Internet Explorer or Netscape Navigator).
                                                                                                                        (3 marks)
Question 2:     a) Prove that the sum of fourth powers of the first n integers is
                                    1/30n(n+1) (2n+1)(3n2+3n+1) .                                    (1½ marks)
                        b) Prove that the sum of the squares of the first n integers is
                                    1/24 (2n) (2n+1) (2n+2).                                              (1½ marks)
                                                           
Question 3:     You have decided to purchase a new pickup truck but want to compare various dealer prices. You are ordering a Ford Ranger XLT with the seven options (air conditioning, automatic transmission, stereo, power steering, anti-lock braking system, cruise control, and an extended warranty) listed in Table 1 below. Create a worksheet to compare prices for this vehicle among the three different dealers.  Include a 3-D column chart that compares the Grand Total prices of dealers A, B, and C . Print the workbook and the chart.
                                                                                                                         (4 marks)

                                                                  Table 1

Question 4:     Give detailed information on the topic “E-Governance” by browsing the Internet. List the browsed URLs and the information associated with them.
                                                                                                                        (5 marks)                                           
Question 5:     a) Show whether:  If  n >=4 then find whether 2.n is less than 4.n or not.
                        b) Create chat account with any chat service provider website (like yahoo, msn, etc.) and explain the different component of this account.
                                                                                                (5 marks)

Question 6:     Explain the use of chart wizard of MS-Excel with the help 7 an example.
(5 marks)