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1) Describe in detail all the options/items on the Menu bar and Tool bar of any Internet Browser (Internet Explorer or Mozilla Firefox or Chrome).

2) You have decided to buy a new pickup truck but would like 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 below. Prepare a worksheet to compare prices for this vehicle among the three different dealers.  Include a 3-D column chart which compares the Grand Total prices of dealers A, B, and C . Print the workbook and the chart.

Cost Comparison Sheet
Make:        Ford
Color:        Red
Model:     Ranger XLT
Pricing Information in Dollars ($)           Dealer A    Dealer B    Dealer C
Air conditioning                                    699            705         739
Automatic transmission                         375           379          397
AM/FM, CD, cassette                             619           625          655
Power steering                                      229           231          243
ABS                                                     797           804          844
Cruise control                                        184          186          196
Extended Warranty                                114          114          119
Base price                                            14770       14915      15639
Grand totals           

3) a) Prove that the sum of fourth powers of the first n integers is
1/30 n (n+1)(2n+1)(3n2+3n-1) .

b) For any prime p >= 5, prove that p2+2 is composite.  (Hint: Recall that any prime p>=5 can take one of the alternative forms  6k+1 or 6k+5).

4) Give detailed information on the topic “Cloud Computing” by browsing the Internet. Name the browsed URLs and the information associated with them.

5) Complete the following tasks using MS-EXCEL:

FUEL ESTIMATES COMPUTATIONS: This project is to find out the fuel needed for two types of airplanes, and the cost of the fuel. You must do all computations using formula, and do a chart. Use Page Setup to make the left margin 0.5 and the right margin 0.5 also. Put your name in the Title line, after “Fuel Estimates”.

Note the following:

• Col. D - H: You should enter correct formulas under Columns D through H (Flying Fuel, Reserve Fuel, Holding Fuel, Total Fuel Needed and Estimated Fuel Cost)!! Read and compute carefully!

• Cells C12, C13, C14, H13 or H14: When you use these in a formula, you should make them absolute cell references (F4 key after your type the cell reference, or enter the $ sign manually)
GRAPH/CHART: Choose cells A3:B8 (Plane and Flight). Hold down the “Control” key and select D3:D8. Hold down the “Control” key and select G3:G8. Create a chart (Insert-Chart, Finish) and position it in a pleasing way under the data for the flight.

PRINT IT  on one sheet, in landscape mode.

PRINT AGAIN, but with formulae: There are two ways to show formulae:

1) Enter Control+` (the key with the ~ at the top left)
OR
2) Tools-Options, and under “Window Options” put a check mark beside "Formulas", then close the window.

Answer all the problems.

1) (a) Find all the eighth roots of (19 + 7 i)
(b) Differentiate tan (5x + 7) w.r.t. cos-1(1-x2/1+x2)
(c) Find complex conjugate of ( 7 + 6i) /(2 + 3i)               

2) (a) Find the equation of the line in two-dimensional space that passes through the point (2, 3) and is parallel to the line 2x + 3y = 5.
(b) Find the equation of the sphere, which contains the circle x2 + y2 + z2 = 18 , 3x + 3y + 3z = 11 and passed through the origin.           

3) (a) Find the area bounded by the x-axis, the curve y = (2x2 + 7x) and the ordinates x = 5 and  x = 7.
(b) Find   (1 + x2) / x2

4) a) Using Simpson’s rule, evaluate the following, taking n = 4, ∫0π(1-sin2x/1+x)

(b) Find the area bounded by the curves y2 = 9x and x2 = 9y

5) (a) Evaluate the following
(i) ∫(x3-4x)/(x2+1)2dx
(ii) ∫(dx/57cosx)

(iii) ∫ x1/2/(1+x1/4)

(b) Prove the following inequalities:
(i) tan –1 x < x            for all positive value of x.
(ii) ex – e–x>= 2 x         for all x > 0.               
(c) Use the Cauchy-Schwartz inequality to solve x3 – 25x2 – 4x + 100 = 0
(d) Find the perimeter of the cord r = a (1 + cos θ)

Answer all the problems.

1) describe Row Major Order and Column Major Order                          
2) prepare a program in ‘C’ language for the conversion of a Tree to a Binary Tree              
3) prepare any two algorithms for finding the minimum cost spanning tree                           
4) describe the process of implementation of two stacks in a single dimensional array.

Math, Academics

  • Category:- Math
  • Reference No.:- M91027

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