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Tec101: Basic Engineering Mathematics. Question Paper
Tec101: Basic Engineering Mathematics.
Course:Bachelor Of Electrical And Electronics Engineering
Institution: Moi University question papers
Exam Year:2011
Basic Engineering Mathematics I
1. Let U={1,2,3,4,5,6,7,8,9,10}, A={1,5}, B={3,5,6,9}, C={1,3,5} and D={2,5,7,9,10}. Determine:
a. A n B' (1mk)
b. (A U C) n (B-D) (2mks)
c. Symmetric difference of A and C (2mks)
2. Thirty computers are assembled in a factory. The operating system options available are Windows Vista, Windows XP and Linux. Given the following:
i. A total of five computers have both Windows Vista and Windows XP
ii. A total of three computers have both Windows XP and Linux
iii. Two computers have Linux as the only installed operating system
iv. Three computers have all the three operating systems
v. The total number of computers with windows Vista is fifteen
vi. The total number of computers with Windows XP is ten
vii. The total number of computers with Linux is eight.
a. Illustrate the above information using venn diagrams and set notation. Assume that V, P and L are the sets representing Windows Vista, Windows XP and Linux respectively (3mks)
b. Determine how many computers have been installed with windows Vista only (2mks)
c. Determine how many computers have not been installed with any operating system (3mks)
3. Given sin (a+x)=2b and sin (a-x)=2c where the numbers a, b, c are constants, determine the condition for the existence of the value x (3mks)
4. Show that sin (A+B) =sinAcosB+cosAsinB by vector method (3mks)
5. Prove that if a and b are position vectors of points A and B, then the position vector of a point P on AB, where the ratio AP:PB =m:n, is given by (m+n)P =na+mb (2mks)
6. Given that A, B and C are the points (1,2,2), (0,5,0) and (4,3,2) respectively, find the equation which must be satisfied by the coordinates (x, y, z) of any point P in the plane ABC. (4mks)
7. Find the angle between the vectors a and b given;
a=i+2j+3k
b=4i+5j+6k (2mks)
8. Given plane ABC defined by 3x-2y-4z=3 and plane DEF defined by x-y-z=3, find out if the two planes are orthogonal (2mks)
9. Calculate the orthogonal projection A' of point A (1, 2, 3) on the plane 3x-y+4z=0 (4mks)
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