BT0063 – MATHEMATICS FOR IT

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ASSIGNMENT

SPRING	2014
PROGRAM	BSc IT
SEMESTER	1
SUBJECT CODE & NAME	BT0063 – MATHEMATICS FOR IT
CREDIT	4
BK ID	B0950
MAX. MARKS	60

Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately of 400 words. Eachquestion is followed by evaluation scheme.

Q.1 (i) Let A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}. Find A – B and B – A.

(ii) In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak at least one of the two languages. How many people speak only English and not Hindi?

How many people speak English?

Answer:

(i) A-B

(ii)  n (A U B )= people who speak in either Hindi and English.

Given people speak at least one of the languages.

n (A U B) = 50.

Q.2 (i) Express 7920 in radians and (7π/12) c in degrees.

(ii) Prove that (tan θ + sec θ – 1)/ (tan θ + sec θ +1) = Cos θ / (1-sin θ) = (1+sin θ)/ Cos θ

Answer: (i) The conversion is 180^O= π radian

So 7920⁰ = (7920*3.14)/180 = 138.247 radians

(7π/12) c in degrees:-

(ii). Solution:-

(tan θ + sec θ – 1)/ (tan θ + sec θ +1) =(1+sin θ)/ Cos θ

If (tan θ + sec θ – 1)/ (

Q.3 (i) Define continuity of a point                      

(ii) Test the continuity of the function f where f is defined by f(x) = {x-2/|x-2| if x ≠ 2, 7 if x = 2.

Answer: (i) Definition of Continuity

Let a be a point in the domain of the function f(x). Then f is continuous at x=a if and only if

lim f(x) = f(a)

x --> a  

(ii) Test the continuity of the function f where f is defined by f(x) = {x-2/|x-2| if x ≠ 2, 7 if x = 2.

Solution:-L.H.L =limx tends to (x-2)/|x-2|

Put x = 2-h , h=0

Q.4 Solve dy/dx = (y+x-2)/(y-x-4).

Answer:dy/dx = (y+x-2)/(y-x-4) -------------------------------- (i)

Put y = vx

Diff w.r.t “x”

Q.5 (i) a bag contains two red balls, three blue balls and five green balls.

Three balls are drawn at random. Find the probability that

a) The three balls are of different colors’.

b) Two balls are of the same color.

Let nCk = number of ways to pick up k items from a set of n items.

Of course you should already know that nCk+=+n%21%2F%28k%21%2A%28n-k%29%21%29 (*)

Bag consists of 2 red balls (R), 3 blue balls (

Q.6 Solve:  2x + 3y + 4z = 20, x + y + 2z = 9, 3x + 2y + z = 10.

Answer: These equations are written as

[2 3 4                                     [20

1 1 2                 =                 9

3 2 1]                                   10]

AX = B

Where A = [2 3 4 , 1 1 2 , 3 2 1 ]  X =[

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