BT0063-Mathematics for IT

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ASSIGNMENT

SUMMER	2014
PROGRAM	BSc IT
SEMESTER	1
SUBJECT CODE & NAME	BT0063-Mathematics for IT
CREDIT	4
BK ID	B0950
MAX. MARKS	60

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

Answer: A-B = {1, 3, 5} , B-A = {8}

(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: 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.

n (A ^ B) =people who speak in both the languages = 25

n (A) = people who speak in English. = x

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

(ii). Solution:-

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

If (tan θ + sec θ – 1)/ (tan θ +

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

               

(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

By applying the limits

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”

dy/dx = v.1+x.dx/dx

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

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

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