BT0063- MATHEMATICS for IT

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ASSIGNMENT

PROGRAM	B.SC IT
SEMESTER	FIRST
SUBJECT CODE & NAME	BT0063- MATHEMATICS for IT
CREDIT	4
BK ID	B0947
MAX.MARKS	60

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

Q.1 Let A = {x: x ÎZ⁺} ; B = {x : x is a multiple of 3, x ÎZ}:

C = {x:x is a negative integer}; D = {x:x is an odd integer}.

Find (i) A Ç B, (ii) A Ç C, (iii) A Ç D, (iv) B Ç C, (v) B ÇD, (vi) C Ç D.

Solution: Z⁺ = set of all positive integers

Let A = (1, 2, 3, 4, 5)

B = (3, 6, 9, 12, 15)

Therefore B is multiple of 3.

                   = f

Q.2 Prove that the set Z₄ = {0, 1, 2, 3} is an abelian group w.r.t. addition modulo 4.

Solution: set Z₄ = {0, 1, 2, 3} is an abelian group

Closure law:  

Let a,b ∈Z. Clearly, a+b‐5 is again an element of Z.

Thus a,b∈Z, a*b=a+b‐5∈ Z

Associative law: Let a,b,c ∈Z.  

Consider ,  

a*(b*c)=  a*x       where x=b*c=b+c‐5

  =a+x‐5=a+(b+c‐5)‐5

  = a+b+c‐10

Q.3 Differentiate

 

Put x = a sin q

Solution:

When X = a sinq 

Y = a sinqÖa² – (a sinq)² /2 + a²/2 sin^-1 a sin q/a

(i)Let y = f(x) --------------------(i)

(ii) Let dy be the increment in the y corresponding to the increment to the element dx in x.

Therefore  y = dy = f(x + dy) ---------------- (ii)

(

Q.4 Integrate the following w.r.t. x

Solution: Let  = ò X² / (1+X⁶)

Put = 1+x² = y

Therefore 2x dx = dy

I = ò 1/y dy

Q.5 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 colours

b) Two balls are of the same colour

c) All the three are of the same colour.

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

Now we should already know that

Q.6 Given below are the marks obtained by five B.Sc. students

Roll No: 101 102 103 104 105

Marks   : 10 30 20 25 15

Calculate Standard Deviation

Solution: The standard deviation measures the spread of the data about the mean value. It is useful in comparing sets of data which may have the same mean but a different range.

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