bit202 smu bsc it spring 2017 (jul/aug 2017 exam) IInd sem assignment

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DRIVE SPRING 2017

PROGRAM Bachelor of Science in Information Technology - B.SC(IT)

SEMESTER II

SUBJECT CODE & NAME BIT202 – Basic Mathematics

Assignment Set -1

1 a) If in group G, (ab)^2 = a^2b^2 for every a, b Î G prove that G is abelian.

b) Show that if every element of a group G is its own inverse then G is abelian.

Answer: a) (ab)^2 = a^2.b^2

Ø  (ab) (ab) = (a . a) (b . b)

Ø  a[b(ab)] = a[a(bb)] (Associative)

Ø  b (ab) =

Ø   

2 If tan A = 1- cos B . show that tan 2A = tan B.

                          sinB

Answer: Given that tan A = 1-cosB

                                                                SinB

i.e tan A = 1-{1-2sin^2 (B/2)}

                     2sin(B/2) cos(B/2)

3 Evaluate dy/dx,  when y = log[√(1+x^2)+x]) / [√(1+x^2)-x])

Answer: d/dx{(log[√(1+x^2)+x]) - log[√(1+x^2)-x])

(Since log A/B = Log A – log B)

Assignment Set -2

1 Integrate the following w.r.t. x

i) x √(x + a)

ii) x /√(a + bx)

Answer: a) x √(x + a)

∫x√(x+a) dx = I                                 (say)

2 If a = cos q + i sin q, 0<q <2p prove that {1+a}/{1-a} = i cot q/2

Answer: i. If a = cos q + i sin q,0 <q < 2p prove that 1+a/1-a = i cot q/2

L.H.S = 1+ cos q + i sin q

                1 - cos q - i sin q

3 Solve: 3/1 + (3.5/1.2) . (1/3) + (3.5.7/1.2.3) . (1/3^2) + …………..∞]

Answer: Comparing the given series with one of the general Binomial series, we get

P=3, q=2, x/q=1/3

x=2/3

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