Question 1

Find all values of Re (i)^(-i).

Accepted Answer

e^(π/2 + 2πk)

Answer

e^(-π/2 + 2πk)

Answer

e^(-π/2 + 2πk)i

Answer

e^-(π/2 + 2πk)

Question 2

Evaluate integral of sinx/x from 0 to infinity

Accepted Answer

π/2

Answer

∞

Answer

0

Answer

π

Question 3

Find the Laplace transform of f(t) = e^3t+1

Accepted Answer

e/(s-3)

Answer

e/(s^2+3)

Answer

e/(s+3)

Answer

e/(s^2-3)

Question 4

Find the Laplace transform of f(t) = t^(3/2)e^-4t.

Accepted Answer

3/4 sq.rt of π(s +4)^-5/2

Answer

3/2 sq.rt of π(s +4)^-5/2

Answer

3/7 sq.rt of π(s +4)^-5/2

Answer

3/2 sq.rt of π(s +4)^-5/2

Question 5

Evaluate Г(5/2)

Accepted Answer

3 sq.rt of π/4

Answer

15 sq.rt of π/4

Answer

3 sq.rt of π/8

Answer

15 sq.rt of π/8

Question 6

Evaluate LT of the function F(t) = Sint for t > 0 to t < π and F(t) = zero for t > π ,

Accepted Answer

(1 – e^-πs) / (s^2 + 4)

Answer

(1 – e^s) / (s^2 + 4)

Answer

(1 + e^-πs) / (s^2 + 4)

Answer

(1 – e^-s) / (s^2 + 4)

Question 7

Evaluate LT of Sin kt Cos kt

Accepted Answer

k (s^2 + 4k^2)

Answer

s / (s^2 + k^2)

Answer

s / (s^2 + k)

Answer

k / (s^2 – k^2)

Question 8

Evaluate LT of t Cos2t

Accepted Answer

(s^2 – 4) / (s^2 + 4)^2

Answer

(s^2 + 2) / (s^2 + 4)^2

Answer

(s^2 – 2) / (s^2 + 4)^2

Answer

(s^2 – 4) / (s^2 + 4)

Question 9

What is the coefficient of the x^3 in the Taylor series polynomial for 1/(1+2x) about x = 0?

Accepted Answer

-8

Answer

8

Answer

4

Answer

-4

Question 10

Find a0 for the equivalent Fourier series of x^2 over the interval –π to π.

Accepted Answer

2π^2/3

Answer

π^2/3

Answer

2π^2/32

Answer

2π^2/5

Question 11

Find the unit vector orthogonal to both vectors 9i +9j and 9i +9k.

Accepted Answer

(i-j-k)/sq.rt of 3

Answer

(i+j+ k)/sq.rt of 3

Answer

(i - j + k)/sq.rt of 3

Answer

(i - j + k)/sq.rt of 5

Question 12

Find the first 3 terms in the power series equivalent of e^x/(1-x) about x = 0.

Accepted Answer

1 + 2x + 2.5x^2 + ...

Answer

1 + 2x - 2.5x^2 + ...

Answer

1 - 2x + 2.5x^2 + ...

Answer

1 - 2x - 2.5x^2 + ...

Question 13

Find the /A x B/ if /A/ and /B/ are 26 and 17 respectively and the angle between them is π/3.

Accepted Answer

383

Answer

221

Answer

121

Answer

441

Question 14

Evaluate the inverse Laplace transform of 1 / s^2(s-2)

Accepted Answer

e^2t – 2t – 1

Answer

(1 – e^-2t) / 2

Answer

(1 + e^2t) / 2

Answer

e^2t – 2t

Question 15

Find the value of 4Sinh πi/3.

Accepted Answer

2i (sq.rt of 3)

Answer

i (sq.rt of 3)

Answer

3i(sq.rt of 3)

Answer

4i (sq.rt of 3)

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