SCE Engineering Mathematics

Question 1

What is the Laplace transform of the function f(t) = e^(-at)?

Accepted Answer

1/(s+a)

Answer

1/(s-a)

Answer

a/(s+a)

Answer

s/(s+a)

Question 2

A matrix A has eigenvalues 2 and 5. What is the determinant of A?

Accepted Answer

10

Answer

7

Answer

3

Answer

25

Question 3

Which numerical method uses the formula x_{n+1} = x_n - f(x_n)/f'(x_n)?

Accepted Answer

Newton-Raphson method

Answer

Bisection method

Answer

Secant method

Answer

Euler's method

Question 4

What is the divergence of the vector field F = (x², xy, xz)?

Accepted Answer

2x + x + x = 4x

Answer

2x + y + z

Answer

x² + xy + xz

Answer

2x + x + x

Question 5

For the differential equation dy/dx + 2y = e^(-x), what is the integrating factor?

Accepted Answer

e^(2x)

Answer

e^(-2x)

Answer

2x

Answer

e^(x)

Question 6

What does the Fourier series represent?

Accepted Answer

A periodic function as a sum of sines and cosines

Answer

A polynomial approximation of any function

Answer

The Taylor expansion around zero

Answer

A matrix decomposition technique