Q 1: Which one of the following is an iterative technique for solving a system of simultaneous linear algebraic equations?
Q 2: The Laplace transform of e^{at}\sin\left(bt\right) is
Q 3: What are the modulus (r) and argument (θ) of the complex number 3 + 4i ?
Q 4: A set of simultaneous linear algebraic equations is represented in a matrix form as shown below.
\begin{bmatrix}0&0&0&4&13\\2&5&5&2&10\\0&0&2&5&3\\0&0&0&4&5\\2&3&2&1&5\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\\x_4\\x_5\end{bmatrix}=\begin{bmatrix}46\\161\\61\\30\\81\end{bmatrix}The value (rounded off to the nearest integer) of x3 is _________.
Q 5: What is the solution for the second-order differential equation \frac{d^2y}{dx^2}+y=0 , with the initial conditions {\left.y\right|}_{x=0}=5 and {\left.\frac{dy}{dx}\right|}_{x=0}=10 ?
Q 6: The model y=mx^2 is to be fit to the data given below.
| X | 1 | \sqrt2 | \sqrt3 |
| y | 2 | 5 | 8 |
Using linear regression, the value (rounded off to the second decimal place) of m is _______.
Q 7: The Lagrange mean-value theorem is satisfied for f\left(x\right)=x^3+5 , in the interval (1, 4) at a value (rounded off to the second decimal place) of x equal to __________.
Q 8: Values of f(x) in the interval [0, 4] are given below.
| x | 0 | 1 | 2 | 3 | 4 |
| f(x) | 3 | 10 | 21 | 36 | 55 |
Using Simpson’s 1/3 rule with a step size of 1, the numerical approximation (rounded off to the second decimal place) of \int_0^4f\left(x\right)\operatorname dx is __________.