# Engineering Mathematics GATE-2016

**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.

The value (rounded off to the nearest integer) of x_{3} 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 __________.