# GATE ME 2016 SET-3

 Question 1
A real square matrix A is called skew-symmetric if
 A $A^{T}=A$ B $A^{T}=A^{-1}$ C $A^{T}=-A$ D $A^{T}=A+A^{-1}$
Engineering Mathematics   Linear Algebra
Question 1 Explanation:
A is skew-symmetric
$\therefore \quad A^{T}=-A$
 Question 2
$\lim_{x\rightarrow 0}\frac{log_{e}(1+4x)}{e^{3x}-1}$ is equal to
 A 0 B $1/12$ C $4/3$ D 1
Engineering Mathematics   Calculus
Question 2 Explanation:
$\lim_{x \rightarrow 0} \frac{\ln (1+4 x)}{e^{3 x}-1}$
$\lim_{x \rightarrow 0} \frac{\frac{1}{1+4 x} \cdot 4}{3 e^{3 x}}=\frac{4}{3}$

 Question 3
Solutions of Laplace's equation having continuous second-order partial derivatives are called
 A biharmonic functions B harmonic functions C conjugate harmonic functions D error functions
Engineering Mathematics   Calculus
Question 3 Explanation:
Solution of laplace equation having continuous
Second order partial derivating
$\therefore \nabla^{2} \phi =0$
$\frac{\partial^{2} \phi}{\partial x^{2}}+\frac{\partial^{2} \phi}{\partial y^{2}} =0$
$\therefore \; \phi$ is harmonic function.
 Question 4
The area (in percentage) under standard normal distribution curve of random variable Z within limits from -3 to +3 is __________
 A 55.2 B 88.6 C 99.8 D 44.6
Engineering Mathematics   Complex Variables
Question 4 Explanation:

 Question 5
The root of the function $f(x)=x^{3}+x-1$ obtained after first iteration on application of NewtonRaphson scheme using an initial guess of $x_{0}=1$ is
 A 0.682 B 0.686 C 0.75 D 1
Engineering Mathematics   Numerical Methods
Question 5 Explanation:
\begin{aligned} f(x)&=x^3+x-1\\ f(1)&=1+1-1=1 \\ f'(x)&=3x^2+1\\ f'(1)&=3+1=4\\ x_1&=x_0-\frac{f(x_0)}{f'(x_0)}\\ &=1-\frac{1}{4}=1-0.25=0.75 \end{aligned}

There are 5 questions to complete.