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.

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