Question 1 |
A real square matrix A is called skew-symmetric if
A^{T}=A | |
A^{T}=A^{-1} | |
A^{T}=-A | |
A^{T}=A+A^{-1} |
Question 1 Explanation:
A is skew-symmetric
\therefore \quad A^{T}=-A
\therefore \quad A^{T}=-A
Question 2 |
\lim_{x\rightarrow 0}\frac{log_{e}(1+4x)}{e^{3x}-1} is equal to
0 | |
1/12 | |
4/3 | |
1 |
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}
\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
biharmonic functions | |
harmonic functions | |
conjugate harmonic functions | |
error functions |
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.
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 __________
55.2 | |
88.6 | |
99.8 | |
44.6 |
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
0.682 | |
0.686 | |
0.75 | |
1 |
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.