Question 1 |
For the below question, one or more OPTIONS are correct
The eigen vector(s) of the matrix
\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0
is (are)
The eigen vector(s) of the matrix
\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0
is (are)
(0,0,\alpha) | |
(\alpha,0,0) | |
(0,0,1) | |
(0,\alpha,0) |
Question 1 Explanation:
Question 2 |
The differential equation
\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0 is:
\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0 is:
linear | |
non- linear | |
homogeneous | |
of degree two |
Question 2 Explanation:
Question 3 |
Simpson's rule for integration gives exact result when f(x) is a polynomial of degree
1 | |
2 | |
3 | |
4 |
Question 3 Explanation:
Question 4 |
Which of the following is (are) valid FORTRAN 77 statement(s)?
DO 13 I = 1 | |
A = DIM ***7 | |
READ = 15.0 | |
GO TO 3 = 10 |
Question 4 Explanation:
Question 5 |
Fourier series of the periodic function (period 2 \pi ) defined by
f(x) = \begin{cases} 0, -p \lt x \lt 0\\x, 0 \lt x \lt p \end{cases} \text { is }\\ \frac{\pi}{4} + \Sigma \left [ \frac{1}{\pi n^2} \left(\cos n\pi - 1 \right) \cos nx - \frac{1}{n} \cos n\pi \sin nx \right ]
But putting x = \pi, we get the sum of the series
1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \cdots \text { is }
f(x) = \begin{cases} 0, -p \lt x \lt 0\\x, 0 \lt x \lt p \end{cases} \text { is }\\ \frac{\pi}{4} + \Sigma \left [ \frac{1}{\pi n^2} \left(\cos n\pi - 1 \right) \cos nx - \frac{1}{n} \cos n\pi \sin nx \right ]
But putting x = \pi, we get the sum of the series
1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \cdots \text { is }
\frac{{\pi }^2 }{4} | |
\frac{{\pi }^2 }{6} | |
\frac{{\pi }^2 }{8} | |
\frac{{\pi }^2 }{12} |
Question 5 Explanation:
There are 5 questions to complete.