GATE CSE 1993


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)
A
(0,0,\alpha)
B
(\alpha,0,0)
C
(0,0,1)
D
(0,\alpha,0)
Engineering Mathematics   Linear Algebra
Question 2
The differential equation
\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0 is:
A
linear
B
non- linear
C
homogeneous
D
of degree two
Engineering Mathematics   Calculus


Question 3
Simpson's rule for integration gives exact result when f(x) is a polynomial of degree
A
1
B
2
C
3
D
4
Engineering Mathematics   Numerical Method
Question 4
Which of the following is (are) valid FORTRAN 77 statement(s)?
A
DO 13 I = 1
B
A = DIM ***7
C
READ = 15.0
D
GO TO 3 = 10
   
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 }
A
\frac{{\pi }^2 }{4}
B
\frac{{\pi }^2 }{6}
C
\frac{{\pi }^2 }{8}
D
\frac{{\pi }^2 }{12}
Engineering Mathematics   


There are 5 questions to complete.

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