# 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 1 Explanation:
 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 2 Explanation:

 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 3 Explanation:
 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 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
$1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \cdots \text { is }$
 A $\frac{{\pi }^2 }{4}$ B $\frac{{\pi }^2 }{6}$ C $\frac{{\pi }^2 }{8}$ D $\frac{{\pi }^2 }{12}$
Engineering Mathematics
Question 5 Explanation:

There are 5 questions to complete.