# 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:
 Question 6
Which of the following improper integrals is (are) convergent?
 A $\int ^{1} _{0} \frac{\sin x}{1-\cos x}dx$ B $\int ^{\infty} _{0} \frac{\cos x}{1+x} dx$ C $\int ^{\infty} _{0} \frac{x}{1+x^2} dx$ D $\int ^{1} _{0} \frac{1-\cos x}{\frac{x^5}{2}} dx$
Engineering Mathematics   Calculus
Question 6 Explanation:
 Question 7
The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ has
 A no local extremum B one local minimum but no local maximum C one local maximum but no local minimum D one local minimum and one local maximum
Engineering Mathematics   Calculus
Question 7 Explanation:
 Question 8
Assume that each character code consists of 8 bits. The number of characters that can be transmitted per second through an asynchronous serial line at 2400 baud rate, and with two stop bits is
 A 109 B 216 C 218 D 219
Computer Network   Physical Layer
Question 8 Explanation:
 Question 9
Identify the logic function performed by the circuit shown in figure.

 A exclusive OR B exclusive NOR C NAND D NOR E None of the above
Computer Organization   Interrupt
Question 9 Explanation:
 Question 10
Refer to the PASCAL program shown below.
 Program PARAM (input, output);
var m, n : integer;
procedure P (var, x, y : integer);
var m : integer;
begin
m : = 1;
x : = y + 1
end;
procedure Q (x:integer; vary : integer);
begin
x:=y+1;
end;
begin
m:=0; P(m,m); write (m);
n:=0; Q(n*1,n); write (n)
end

The value of m, output by the program PARAM is:
 A 1, because m is a local variable in P B 0, because m is the actual parameter that corresponds to the formal parameter in p C 0, because both x and y are just reference to m, and y has the value 0 D 1, because both x and y are just references to m which gets modified in procedure P E none of the above
C Programming   Function
Question 10 Explanation:
There are 10 questions to complete.