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   
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 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 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 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 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
There are 10 questions to complete.

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