GATE CSE 1994

Question 1
FORTRAN implementation do not permit recursion because
A
they use static allocation for variables
B
they use dynamic allocation for variables
C
stacks are not available on all machines
D
it is not possible to implement recursion on all machines
   
Question 2
Let A and B be real symmetric matrices of size n \times n. Then which one of the following is true?
A
AA'=I
B
A=A^{-1}
C
AB=BA
D
(AB)'=BA
Engineering Mathematics   Linear Algebra
Question 3
Backward Euler method for solving the differential equation \frac{dy}{dx}=f(x, y) is specified by, (choose one of the following).
A
y_{n+1}=y_n+hf(x_n, y_n)
B
y_{n+1}=y_n+hf(x_{n+1}, y_{n+1})
C
y_{n+1}=y_{n-1}+2hf(x_n, y_n)
D
y_{n+1}= (1+h)f(x_{n+1}, y_{n+1})
Engineering Mathematics   Calculus
Question 4
Let A and B be any two arbitrary events, then, which one of the following is TRUE?
A
P (A \cap B) = P(A)P(B)
B
P (A \cup B) = P(A)+P(B)
C
P (A \mid B) = P(A \cap B)P(B)
D
P (A \cup B) \leq P(A) + P(B)
Discrete Mathematics   Probability Theory
Question 5
An unrestricted use of the "goto" statement is harmful because
A
it makes it more difficult to verify programs
B
it increases the running time of the programs
C
it increases the memory required for the programs
D
it results in the compiler generating longer machine code
C Programming   Conditional Statement
Question 6
The number of distinct simple graphs with up to three nodes is
A
15
B
10
C
7
D
9
Discrete Mathematics   Graph Theory
Question 7
The recurrence relation that arises in relation with the complexity of binary search is:
A
T(n) = 2T\left(\frac{n}{2}\right)+k, \text{ k is a constant }
B
T(n) = T\left(\frac{n}{2}\right)+k, \text{ k is a constant }
C
T(n) = T\left(\frac{n}{2}\right)+\log n
D
T(n) = T\left(\frac{n}{2}\right)+n
Algorithm   Recurrence Relation
Question 8
The logic expression for the output of the circuit shown in figure below is:

A
\overline{AC} + \overline{BC} +CD
B
\overline{A}C + \overline{B}C + CD
C
ABC +\overline {C}\; \overline{D}
D
\overline{A}\; \overline{B} + \overline{B}\; \overline{C} +CD
Digital Logic   Boolean Algebra
Question 9
The rank of matrix \begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}is:
A
0
B
1
C
2
D
3
Engineering Mathematics   Linear Algebra
Question 10
Some group (G, o) is known to be abelian. Then, which one of the following is true for G?
A
g=g^{-1} \text{ for every } g \in G
B
g=g^2 \text{ for every }g \in G
C
(goh)^2 = g^2oh^2 \text{ for every } g, h \in G
D
G is of finite order
Discrete Mathematics   Group Theory
There are 10 questions to complete.

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