# 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 1 Explanation:
 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 2 Explanation:
 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 3 Explanation:
 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 4 Explanation:
 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 5 Explanation:
 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 6 Explanation:
 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 7 Explanation:
 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 8 Explanation:
 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 9 Explanation:
 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
Question 10 Explanation:
There are 10 questions to complete.