GATE CSE 2000


Question 1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is
A
3
B
8
C
9
D
12
Discrete Mathematics   Combination
Question 2
An n \times n array v is defined as follows:
v\left[i,j\right] = i - j for all i, j, i \leq n, 1 \leq j \leq n
The sum of the elements of the array v is
A
0
B
n-1
C
n^2 - 3n +2
D
n^2 \frac{\left(n+1\right)}{2}
Data Structure   Array


Question 3
The determinant of the matrix
\begin{bmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{bmatrix}
A
4
B
0
C
15
D
20
Engineering Mathematics   Linear Algebra
Question 4
Let S and T be languages over \Sigma=\{a.b\} represented by the regular expressions (a+b^*)^* \text{ and } (a+b)^*, respectively. Which of the following is true?
A
S \subset T
B
T \subset S
C
S = T
D
S \cap T = \phi
Theory of Computation   Regular Expression
Question 5
Let L denote the languages generated by the grammar S \to 0S0 \mid 00. Which of the following is TRUE?
A
L = 0^+
B
L is regular but not 0^+
C
L is context free but not regular
D
L is not context free
Theory of Computation   Context Free Language


There are 5 questions to complete.

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