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 1 Explanation:
 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 2 Explanation:

 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 3 Explanation:
 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 4 Explanation:
 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
Question 5 Explanation:

There are 5 questions to complete.