GATE CSE 1997

The probability that it will rain today is 0.5. The probability that it will rain tomorrow is 0.6. The probability that it will rain either today or tomorrow is 0.7. What is the probability that it will rain today and tomorrow?

The Newton-Raphson method is used to find the root of the equation X^2-2=0. If the iterations are started from -1, the iterations will

The determinant of the matrix \begin{bmatrix} 6 & -8 & 1 & 1 \\ 0 & 2 & 4 & 6 \\ 0 & 0 & 4 & 8 \\ 0 & 0 & 0 & -1 \end{bmatrix}

The concatenation of two lists is to be performed on O(1) time. Which of the following implementations of a list should be used?

The correct matching for the following pairs is
\begin{array}{ll|ll}\hline \text{A.} & \text{All pairs shortest path} & \text{1.} & \text{Greedy} \\\hline \text{B.} & \text{Quick Sort} & \text{2.}& \text{Depth-First Search} \\\hline \text{C.}& \text{Minimum weight spanning tree} & \text{3.} & \text{Dynamic Programming} \\\hline \text{D.} & \text{Connected Components} &\text{4.} & \text{Divide and Conquer} \\\hline \end{array}

In the following grammar
\begin{aligned} X &::= X \oplus Y \mid Y \\ Y&::= Z * Y \mid Z\\ Z&::= id \end{aligned}
Which of the following is true?

Which of the following is essential for converting an infix expression to the postfix form efficiently?

A language L allows declaration of arrays whose sizes are not known during compilation. It is required to make efficient use of memory. Which one of the following is true?

The conditional expansion facility of macro processor is provided to

Heap allocation is required for languages.