List of top Software Engineering Questions asked in GATE CS

Consider the following two regular expressions over the alphabet \(\{0,1\}\): \[ r = 0^* + 1^* \quad \text{and} \quad s = 01^* + 10^*. \] The total number of strings of length less than or equal to 5, which are neither in \( r \) nor in \( s \), is \_\_\_\_\_\_.
Consider a memory management system that uses a page size of 2 KB. Assume that both the physical and virtual addresses start from 0. Assume that the pages 0, 1, 2, and 3 are stored in the page frames 1, 3, 2, and 0, respectively. The physical address (in decimal format) corresponding to the virtual address 2500 (in decimal format) is \_\_\_\_\_.
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let \( G \) be any graph with \( n \) vertices and chromatic number \( k \). Which of the following statements is/are always TRUE?
Consider the operators \( \diamondsuit \) and \( \square \) defined by \( a \diamondsuit b = a + 2b \) and \( a \square b = ab \), for positive integers. Which of the following statements is/are TRUE?
Consider two set-associative cache memory architectures: \( WBC \), which uses the write-back policy, and \( WTC \), which uses the write-through policy. Both of them use the LRU (Least Recently Used) block replacement policy. The cache memory is connected to the main memory. Which of the following statements is/are TRUE?