GATE CS question library

Consider two processors $P_1$ and $P_2$ executing the same instruction set. Assume that under identical conditions, for the same input, a program running on $P_2$ takes $\text{25\%}$ less time but incurs $\text{20\%}$ more CPI (clock cycles per instruction) as compared to the program running on $P_1$. If the clock frequency of $P_1$ is …

Given the following schema: employees(emp-id, first-name, last-name, hire-date, dept-id, salary) departments(dept-id, dept-name, manager-id, location-id) You want to display the last names and hire dates of all latest hires in their respective departments in the location $\text{ID 1700.}$ You issue the following query: SQL>SELECT last-name, hire-date …

Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE?

An ordered $n-$tuple $(d_1, d_2,\ldots,d_n)$ with $d_1 \geq d_2 \geq \ldots \geq d_n$ is called graphic if there exists a simple undirected graph with $n$ vertices having degrees $d_1,d_2,\ldots,d_n$ respectively. Which one of the following $6$-tuples is NOT graphic?

Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.

Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $\log_2 \log_2N$ is _______.

A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. The set of all possible $1-$pennants is ${(1)}$, the set of all possible $2-$pennants is ${(2), (1,1)}$ and the set of all $3-$pennants is ${(2,1), (1,1,1), (1,2)}$. …

Four fair six-sided dice are rolled. The probability that the sum of the results being $22$ is $\dfrac{X}{1296}$. The value of $X$ is _______

A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true?

The function $f(x) =x \sin x$ satisfies the following equation: $$f''(x) + f(x) +t \cos x = 0$$The value of $t$ is______.

Consider the $4\text{-to-1}$ multiplexer with two select lines $S_1$ and $S_0$ given below The minimal sum-of-products form of the Boolean expression for the output $F$ of the multiplexer is

An access sequence of cache block addresses is of length $N$ and contains n unique block addresses. The number of unique block addresses between two consecutive accesses to the same block address is bounded above by $k$. What is the miss ratio if the access sequence is passed through a cache of associativity $A\geq k$ exercising least-recently-used …

Consider a $6$-stage instruction pipeline, where all stages are perfectly balanced. Assume that there is no cycle-time overhead of pipelining. When an application is executing on this $6$-stage pipeline, the speedup achieved with respect to non-pipelined execution if $25$% of the instructions incur $2$ pipeline stall cycles is ____________

Consider the following pseudo code. What is the total number of multiplications to be performed? D = 2 for i = 1 to n do for j = i to n do for k = j + 1 to n do D = D * 3

Consider the following C function in which size is the number of elements in the array E: int MyX(int *E, unsigned int size) { int Y = 0; int Z; int i, j, k; for(i = 0; i< size; i++) Y = Y + E[i]; for(i=0; i < size; i++) for(j = i; j < size; j++) { Z = 0; for(k = i; k <= j; k++) Z = Z + E[k]; if(Z > Y) Y = Z; } return Y; } The value returned …

The minimum number of comparisons required to find the minimum and the maximum of $100$ numbers is ________

Consider a hash table with $9$ slots. The hash function is $h(k)= k \mod 9$. The collisions are resolved by chaining. The following $9$ keys are inserted in the order: $5, 28, 19, 15, 20, 33, 12, 17, 10$. The maximum, minimum, and average chain lengths in the hash table, respectively, are

Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. In this scenario, which one of the following represents the correct Venn diagram of the complexity classes P, NP and NP Complete (NPC)?

There are $5$ bags labeled $1$ to $5$. All the coins in a given bag have the same weight. Some bags have coins of weight $10$ gm, others have coins of weight $11$ gm. I pick $1, 2, 4, 8, 16$ coins respectively from bags $1$ to $5$ Their total weight comes out to $323$ gm. Then the product of the labels of the bags having $11$ gm coins is …

Which of the regular expressions given below represent the following DFA? $0^*1(1+00^*1)^*$ $0^*1^*1+11^*0^*1$ $(0+1)^*1$