GATE CS question library

In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift $Rs\; 750$ to each male senior citizen in the town and $Rs\; 1000$ to each female senior citizen. Altogether, there were 300 senior citizens eligible for this gift. However, only $\dfrac{8}{9}^{\text{th}}$ of the eligible men and …

The area of a square is $d$. What is the area of the circle which has the diagonal of the square as its diameter?

What would be the smallest natural number which when divided either by $20$ or by $42$ or by $76$ leaves a remainder of $7$ in each case?

A ________ investigation can sometimes yield new facts, but typically organized ones are more successful. The word that best fills the blank in the above sentence is

"From where are they bringing their books? _______ bringing _______ books from ________" The words that best fill the blanks in the above sentence are

A cache memory unit with capacity of $N$ words and block size of $B$ words is to be designed. If it is designed as a direct mapped cache, the length of the $\textsf{TAG}$ field is $10$ bits. If the cache unit is now designed as a $16$-way set-associative cache, the length of the $\textsf{TAG}$ field is ____________ bits.

Consider the expression $(a-1) * (((b+c)/3)+d)$. Let $X$ be the minimum number of registers required by an optimal code generation (without any register spill) algorithm for a load/store architecture, in which only load and store instructions can have memory operands and arithmetic instructions can have only register or immediate operands. ​​​​​​​The …

Consider a $2$-way set associative cache with $256$ blocks and uses $\text{LRU}$ replacement. Initially the cache is empty. Conflict misses are those misses which occur due to the contention of multiple blocks for the same cache set. Compulsory misses occur due to first time access to the block. The following sequence of access to memory blocks : …

Consider the C code fragment given below. typedef struct node { int data; node* next; } node; void join(node* m, node* n) { node* p = n; while(p->next != NULL) { p = p->next; } p->next = m; } Assuming that m and n point to valid NULL-terminated linked lists, invocation of join will

Instruction execution in a processor is divided into $5$ stages, Instruction Fetch (IF), Instruction Decode (ID), Operand fetch (OF), Execute (EX), and Write Back (WB). These stages take 5, 4, 20, 10 and 3 nanoseconds (ns) respectively. A pipelined implementation of the processor requires buffering between each pair of consecutive stages with a delay of 2 …

Consider the following table: …

Consider the following functions from positive integers to real numbers: $10$, $\sqrt{n}$, $n$, $\log_{2}n$, $\frac{100}{n}$. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:

Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$

The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$

The output of executing the following C program is _______________ . #include<stdio.h> int total(int v) { static int count = 0; while(v) { count += v&1; v >>= 1; } return count; } void main() { static int x=0; int i=5; for(; i>0; i--) { x = x + total(i); } printf("%d\n", x); }

Consider the following C program. #include<stdio.h> #include<string.h> void printlength(char *s, char *t) { unsigned int c=0; int len = ((strlen(s) - strlen(t)) > c) ? strlen(s) : strlen(t); printf("%d\n", len); } void main() { char *x = "abc"; char *y = "defgh"; printlength(x,y); } Recall that $strlen$ is defined in $string.h$ as …

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at $25$ m intervals in this plot. If in a flood, the water level rises to $525$ m, which of the villages $P, Q, R, S, T$ get submerged?

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes?

The expression $\large \frac{(x+y) - |x-y|}{2}$ is equal to :

"The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history." Which of the following statements best reflects the author's opinion?