GATE CS question library

Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$

Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$

Find the minimum value of $3-4x+2x^2$.

How many minimum spanning trees does the following graph have? Draw them. (Weights are assigned to edges).

Determine the number of divisors of $600.$

A computer system has a $4 \ K$ word cache organized in block-set-associative manner with $4$ blocks per set, $64$ words per block. The number of bits in the SET and WORD fields of the main memory address format is:

Let $\Sigma=\left\{0,1\right\}, L = \Sigma^*$ and $R=\left\{0^n1^n \mid n > 0\right\}$ then the languages $L \cup R$ and $R$ are respectively

A finite state machine with the following state table has a single input $x$ and a single out $z$. …

Which of the following statements is true? As the number of entries in a hash table increases, the number of collisions increases. Recursive programs are efficient The worst case complexity for Quicksort is $O(n^2)$ Binary search using a linear linked list is efficient

The postfix expression for the infix expression $A+B*(C+D)/F+D*E$ is:

Which of the following definitions below generate the same language as $L$, where $L=\{x^ny^n \text{ such that } n\geq 1 \}$? $E \rightarrow xEy\mid xy$ $x y \mid (x^+xyy^+$) $x^+y^+$

If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is

The solution of differential equation $y''+3y'+2y=0$ is of the form

Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then

In a virtual memory system the address space specified by the address lines of the CPU must be _____ than the physical memory size and ____ than the secondary storage size.

A bag contains $10$ white balls and $15$ black balls. Two balls are drawn in succession. The probability that one of them is black and the other is white is:

A unit vector perpendicular to both the vectors $a=2i-3j+k$ and $b=i+j-2k$ is:

The number of $1$'s in the binary representation of $(3\ast4096 + 15\ast256 + 5\ast16 + 3)$ are:

A shift reduce parser carries out the actions specified within braces immediately after reducing with the corresponding rule of grammar $S \rightarrow xxW \;\text{{print“1"}}$ $S \rightarrow y \;\text{{print“2"}}$ $W \rightarrow Sz\; \text{{print“3"}}$ What is the translation of $xxxxyzz$ using the syntax directed translation scheme described by the …

If the cube roots of unity are $1, \omega$ and $\omega^2$, then the roots of the following equation are $$(x-1)^3 +8 =0$$