GATE CS question library

The matrices $\begin{bmatrix} \cos\theta && -\sin\theta \\ \sin\theta && \cos\theta \end{bmatrix}$ and $\begin{bmatrix} a && 0\\ 0&& b \end{bmatrix}$ commute under multiplication

Which one of the following is false?

Which of the following is NOT True? (Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication)

Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement)

Consider the following floating-point number representation. $$\overset{31 \quad \qquad 24 \quad 23 \qquad\quad 0} {\begin{array}{|l|l|}\hline \text{Exponent} & \text{Mantissa} \\ \hline \end{array}}$$ The exponent is in $2’s$ complement representation and the mantissa is in the sign-magnitude representation. The range of the magnitude of the …

Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is given by

For the daisy chain scheme of connecting I/O devices, which of the following statements is true?

Booth’s algorithm for integer multiplication gives worst performance when the multiplier pattern is

A ROM is used to store the table for multiplication of two $8$-bit unsigned integers. The size of ROM required is

Which of the following is an example of spooled device?

A critical section is a program segment

The process state transition diagram in the below figure is representative of

The pass numbers for each of the following activities object code generation literals added to literal table listing printed address resolution of local symbols that occur in a two pass assembler respectively are

Relative mode of addressing is most relevant to writing:

Which of the following sequences denotes the post order traversal sequence of the below tree?

In the balanced binary tree in the below figure, how many nodes will become unbalanced when a node is inserted as a child of the node “g”?

An advantage of chained hash table (external hashing) over the open addressing scheme is

Consider the following statements: First-in-first out types of computations are efficiently supported by STACKS. Implementing LISTS on linked lists is more efficient than implementing LISTS on an array for almost all the basic LIST operations. Implementing QUEUES on a circular array is more efficient than implementing QUEUES on a linear array with two …

Which of the following statements is false?

Let $L \subseteq \Sigma^*$ where $\Sigma = \left\{a,b \right\}$. Which of the following is true?