# Computer Science and Information Technology - GATE 2019 Paper Solution

The expenditure on the project _____ as follows: equipment Rs.20 lakhs, salaries Rs.12 lakhs, and contingency Rs.3 lakhs.

The search engine’s business model ___________ around the fulcrum of trust.

Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 km/h and the speed of the second car is 60 km/h. The number of hours it takes for the distance between the two cars to be 20 km is ___.

Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs 150 more. The cost of the gift was Rs. ____.

A court is to a judge as _____________ is to a teacher.

The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:

P says “Q committed the crime.”

Q says “S committed the crime.”

R says “I did not do it.”

S says “What Q said about me is false.”

Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?

In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of the people, the percentage of administrators shall be in the range of ___________. “A recent High Court judgement has sought to dispel the idea of begging as a disease — which leads to its stigmatization and criminalization — and to regard it as a symptom. The underlying disease is the failure of the state to protect citizens who fall through the social security net.”

Which one of the following statements can be inferred from the given passage?

In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is _____.

Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests.

Request by X: Due to pollen allergy, I want to avoid a wing next to the garden.

Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell.

Request by Z: I believe in Vaastu and so want to stay in the South-west wing.

A certain processor uses a fully associative cache of size 16 kB. The cache block size is 16 bytes. Assume that the main memory is byte addressable and uses a 32-bit address. How many bits are required for the Tag and the Index fields respectively in the addresses generated by the processor?

The chip select logic for a certain DRAM chip in a memory system design is shown below. Assume that the memory system has 16 address lines denoted by A15 to A0. What is the range of addresses (in hexadecimal) of the memory system that can get enabled by the chip select (CS) signal? Which one of the following kinds of derivation is used by LR parsers?

In 16-bit 2’s complement representation, the decimal number −28 is:

Let $U=\{1,2,\;...\;,\;n\}.$ Let $A=\{(x,\;X)\;\vert x\in X,\;X\subseteq U\}.$ Consider the following two statements on |A|.

I.  $\vert A\vert=n2^{n-1}$

II. $\vert A\vert={\textstyle\sum_{k=1}^n}k\begin{pmatrix}n\\k\end{pmatrix}$

Which of the above statements is/are TRUE?

Which one of the following is NOT a valid identity?

If $L$ is a regular language over $\mathrm\Sigma=(a,\;b),$ which one of the following languages is NOT regular ?

Consider Z = X – Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of:

Let X be a square matrix. Consider the following two statements on X.

I.           X is invertible.

II.          Determinant of X is non-zero.

Which one of the following is TRUE?

Let $G$ be an arbitrary group. Consider the following relations on $G$:
$R_1:\forall a,\;b\in G,\;a\;R_1b$ if and only if $\exists g\in G$ such that $a=g^{-1}bg$
$R_2:\forall a,\;b\in G,\;a\;R_2b$ if and only if $a=b^{-1}$