GATE CS question library

In a survey, $300$ respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter? …

Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy. On which of the following assumptions does the statement above rely? Select one:

Round-trip tickets to a tourist destination are eligible for a discount of $10\%$ on the total fare. In addition, groups of $4$ or more get a discount of $5\%$ on the total fare. If the one way single person fare is $Rs$ $100$, a group of $5$ tourists purchasing round-trip tickets will be charged $Rs$ __________

The Palghat Gap (or Palakkad Gap) , a region about $30\;\text{km}$ wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the …

If $\large\left(z + \dfrac{1}{z}\right)^{2}= 98$, compute $\large \left(z^{2} +\dfrac{1}{z^{2}}\right)$.

In a press meet on the recent scam, the minister said, "The buck stops here". What did the minister convey by the statement?

Choose the most appropriate word from the options given below to complete the following sentence. She could not understand the judges awarding her the first prize, because she thought that her performance was quite _________.

The roots of $ax^{2}+bx+c = 0$ are real and positive. $a, b$ and $c$ are real. Then $ax^{2}+b\mid x \mid + c =0$ has

Consider the statement "Not all that glitters is gold” Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ is gold. Which one of the following logical formulae represents the above statement?

Which of the following options is the closest in meaning to the phrase in bold in the sentence below? It is fascinating to see life forms cope with varied environmental conditions.

Consider the main memory system that consists of $8$ memory modules attached to the system bus, which is one word wide. When a write request is made, the bus is occupied for $100$ nanoseconds (ns) by the data, address, and control signals. During the same $100$ ns, and for $500$ ns thereafter, the addressed memory module executes one cycle accepting …

SQL allows duplicate tuples in relations, and correspondingly defines the multiplicity of tuples in the result of joins. Which one of the following queries always gives the same answer as the nested query shown below: select * from R where a in (select S.a from S)

Which one of the following Boolean expressions is NOT a tautology?

The number of distinct minimum spanning trees for the weighted graph below is _____

A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.

Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the following two statements: $S1$: There is a subset of $S$ that is larger than every other …

The number of distinct positive integral factors of $2014$ is _____________

The probability that a given positive integer lying between $1$ and $100$ (both inclusive) is NOT divisible by $2$, $3$ or $5$ is ______ .

The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$

In the Newton-Raphson method, an initial guess of $x_0= 2$ is made and the sequence $x_0,x_1,x_2\:\dots$ is obtained for the function $$0.75x^3-2x^2-2x+4=0$$ Consider the statements $x_3\:=\:0$ The method converges to a solution in a finite number of iterations. Which of the following is TRUE?