GATE CS question library

Match the following: …

If $g(x) = 1 - x$ and $h(x) = \frac{x}{x-1}$, then $\frac{g(h(x))}{h(g(x))}$ is:

$\displaystyle \lim_{x\rightarrow \infty } x^{ \tfrac{1}{x}}$ is

For any two languages $L_{1}$ and $L_{2}$ such that $L_{1}$ is context-free and $L_{2}$ is recursively enumerable but not recursive, which of the following is/are necessarily true? $\bar{L}_{1}$ ( Complement of $L_{1}$) is recursive $\bar{L}_{2}$ ( Complement of $L_{2}$) is recursive $\bar{L}_{1}$ is context-free $\bar{L}_{1}$ ∪ $L_{2}$ …

Which one of the following is the recurrence equation for the worst case time complexity of the quick sort algorithm for sorting $n\;( \geq 2)$ numbers? In the recurrence equations given in the options below, $c$ is a constant.

Match the following: (P) Condition Coverage (i) Black-box testing (Q) Equivalence class partitioning (ii) System testing (R) Volume testing (iii) White-box testing (S) Alpha testing (iv) Performance testing

The probabilities that a student passes in mathematics, physics and chemistry are $m,p$ and $c$ respectively. Of these subjects, the student has $75\%$ chance of passing in at least one, a $50\%$ chance of passing in at least two and a $40\%$ chance of passing in exactly two. Following relations are drawn in $m, p, c$: $p + m + c = 27/20$ …

The pie chart below has the breakup of the number of students from different departments in an engineering college for the year $2012$. The proportion of male to female students in each department is $5:4$. There are $40$ males in Electrical Engineering. What is the difference between the numbers of female students in the civil department and the …

The given statement is followed by some courses of action. Assuming the statement to be true, decide the correct option. Statement: There has been a significant drop in the water level in the lakes supplying water to the city. Course of action: The water supply authority should impose a partial cut in supply to tackle the situation. The government should …

Select the alternative meaning of the underlined part of the sentence. The chain snatchers $\underline{\text{took to their heels}}$ when the police party arrived.

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking. …

Which one of the following combinations is incorrect?

Based on the given statements, select the most appropriate option to solve the given question. If two floors in a certain building are $9$ feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building? Statements: Each step is $3/4$ foot high. Each step is $1$ foot wide.

Given Set $A= {2, 3, 4, 5}$ and Set $B= { 11, 12, 13, 14, 15}$, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals $16$?

Which of the following options is the closest in meaning of the sentence below? She enjoyed herself immensely at the party.

Didn't you buy ____ when you went shopping?

Which one of the following well-formed formulae is a tautology?

Let $X$ and $Y$ denote the sets containing $2$ and $20$ distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being one-to-one is ______.

The number of states in the minimal deterministic finite automaton corresponding to the regular expression $(0+1)^* (10)$ is _____.

$\text{Host A}$ sends a $\text{UDP}$ datagram containing $8880\text{ bytes}$ of user data to $\text{host B}$ over an $\text{Ethernet LAN}.$ Ethernet frames may carry data up to $1500\text{ bytes (i.e. MTU = 1500 bytes)}.$ Size of $\text{UDP}$ header is $8\text{ bytes}$ and size of $\text{IP}$ header is $20\text{ bytes}.$ There is no …