List of top Questions asked in GATE CS

A series of natural numbers $F_1, F_2, F_3, F_4, F_5, F_6, F_7, \ldots$ obeys \[ F_{n+1} = F_n + F_{n-1}, \text{for all integers } n \geq 2. \] If $F_6 = 37$ and $F_7 = 60$, then what is $F_1$?

A survey for a certain year found that 90% of pregnant women received medical care at least once before giving birth. Of these women, 60% received medical care from doctors, while 40% received medical care from other healthcare providers. Given this information, which one of the following statements can be inferred with certainty?

Looking at the surface of a smooth 3-dimensional object from the outside, which one of the following options is TRUE?

We reached the station late, and ________ missed the train.}

Which of the following sequences when stored in an array at locations A[1],..., A[10] forms a max-heap?

The Lucas sequence L_n is defined by the recurrence relation: L_n = L_n−1 + L_n−2, for n ≥ 3, with L₁ = 1 and L₂ = 3. Which one of the options given is TRUE?

The _________ is too high for it to be considered _________.

A function $ y(x) $ is defined in the interval [0, 1] on the x-axis as
\[ y(x) = \begin{cases} 2 & \text{if } 0 \leq x<\frac{1}{3} \\ 3 & \text{if } \frac{1}{3} \leq x<\frac{3}{4} \\ 1 & \text{if } \frac{3}{4} \leq x \leq 1 \end{cases} \] Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?

Let $r$ be a root of the equation $x^2 + 2x + 6 = 0$. Then the value of the expression $(r+2)(r+3)(r+4)(r+5)$ is

Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.
\[ \boxed{A} \qquad \boxed{D} \] From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome? The player should use all the five plates exactly once. The plates can be rotated in their plane.

Some people believe that “what gets measured, improves”. Some others believe that “what gets measured, gets gamed”. One possible reason for the difference in the beliefs is the work culture in organizations. In organizations with good work culture, metrics help improve outcomes. However, the same metrics are counterproductive in organizations with poor work culture. Which one of the following is the CORRECT logical inference based on the information in the above passage?

In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of the qualified candidates.
Which one of the following is the correct logical inference based on the information provided in the above passage?

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball. First ball is drawn. What is the probability of getting an orange ball in the next draw?

The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T, and U, but not necessarily in the same order. Consider the following statements:

The line joining P and R is parallel to the line joining Q and S.
P is placed on the side opposite to the corner T.
S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above information?

A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and R2, are already present and cannot be moved.
What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.

Which one of the following statements is TRUE for all positive functions $ f(n) $?

Which one of the following regular expressions correctly represents the language of the finite automaton given below?

Which one of the following statements is TRUE?

In a relational data model, which one of the following statements is TRUE?

Consider the problem of reversing a singly linked list. To take an example, given the linked list below,

The reversed linked list should look like

Which one of the following statements is TRUE about the time complexity of algorithms that solve the above problem in $ O(1) $ space?

Suppose we are given $n$ keys, $m$ hash table slots, and two simple uniform hash functions $h_1$ and $h_2$. Further suppose our hashing scheme uses $h_1$ for the odd keys and $h_2$ for the even keys. What is the expected number of keys in a slot?

Which one of the following facilitates transfer of bulk data from hard disk to main memory with the highest throughput?

Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?

Consider the following threads, T1, T2, and T3 executing on a single processor, synchronized using three binary semaphore variables, S1, S2, and S3, operated upon using standard wait() and signal(). The threads can be context switched in any order and at any time.