GATE Overflow for GATE CSE - Recent questions in IIITH-PGEE

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 1

Fri, 08 May 2026 08:08:00 +0000

$x = \sqrt{12 + \sqrt{12 + \sqrt{12 + \cdots}}}$. Find $x$.

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 2

Fri, 08 May 2026 08:07:59 +0000

$3$ positive numbers are in AP whose sum is $21$. When $2$ is added to the smallest number, $3$ is added to the middle number, and $9$ is added to the largest number, the resulting numbers form a GP. Find the smallest and middle numbers.

$3$ and $7$
$4$ and $7$
$3$ and $9$
$5$ and $7$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 3

Fri, 08 May 2026 08:07:57 +0000

If $A$, $B$ and $C$ complete a work individually in $12$, $16$, and $24$ days and if $A$ leaves after $2$ days how many more days will be required to complete the entire work by $B$ and $C$?

$4$ days
$5$ days
$6$ days
$8$ days

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 4

Fri, 08 May 2026 08:07:56 +0000

A person has to deliver a box to a remote location. He travels $8\mathrm{km}$ north, then turns $60^\circ$ to the right and travels another $7\mathrm{km}$, where he stops and drops the box. What is the distance and direction he must travel to return to the starting point?

$13\mathrm{km}$, South-West
$13\mathrm{km}$, North-East
$15\mathrm{km}$, South-West
$15\mathrm{km}$, North-West

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 5

Fri, 08 May 2026 08:07:55 +0000

$\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F}, \mathrm{G}$ are seated around a circular table with given constraints. Find the position of a specific person.

$\mathrm{A}$
$\mathrm{B}$
$\mathrm{C}$
$\mathrm{D}$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 6

Fri, 08 May 2026 08:07:54 +0000

$\mathrm{R}$ and $\mathrm{S}$ run a $400\mathrm{m}$ race. $\mathrm{R}$ runs at $10\mathrm{m/s}$ and $\mathrm{S}$ runs at $8\mathrm{m/s}$. $\mathrm{S}$ gets a head start of $60\mathrm{m}$, so $\mathrm{S}$ runs only $340\mathrm{m}$. Who wins and by how much time?

$\mathrm{R}$ wins by $2.5\mathrm{s}$
$\mathrm{S}$ wins by $2.5\mathrm{s}$
$\mathrm{R}$ wins by $1.5\mathrm{s}$
$\mathrm{S}$ wins by $1.5\mathrm{s}$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 7

Fri, 08 May 2026 08:07:53 +0000

How many integers between $1$ and $1000$ are divisible by $3$ or $7$?

$420$
$428$
$438$
$442$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 8

Fri, 08 May 2026 08:07:51 +0000

Consider the sequence formed by writing natural numbers starting from $1$ with the following rules:

Replace every multiple of $3$ with dhoni,
Replace every multiple of $5$ with kohli,
Replace every multiple of both $3$ and $5$ with dhoni-kohli.
Only actual numbers are counted; dhoni, kohli, and dhoni kohli are not counted as numbers.

Example sequence (first few terms)
$1$, $2$, dhoni, $4$, kohli, dhoni, $7$, $8$, dhoni, kohli, $11$, dhoni, $13$, $14$, dhoni-kohli, $16$, ...

What is the $100$th actual number in this filtered sequence?

$181$
$184$
$187$
$190$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 9

Fri, 08 May 2026 08:07:50 +0000

Let $N = 2^{10} \times 3^{16}$. Find the number of distinct positive factors of $N$.

$170$
$176$
$187$
$198$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 10

Fri, 08 May 2026 08:07:49 +0000

What was the day on $25$th April $2026$?

Monday
Friday
Saturday
Sunday

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 11

Fri, 08 May 2026 08:07:48 +0000

An electricity bill is calculated for $2$ months. In January, $350$ units are consumed, and in February, $80$ units are consumed. The rates are: first $100$ units at $4$ per unit, units from $101$ to $300$ at $6$ per unit, and units above $300$ at $9$ per unit. The fixed meter charge is $50$ per month. A government tax of $10\%$ is charged on the overall cost. Find the total bill.

$2617$
$2670$
$2717$
$2770$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 12

Fri, 08 May 2026 08:07:46 +0000

A train running at $60\mathrm{~km/h}$ crosses a stationary pole in $30\mathrm{s}$. What is the length of the train?

$300 \mathrm{m}$
$400\mathrm{m}$
$500\mathrm{m}$
$600\mathrm{m}$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 13

Fri, 08 May 2026 08:07:45 +0000

Four students, Aditi, Karan, Neha, and Rohan, make the following statements. Exactly one person copied the assignment and exactly one person lied.

Aditi: Karan copied the assignment.
Karan: Rohan did not copy the assignment.
Neha: Aditi is telling the truth.
Rohan: Neha is telling a lie.

Which person cheated?

Aditi
Karan
Neha
Rohan

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 14

Fri, 08 May 2026 08:07:44 +0000

A solid cylinder has a height of $15\mathrm{cm}$ and a diameter of $10\mathrm{cm}$. From the top of the cylinder, a conical cavity of the same base diameter and height $6\mathrm{cm}$ is removed. At the bottom of the cylinder, a hemisphere of the same diameter is attached. Find the total volume of the resulting solid.

$\frac{1125\pi}{3}\mathrm{cm}^3$
$\frac{1175\pi}{3}\mathrm{cm}^3$
$\frac{1225\pi}{3}\mathrm{cm}^3$
$\frac{1275\pi}{3}\mathrm{cm}^3$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 15

Fri, 08 May 2026 08:07:43 +0000

Two circles intersect at points $\mathrm{A}$ and $\mathrm{B}$. The length of the common chord $\mathrm{AB}$ is $16\mathrm{cm}$. The distance between the centres is $21\mathrm{cm}$. If the radius of the larger circle is $17\mathrm{cm}$, find the radius of the smaller circle.

$8\mathrm{cm}$
$10\mathrm{cm}$
$12\mathrm{cm}$
$15\mathrm{cm}$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 16

Fri, 08 May 2026 08:07:42 +0000

A $3 \times 3 \times 3$ cube has its top and bottom faces painted red, and the remaining faces painted blue. How many unit cubes are painted only blue and not red?

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 17

Fri, 08 May 2026 08:07:41 +0000

Find the missing number.

$25$
$56$
$38$
$9$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 18

Fri, 08 May 2026 08:07:39 +0000

Given rectangle $A B C D$. $P$ is the middle point of $AB$, $Q$ divides $BC$ in the ratio $1:3$ and $R$ divides $AD$ in the ratio $3:1$. What is the ratio of the shaded region.

$\frac{\mathbf{1}}{\mathbf{4}}$
$\frac{\mathbf{1}}{\mathbf{2}}$
$\frac{\mathbf{3}}{\mathbf{4}}$
$\frac{\mathbf{2}}{\mathbf{3}}$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 19

Fri, 08 May 2026 08:07:37 +0000

River Crossing Problem: Three men and three tigers need to cross a river from the left bank to the right bank using a boat. The boat can carry at most $2$ passengers at a time and needs at least $1$ person to navigate it. If tigers outnumber men on either bank at any point, the tigers will kill the men. What is the minimum number of boat trips required to transport everyone safely to the other side?

$9$
$10$
$11$
$12$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 20

Fri, 08 May 2026 08:07:37 +0000

Compare $2^{2^x}$, $e^{e^x}$, $e^{e^{\log x}}$, and $100000^x$. Which grows fastest?

$2^{2^x}$
$e^{e^x}$
$e^{e^{\log x}}$
$100000^x$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 21

Fri, 08 May 2026 08:07:36 +0000

Bar Graph (Data Interpretation) two questions.

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 22

Fri, 08 May 2026 08:07:36 +0000

Reading Comprehension two passages (4 questions each)

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 23

Fri, 08 May 2026 08:07:35 +0000

Differentiate $f(x)=\sin x + e^x$.

$\cos x + e^x$
$-\cos x + e^x$
$\sin x + e^x$
$\cos x - e^x$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 24

Fri, 08 May 2026 08:07:34 +0000

$P(A)=0.3$, $P(B)=0.2$, $P(A \cup B)=0.5$. Which is true?

$A$ and $B$ are mutually exclusive.
$A$ and $B$ are independent.
Such probabilities are not possible.
Both A and B.

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 25

Fri, 08 May 2026 08:07:33 +0000

$P(A)=0.2$, $P(B)=0.3$, $P(A \cup B)=0.6$. Then A and B are?

$A$ and $B$ are mutually exclusive
$A$ and $B$ are independent
Such probabilities are not possible
Both A and B

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 26

Fri, 08 May 2026 08:07:32 +0000

$P(A)=0.5$ and $P(B)=0.3$, $P(A \cap B)=?$
(The answer depends on the relationship: Independent or Mutually Exclusive)

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 27

Fri, 08 May 2026 08:07:31 +0000

Find all number of ordered combinations of $3$ positive integers whose sum is $10$, where $(2,2,6)$ and $(6,2,2)$ are considered different combinations.

$28$
$32$
$36$
$45$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 28

Fri, 08 May 2026 08:07:29 +0000

Find the number of permutations of the numbers $\{1,2,3,4,5\}$ that generate $5$-digit numbers such that no two even numbers are adjacent to each other and the number formed is not divisible by $5$.

$48$
$54$
$60$
$72$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 29

Fri, 08 May 2026 08:07:28 +0000

Total $150$ people: $75$ use train, $65$ use bus, $55$ use plane, $45$ use at least $2$, and $15$ use all $3$. How many use at least one?

$120$
$125$
$135$
$145$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 30

Fri, 08 May 2026 08:07:27 +0000

In a box, there are $4$ coins. One coin is biased with probability of head $0.8$, and the other $3$ coins are fair coins with probability of head $0.5$. If one coin is chosen at random, what is the probability of getting a head?

$0.525$
$0.575$
$0.625$
$0.675$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 31

Fri, 08 May 2026 08:07:25 +0000

Three dice are rolled independently. What is the probability that the difference between the highest and lowest values on the dice is exactly $4$?

$\frac{1}{6}$
$\frac{2}{9}$
$\frac{1}{4}$
$\frac{5}{18}$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 32

Fri, 08 May 2026 08:07:24 +0000

If $f(x)=x^2-3x+2$, find $x$ for which $f(f(x))=0$.

$x=0,3,\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}$
$x=1,2,\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}$
$x=0,2,\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}$
$x=0,3,\frac{1+\sqrt{5}}{2},\frac{1-\sqrt{5}}{2}$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 33

Fri, 08 May 2026 08:07:22 +0000

Find the number of bijective functions from $\{a,b,c,d\}$ to $\{1,2,3,4\}$.

$12$
$16$
$24$
$32$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 34

Fri, 08 May 2026 08:07:21 +0000

If the number of elements in the power set of the power set of $N$ is $256$, find the number of elements in $N$.

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 35

Fri, 08 May 2026 08:07:20 +0000

If $f(x)=\frac{1}{x-5}$ and $g(x)=\sqrt{x+2}$, find the domain of $f(g(x))$.

$[-2,\infty)$
$(-2,23)\cup(23,\infty)$
$[-2,23)\cup(23,\infty)$
$[-2,23]\cup(23,\infty)$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 36

Fri, 08 May 2026 08:07:19 +0000

Given $(P \to (Q \land R)) \land (Q \to R)$, what is the conjunctive normal form?

$(\neg P \lor Q)\land(\neg P \lor R)\land(\neg Q \lor R)$
$(P \lor Q)\land(P \lor R)\land(Q \lor R)$
$(\neg P \land Q)\lor(\neg P \land R)\lor(\neg Q \land R)$
$(P \to Q)\land(P \to R)\land(Q \to R)$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 37

Fri, 08 May 2026 08:07:18 +0000

Find the rank of the matrix $A$ if $A^{-1}$ exists, where $A=\begin{bmatrix}1&2&a\\2&4&b\\3&c&6\end{bmatrix}$.

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 38

Fri, 08 May 2026 08:07:17 +0000

Find the sum of eigenvalues of the given $4 \times 4$ matrix.

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 39

Fri, 08 May 2026 08:07:15 +0000

Let $f:\mathbb{R}\to\mathbb{R}$. If $f'(x)=0$ at $x=x^*$, then what can we conclude about $\frac{df}{dx}$?

$f$ is continuous and differentiable at $x^*$
$f$ has a minimum at $x^*$
Both A and B
Nothing can be said

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 40

Fri, 08 May 2026 08:07:14 +0000

If $P$ is of order $2 \times 2$, $Q$ is of order $3 \times 2$, and $R$ is of order $2 \times 1$, which one of the following matrix products is correct?

$Q \times R \times P$
$P \times Q \times R$
$R \times Q \times P$
$Q \times P \times R$

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 41

Fri, 08 May 2026 08:07:13 +0000

What is the minimum number of people required such that the probability of at least $2$ people sharing a birth month is $\geq 50\%$?

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 42

Fri, 08 May 2026 08:07:11 +0000

Which of the following scenarios is most likely to have the mean significantly less than the mode?

Outcomes obtained from rolling a fair die, uniform distribution.
Heights of adults following a normal distribution.
Most people retire at the age of $60$, but a few retire at $40$.
Annual income distribution where most people earn average salaries, but a few individuals earn extremely high incomes, billionaires

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 43

Fri, 08 May 2026 08:07:10 +0000

What is the output of the following program for string: "ABCDE FGHIJ"?

fun(char *a) {
    if(*a && *a != ' '){
        char c = *a;
        fun(a+1);
        putchar(c);
    };
}

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 44

Fri, 08 May 2026 08:07:08 +0000

What is the output of the following program?

main() {
    int i=-1, j=-1, k=1, l=2, m;
    m = i++ && j++ | k++8&1++;
    printf("%d %d %d %d %d", i, J, k, 1, m);
}

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 45

Fri, 08 May 2026 08:07:07 +0000

What is the output of the following program?

int main() {
    static int var = 5;
    printf("%d ", var--);
    if (var) {
        main();
    }
}

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 46

Fri, 08 May 2026 08:07:06 +0000

Which of the data structures supports both insertion of unique elements (no duplicates allowed) and deletion of the minimum element in $\mathrm{O}(\log n)$ time complexity?

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 47

Fri, 08 May 2026 08:07:05 +0000

How many distinct binary trees can be formed using $3$ unlabelled nodes?

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 48

Fri, 08 May 2026 08:07:03 +0000

Given the Post-order and In-order traversals of a binary tree:

Post-order: $\{8,6,7,3,4,2,5,1\}$
In-order: $\{8,6,3,7,2,4,1,5\}$

Construct the binary tree and find the height of the tree (maximum path length from root to leaf).

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 49

Fri, 08 May 2026 08:07:01 +0000

What is the worst-case time complexity of inserting $n^{2}$ elements into an AVL Tree that already contains $n$ elements?

GO Classes | IIITH PGEE 2026 | Memory Based | Question: 50

Fri, 08 May 2026 08:07:00 +0000

Which algorithm detects cycles in an undirected graph

Topological Sort
Prims
Union Find
Dijkstras