Recent questions and answers in IIITH-PGEE

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 for...

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...

If $f(x)=\frac{1}{x-5}$ and $g(x)=\sqrt{x+2}$, find the domain of $f(g(x))$.$[-2,\infty)$ $(-2,23)\cup(23,\infty)$ $[-2,23)\cup(23,\infty)$ $[-2,23]\cup(23,\infty)$

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 ch...

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

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...

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 r...

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?$4$ $6$...

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\ma...

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...

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 ...

How many integers between $1$ and $1000$ are divisible by $3$ or $7$?$420$ $428$ $438$ $442$

$\mathrm{R}$ 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 o...

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...

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 ...

Which Relational Algebra operation gives the maximum number of tuples?Selection Projection Cross Product Inner Join

What is the condition for the validity of the SQL set operation $\mathrm{P}-\mathrm{R}$ (Set Difference), if P and R are two database tables?

Table A has $7$ rows, Table B has 5 rows, and they share $3$ rows in common. How many rows will a FULL OUTER JOIN return?

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 $5$...

Given $100$ processes with a $32$-bit virtual address space, a page size of $2$ KB, and each page table entry of $4$ bytes. Find the total size required for all page tabl...

Consider Round Robin Scheduling with Time Quantum $=2 \mathrm{~ms}$. Three processes arrive at time $0: \mathrm{P} 1=4 \mathrm{~ms}, \mathrm{P} 2=5 \mathrm{~ms}, \mathrm{...

Find the rank of the matrix $A$ if $A^{-1}$ exists, where $A=\begin{bmatrix}1&2&a\\2&4&b\\3&c&6\end{bmatrix}$.$0$ $1$ $2$ $3$

Which algorithm detects cycles in an undirected graphTopological Sort Prims Union Find Dijkstras

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

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...

Find the missing number. $25$ $56$ $38$ $9$

Find the sum of eigenvalues of the given $4 \times 4$ matrix.$0$ $1$ $2$ $3$

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...

If the number of elements in the power set of the power set of $N$ is $256$, find the number of elements in $N$.$2$ $3$ $4$ $8$

Find the number of bijective functions from $\{a,b,c,d\}$ to $\{1,2,3,4\}$.$12$ $16$ $24$ $32$

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+\sqr...

$P(A)=0.2$, $P(B)=0.3$, $P(A \cup B)=0.6$. Then A and B are?$A$ and $B$ are mutually exclusive $A$ and $B$ are independent Such probabilities are not possible Both A and ...

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

$P(A)=0.3$, $P(B)=0.2$, $P(A \cup B)=0.5$. Which is true?$A$ and $B$ are mutually exclusive. $A$ and $B$ are independent. Such probabilities are not possible. Both A and ...

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 $4$ ...

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\m...

What was the day on $25$th April $2026$?Monday Friday Saturday Sunday

Let $N = 2^{10} \times 3^{16}$. Find the number of distinct positive factors of $N$.$170$ $176$ $187$ $198$

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

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 ...