Recent activity in IIITH-PGEE

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...

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

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...

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...

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{...

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

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

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...

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

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...

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

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