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1 vote
0 answers
1
The figure below describes the network of streets in a city where Motabhai sells $\text{pakoras}$ from his cart. The number next to an edge is the time (in minutes) taken to traverse the corresponding street. At present, the cart is required to start at point $s$ and, after visiting each street ... : $s, t, b$ and $f$ are the only odd degree nodes in the figure above. $430$ $440$ $460$ $470$ $480$
asked Feb 11 in Others Lakshman Patel RJIT 176 views
0 votes
1 answer
2
Suppose $X_{1a}, X_{1b},X_{2a},X_{2b},\dots , X_{5a},X_{5b}$ are ten Boolean variables each of which can take the value TRUE or FLASE. Recall the Boolean XOR $X\oplus Y:=(X\wedge \neg Y)\vee (\neg X \wedge Y)$ ... $H$ have? $20$ $30$ $32$ $160$ $1024$
asked Feb 11 in Others Lakshman Patel RJIT 113 views
0 votes
1 answer
3
Let $G$ be an undirected graph. An Eulerian cycle of $G$ is a cycle that traverses each edge of $G$ exactly once. A Hamiltonian cycle of $G$ is a cycle that traverses each vertex of $G$ exactly once. Which of the following must be true? Checking if ... , then it has a Hamiltonian cycle A complete graph always has both an Eulerian cycle and a Hamiltonian cycle All of the other statements are true
asked Feb 11 in Others Lakshman Patel RJIT 88 views
0 votes
2 answers
4
Given the pseudocode below for the function $\textbf{remains()}$, which of the following statements is true about the output, if we pass it a positive integer $n>2$? int remains(int n) { int x = n; for (i=(n-1);i>1;i--) { x = x % i ; } return x; } Output is always $0$ Output is always $1$ Output is $0$ only if $n$ is NOT a prime number Output is $1$ only if $n$ is a prime number None of the above
asked Feb 11 in Others Lakshman Patel RJIT 74 views
0 votes
3 answers
5
Which of the following graphs are bipartite? Only $(1)$ Only $(2)$ Only $(2)$ and $(3)$ None of $(1),(2),(3)$ All of $(1),(2),(3)$
asked Feb 11 in Graph Theory Lakshman Patel RJIT 177 views
4 votes
4 answers
6
Among the following asymptotic expressions, which of these functions grows the slowest (as a function of $n$) asymptotically? $2^{\log n}$ $n^{10}$ $(\sqrt{\log n})^{\log ^{2} n}$ $(\log n)^{\sqrt{\log n}}$ $2^{2^{\sqrt{\log\log n}}}$
asked Feb 11 in Algorithms Lakshman Patel RJIT 464 views
0 votes
2 answers
7
A particular Panini-Backus-Naur Form definition for a $<\text{word}>$ is given by the following rules: $<\text{word}>:: = \:<\text{letter}> \mid <\text{letter}>\:<\text{pairlet}>\mid <\text{letter}>\:<\text{pairdig}>$ ... $c22$ None of $I,II\:\text{or}\:III$ $I$ and $II$ only $I$ and $III$ only $II$ and $III$ only $I,II$ and $III$
asked Feb 11 in Others Lakshman Patel RJIT 78 views
1 vote
2 answers
8
Jobs keep arriving at a processor. A job can have an associated time length as well as a priority tag. New jobs may arrive while some earlier jobs are running. Some jobs may keep running indefinitely. A ... the following job-scheduling policies is starvation free? Round - robin Shortest job first Priority queuing Latest job first None of the others
asked Feb 11 in Operating System Lakshman Patel RJIT 167 views
0 votes
0 answers
9
Consider the following algorithm (Note: For positive integers, $p,q,p/q$ denotes the floor of the rational number $\dfrac{p}{q}$, assume that given $p,q,p/q$ can be computed in one step): $\textbf{Input:}$ Two positive integers $a,b,a\geq b.$ $\textbf{Output:}$ A positive integers $g.$ while(b> ... worst case? $\Theta(\log K)$ $\Theta({K})$ $\Theta({K\log K})$ $\Theta({K^{2}})$ $\Theta({2^{K}})$
asked Feb 11 in Others Lakshman Patel RJIT 53 views
0 votes
1 answer
10
Consider the context-free grammar below ($\epsilon$ denotes the empty string, alphabet is $\{a,b\}$): $S\rightarrow \epsilon \mid aSb \mid bSa \mid SS.$ What language does it generate? $(ab)^{\ast} + (ba)^{\ast}$ $(abba) {\ast} + (baab)^{\ast}$ $(aabb)^{\ast} + (bbaa)^{\ast}$ Strings of the form $a^{n}b^{n}$ or $b^{n}a^{n},n$ any positive integer Strings with equal numbers of $a$ and $b$
asked Feb 11 in Others Lakshman Patel RJIT 57 views
0 votes
1 answer
11
Let $u$ be a point on the unit circle in the first quadrant (i.e., both coordinates of $u$ are positive). Let $\theta$ be the angle subtended by $u$ and the $x$ axis at the origin. Let $\ell _{u}$ denote the infinite line passing through the origin and $u$ ... $w$ and the $x$-axis at the origin? $50^{\circ}$ $85^{\circ}$ $90^{\circ}$ $145^{\circ}$ $165^{\circ}$
asked Feb 11 in Others Lakshman Patel RJIT 50 views
0 votes
1 answer
12
A $\textit{clamp}$ gate is an analog gate parametrized by two real numbers $a$ and $b$, and denoted as $\text{clamp}_{a,b}$. It takes as input two non-negative real numbers $x$ and $y$ ... $y$ outputs the maximum of $x$ and $y?$ $1$ $2$ $3$ $4$ No circuit composed only of clamp gates can compute the max function
asked Feb 11 in Others Lakshman Patel RJIT 70 views
1 vote
1 answer
13
Consider the (decimal) number $182$, whose binary representation is $10110110$. How many positive integers are there in the following set?$\{n\in \mathbb{N}: n\leq 182 \text{ and n has } \textit{exactly four} \text{ ones in its binary representation}\}$ $91$ $70$ $54$ $35$ $27$
asked Feb 11 in Digital Logic Lakshman Patel RJIT 255 views
1 vote
2 answers
14
Consider the following statements. The intersection of two context-free languages is always context-free The super-set of a context-free languages is never regular The subset of a decidable language is always decidable Let $\Sigma = \{a,b,c\}.$ Let $L\subseteq \Sigma$ be the language of all strings in which either ... $(2)$ Only $(1),(2)$ and $(3)$ Only $(4)$ None of $(1),(2),(3),(4)$ are true.
asked Feb 11 in Theory of Computation Lakshman Patel RJIT 181 views
0 votes
0 answers
15
Consider the following Boolean valued function on $n$ Boolean variables: $f(x_{1},\dots,x_{n}) = x_{1} + \dots + x_{n}(\text{mod } 2)$, where addition is over integers, mapping $\textbf{ FALSE'}$ to $0$ and $\textbf{ TRUE'}$ to $1.$ Consider Boolean circuits (with no feedback) that use ... $n^{c}$, for some fixed constant $c$ $n^{\omega(1)}$, but $n^{O(\log n)}$ $2^{\Theta(n)}$ None of the others
asked Feb 11 in Digital Logic Lakshman Patel RJIT 87 views
0 votes
2 answers
16
The sequence $s_{0},s_{1},\dots , s_{9}$ is defined as follows: $s_{0} = s_{1} + 1$ $2s_{i} = s_{i-1} + s_{i+1} + 2 \text{ for } 1 \leq i \leq 8$ $2s_{9} = s_{8} + 2$ What is $s_{0}$? $81$ $95$ $100$ $121$ $190$
asked Feb 11 in Numerical Ability Lakshman Patel RJIT 170 views
0 votes
1 answer
17
A ball is thrown directly upwards from the ground at a speed of $10\: ms^{-1}$, on a planet where the gravitational acceleration is $10\: ms^{-2}$. Consider the following statements: The ball reaches the ground exactly $2$ seconds after it is thrown up The ball travels a ... Statement $3$ is correct None of the Statements $1,2$ or $3$ is correct All of the Statements $1,2$ and $3$ are correct
asked Feb 11 in Numerical Ability Lakshman Patel RJIT 118 views
0 votes
1 answer
18
What is the area of the largest rectangle that can be inscribed in a circle of radius $R$? $R^{2}/2$ $\pi \times R^{2}/2$ $R^{2}$ $2R^{2}$ None of the above
asked Feb 11 in Calculus Lakshman Patel RJIT 67 views
0 votes
1 answer
19
The hour needle of a clock is malfunctioning and travels in the anti-clockwise direction, i.e., opposite to the usual direction, at the same speed it would have if it was working correctly. The minute needle is working correctly. Suppose the two needles show the correct time at $12$ noon, thus ... ? $\dfrac{10}{11}$ hour $\dfrac{11}{12}$ hour $\dfrac{12}{13}$ hour $\dfrac{19}{22}$ hour One hour
asked Feb 11 in Linear Algebra Lakshman Patel RJIT 88 views
2 votes
1 answer
20
Suppose we toss $m=3$ labelled balls into $n=3$ numbered bins. Let $A$ be the event that the first bin is empty while $B$ be the event that the second bin is empty. $P(A)$ and $P(B)$ denote their respective probabilities. Which of the following is true? $P(A)>P(B)$ $P(A) = \dfrac{1}{27}$ $P(A)>P(A\mid B)$ $P(A)<P(A\mid B)$ None of the above
asked Feb 11 in Probability Lakshman Patel RJIT 118 views
0 votes
1 answer
21
A contiguous part, i.e., a set of adjacent sheets, is missing from Tharoor's GRE preparation book. The number on the first missing page is $183$, and it is known that the number on the last missing page has the same three digits, but in a different order. Note that every sheet ... one at the front and one at the back. How many pages are missing from Tharoor's book? $45$ $135$ $136$ $198$ $450$
asked Feb 11 in Verbal Ability Lakshman Patel RJIT 97 views
0 votes
2 answers
22
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall that January has $31$ days)? Sunday Monday Wednesday Friday None of the others
asked Feb 10 in Probability Lakshman Patel RJIT 227 views
0 votes
1 answer
23
Consider a function $f:[0,1]\rightarrow [0,1]$ which is twice differentiable in $(0,1).$ Suppose it has exactly one global maximum and exactly one global minimum inside $(0,1)$. What can you say about the behaviour of the first derivative $f'$ and and second derivative $f''$ ... $f'$ is zero at at least two points, $f''$ is zero at at least two points
asked Feb 10 in Calculus Lakshman Patel RJIT 120 views
1 vote
2 answers
24
A lottery chooses four random winners. What is the probability that at least three of them are born on the same day of the week? Assume that the pool of candidates is so large that each winner is equally likely to be born on any of the seven days of the week independent of the other winners. ... $\dfrac{48}{2401} \\$ $\dfrac{105}{2401} \\$ $\dfrac{175}{2401} \\$ $\dfrac{294}{2401}$
asked Feb 10 in Probability Lakshman Patel RJIT 192 views
0 votes
1 answer
25
What is the maximum number of regions that the plane $\mathbb{R}^{2}$ can be partitioned into using $10$ lines? $25$ $50$ $55$ $56$ $1024$ Hint: Let $A(n)$ be the maximum number of partitions that can be made by $n$ lines. Observe that $A(0) = 1, A(2) = 2, A(2) = 4$ etc. Come up with a recurrence equation for $A(n)$.
asked Feb 10 in Numerical Ability Lakshman Patel RJIT 84 views
0 votes
0 answers
26
Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of the particle be denoted by $\overrightarrow{\pi}.$ In the first step, if the particle is at position $i,$ it moves to one ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$
asked Feb 10 in Probability Lakshman Patel RJIT 86 views
0 votes
1 answer
27
Let $A$ be am $n\times n$ invertible matrix with real entries whose column sums are all equal to $1$. Consider the following statements: Every column in the matrix $A^{2}$ sums to $2$ Every column in the matrix $A^{3}$ sums to $3$ Every column in the matrix $A^{-1}$ ... $(3)$ is correct but not statements $(1)$ or $(2)$ all the $3$ statements $(1),(2),$ and $(3)$ are correct
asked Feb 10 in Linear Algebra Lakshman Patel RJIT 150 views
0 votes
0 answers
28
Let $d\geq 4$ and fix $w\in \mathbb{R}.$ Let $S = \{a = (a_{0},a_{1},\dots ,a_{d})\in \mathbb{R}^{d+1}\mid f_{a}(w) = 0\: \text{and}\: f'_{a}(w) = 0\},$ where the polynomial function $f_{a}(x)$ ... $d$-dimensional vector subspace of $\mathbb{R}^{d+1}$ $S$ is a $(d-1)$-dimensional vector subspace of $\mathbb{R}^{d+1}$ None of the other options
asked Feb 10 in Linear Algebra Lakshman Patel RJIT 81 views
2 votes
1 answer
29
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above
asked Feb 10 in Linear Algebra Lakshman Patel RJIT 118 views
1 vote
2 answers
30
Two balls are drawn uniformly at random without replacement from a set of five balls numbered $1,2,3,4,5.$ What is the expected value of the larger number on the balls drawn? $2.5$ $3$ $3.5$ $4$ None of the above
asked Feb 10 in Probability Lakshman Patel RJIT 178 views
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