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Recent questions tagged tifr2020
4
votes
1
answer
1
TIFR CSE 2020 | Part B | Question: 14
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 $s$ ... $f$ are the only odd degree nodes in the figure above. $430$ $440$ $460$ $470$ $480$
Lakshman Bhaiya
asked
in
Graph Theory
Feb 11, 2020
by
Lakshman Bhaiya
812
views
tifr2020
graph-theory
euler-graph
2
votes
1
answer
2
TIFR CSE 2020 | Part B | Question: 15
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 $X\oplus Y:=(X\wedge \neg Y)\vee (\neg X \wedge Y)$. Define the Boolean logic ... $H$ have? $20$ $30$ $32$ $160$ $1024$
Lakshman Bhaiya
asked
in
Digital Logic
Feb 11, 2020
by
Lakshman Bhaiya
678
views
tifr2020
digital-logic
boolean-algebra
1
vote
1
answer
3
TIFR CSE 2020 | Part B | Question: 13
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 ... has a Hamiltonian cycle A complete graph always has both an Eulerian cycle and a Hamiltonian cycle All of the other statements are true
Lakshman Bhaiya
asked
in
Graph Theory
Feb 11, 2020
by
Lakshman Bhaiya
616
views
tifr2020
graph-theory
euler-graph
1
vote
2
answers
4
TIFR CSE 2020 | Part B | Question: 12
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 ; } ... $1$ 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
Lakshman Bhaiya
asked
in
Programming
Feb 11, 2020
by
Lakshman Bhaiya
719
views
tifr2020
programming
programming-in-c
functions
0
votes
3
answers
5
TIFR CSE 2020 | Part B | Question: 11
Which of the following graphs are bipartite? Only $(1)$ Only $(2)$ Only $(2)$ and $(3)$ None of $(1),(2),(3)$ All of $(1),(2),(3)$
Lakshman Bhaiya
asked
in
Graph Theory
Feb 11, 2020
by
Lakshman Bhaiya
2.2k
views
tifr2020
engineering-mathematics
graph-theory
graph-coloring
bipartite-graph
8
votes
4
answers
6
TIFR CSE 2020 | Part B | Question: 10
Among the following asymptotic expressions, which of these functions grows the slowest (as a function of $n$) asymptotically? $2^{\log n}$ $n^{10}$ $(\sqrt{\log n})^{\log ^{2} n}$ $(\log n)^{\sqrt{\log n}}$ $2^{2^{\sqrt{\log\log n}}}$
Lakshman Bhaiya
asked
in
Algorithms
Feb 11, 2020
by
Lakshman Bhaiya
4.2k
views
tifr2020
algorithms
asymptotic-notations
time-complexity
0
votes
2
answers
7
TIFR CSE 2020 | Part B | Question: 9
A particular Panini-Backus-Naur Form definition for a $<\textsf{word}>$ is given by the following rules: $<\textsf{word}>:: = \:<\text{letter}> \mid <\text{letter}>\:<\text{pairlet}>\mid <\text{letter}>\:<\text{pairdig}>$ ... $\text{III}$ only $\text{II}$ and $\text{III}$ only $\text{I},\text{II}$ and $\text{III}$
Lakshman Bhaiya
asked
in
Compiler Design
Feb 11, 2020
by
Lakshman Bhaiya
718
views
tifr2020
compiler-design
lexical-analysis
3
votes
3
answers
8
TIFR CSE 2020 | Part B | Question: 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 $\textsf{starvation free}$ ... job-scheduling policies is starvation free? Round - robin Shortest job first Priority queuing Latest job first None of the others
Lakshman Bhaiya
asked
in
Operating System
Feb 11, 2020
by
Lakshman Bhaiya
876
views
tifr2020
operating-system
process-scheduling
round-robin-scheduling
0
votes
0
answers
9
TIFR CSE 2020 | Part B | Question: 7
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 ... $\Theta(\log K)$ $\Theta({K})$ $\Theta({K\log K})$ $\Theta({K^{2}})$ $\Theta({2^{K}})$
Lakshman Bhaiya
asked
in
Algorithms
Feb 11, 2020
by
Lakshman Bhaiya
409
views
tifr2020
algorithms
identify-function
time-complexity
0
votes
1
answer
10
TIFR CSE 2020 | Part B | Question: 6
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? $(ab)^{\ast} + (ba)^{\ast}$ $(abba) {\ast} + (baab)^{\ast}$ ... of the form $a^{n}b^{n}$ or $b^{n}a^{n},n$ any positive integer Strings with equal numbers of $a$ and $b$
Lakshman Bhaiya
asked
in
Theory of Computation
Feb 11, 2020
by
Lakshman Bhaiya
375
views
tifr2020
theory-of-computation
context-free-grammar
1
vote
1
answer
11
TIFR CSE 2020 | Part B | Question: 5
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 $u$. ... and the $x$-axis at the origin? $50^{\circ}$ $85^{\circ}$ $90^{\circ}$ $145^{\circ}$ $165^{\circ}$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Feb 11, 2020
by
Lakshman Bhaiya
367
views
tifr2020
quantitative-aptitude
cartesian-coordinates
0
votes
2
answers
12
TIFR CSE 2020 | Part B | Question: 4
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 $y$ ... outputs the maximum of $x$ and $y?$ $1$ $2$ $3$ $4$ No circuit composed only of clamp gates can compute the max function
Lakshman Bhaiya
asked
in
Calculus
Feb 11, 2020
by
Lakshman Bhaiya
563
views
tifr2020
calculus
maxima-minima
5
votes
1
answer
13
TIFR CSE 2020 | Part B | Question: 3
Consider the (decimal) number $182$, whose binary representation is $10110110$. How many positive integers are there in the following set?$\{n\in \mathbb{N}: n\leq 182 \text{ and n has } \textit{exactly four} \text{ ones in its binary representation}\}$ $91$ $70$ $54$ $35$ $27$
Lakshman Bhaiya
asked
in
Digital Logic
Feb 11, 2020
by
Lakshman Bhaiya
1.5k
views
tifr2020
digital-logic
number-representation
2
votes
4
answers
14
TIFR CSE 2020 | Part B | Question: 2
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 ... Only $(1),(2)$ and $(3)$ Only $(4)$ None of $(1),(2),(3),(4)$ are true.
Lakshman Bhaiya
asked
in
Theory of Computation
Feb 11, 2020
by
Lakshman Bhaiya
1.3k
views
tifr2020
theory-of-computation
context-free-language
decidability
0
votes
0
answers
15
TIFR CSE 2020 | Part B | Question: 1
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 ... , for some fixed constant $c$ $n^{\omega(1)}$, but $n^{O(\log n)}$ $2^{\Theta(n)}$ None of the others
Lakshman Bhaiya
asked
in
Digital Logic
Feb 11, 2020
by
Lakshman Bhaiya
493
views
tifr2020
digital-logic
boolean-algebra
time-complexity
3
votes
2
answers
16
TIFR CSE 2020 | Part A | Question: 15
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 $s_{0}$? $81$ $95$ $100$ $121$ $190$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Feb 11, 2020
by
Lakshman Bhaiya
640
views
tifr2020
quantitative-aptitude
number-theory
1
vote
1
answer
17
TIFR CSE 2020 | Part A | Question: 14
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 ... $1,2$ or $3$ is correct All of the Statements $1,2$ and $3$ are correct
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Feb 11, 2020
by
Lakshman Bhaiya
475
views
tifr2020
quantitative-aptitude
speed-time-distance
1
vote
1
answer
18
TIFR CSE 2020 | Part A | Question: 13
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
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Feb 11, 2020
by
Lakshman Bhaiya
430
views
tifr2020
quantitative-aptitude
geometry
circle
0
votes
1
answer
19
TIFR CSE 2020 | Part A | Question: 12
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 ... $\dfrac{11}{12}$ hour $\dfrac{12}{13}$ hour $\dfrac{19}{22}$ hour One hour
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Feb 11, 2020
by
Lakshman Bhaiya
517
views
tifr2020
quantitative-aptitude
clock-time
4
votes
1
answer
20
TIFR CSE 2020 | Part A | Question: 11
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
Lakshman Bhaiya
asked
in
Probability
Feb 11, 2020
by
Lakshman Bhaiya
678
views
tifr2020
probability
conditional-probability
3
votes
2
answers
21
TIFR CSE 2020 | Part A | Question: 9
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 ... the front and one at the back. How many pages are missing from Tharoor's book? $45$ $135$ $136$ $198$ $450$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Feb 11, 2020
by
Lakshman Bhaiya
716
views
tifr2020
quantitative-aptitude
number-theory
1
vote
2
answers
22
TIFR CSE 2020 | Part A | Question: 10
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
Lakshman Bhaiya
asked
in
Probability
Feb 10, 2020
by
Lakshman Bhaiya
1.7k
views
tifr2020
engineering-mathematics
probability
0
votes
2
answers
23
TIFR CSE 2020 | Part A | Question: 8
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 ... at at least one point $f'$ is zero at at least two points, $f''$ is zero at at least two points
Lakshman Bhaiya
asked
in
Calculus
Feb 10, 2020
by
Lakshman Bhaiya
815
views
tifr2020
engineering-mathematics
calculus
maxima-minima
4
votes
2
answers
24
TIFR CSE 2020 | Part A | Question: 7
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 ... $\dfrac{48}{2401} \\$ $\dfrac{105}{2401} \\$ $\dfrac{175}{2401} \\$ $\dfrac{294}{2401}$
Lakshman Bhaiya
asked
in
Probability
Feb 10, 2020
by
Lakshman Bhaiya
917
views
tifr2020
engineering-mathematics
probability
independent-events
2
votes
1
answer
25
TIFR CSE 2020 | Part A | Question: 6
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 $A(n)$.
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Feb 10, 2020
by
Lakshman Bhaiya
670
views
tifr2020
general-aptitude
quantitative-aptitude
number-theory
0
votes
0
answers
26
TIFR CSE 2020 | Part A | Question: 4
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 ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$
Lakshman Bhaiya
asked
in
Probability
Feb 10, 2020
by
Lakshman Bhaiya
577
views
tifr2020
engineering-mathematics
probability
uniform-distribution
1
vote
1
answer
27
TIFR CSE 2020 | Part A | Question: 5
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 ... $(1)$ or $(2)$ all the $3$ statements $(1),(2),$ and $(3)$ are correct
Lakshman Bhaiya
asked
in
Linear Algebra
Feb 10, 2020
by
Lakshman Bhaiya
831
views
tifr2020
engineering-mathematics
linear-algebra
matrix
0
votes
0
answers
28
TIFR CSE 2020 | Part A | Question: 3
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
Lakshman Bhaiya
asked
in
Linear Algebra
Feb 10, 2020
by
Lakshman Bhaiya
551
views
tifr2020
engineering-mathematics
linear-algebra
vector-space
2
votes
1
answer
29
TIFR CSE 2020 | Part A | Question: 2
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
Lakshman Bhaiya
asked
in
Linear Algebra
Feb 10, 2020
by
Lakshman Bhaiya
1.1k
views
tifr2020
engineering-mathematics
linear-algebra
rank-of-matrix
eigen-value
6
votes
2
answers
30
TIFR CSE 2020 | Part A | Question: 1
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
Lakshman Bhaiya
asked
in
Probability
Feb 10, 2020
by
Lakshman Bhaiya
2.0k
views
tifr2020
engineering-mathematics
probability
expectation
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