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Recent questions tagged tifr2019
+3
votes
6
answers
1
TIFR2019A1
Let $X$ be a set with $n$ elements. How many subsets of $X$ have odd cardinality? $n$ $2^n$ $2^{n/2}$ $2^{n1}$ Can not be determined without knowing whether $n$ is odd or even
asked
Dec 18, 2018
in
Set Theory & Algebra
by
Arjun
Veteran
(
425k
points)

574
views
tifr2019
engineeringmathematics
discretemathematics
settheory&algebra
sets
+3
votes
2
answers
2
TIFR2019A2
How many proper divisors (that is, divisors other than $1$ or $7200$) does $7200$ have ? $18$ $20$ $52$ $54$ $60$
asked
Dec 18, 2018
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

368
views
tifr2019
modulararithmetic
numericalability
+5
votes
2
answers
3
TIFR2019A3
$A$ is $n \times n$ square matrix for which the entries in every row sum to $1$. Consider the following statements: The column vector $[1,1,\ldots,1]^T$ is an eigen vector of $A.$ $ \text{det}(AI) = 0.$ $\text{det}(A) = 0.$ Which of the above statements must be TRUE? Only $(i)$ Only $(ii)$ Only $(i)$ and $(ii)$ Only $(i)$ and $(iii)$ $(i),(ii) \text{ and }(iii)$
asked
Dec 18, 2018
in
Linear Algebra
by
Arjun
Veteran
(
425k
points)

534
views
tifr2019
engineeringmathematics
linearalgebra
eigenvalue
+3
votes
1
answer
4
TIFR2019A4
What is the probability that a point $P=(\alpha,\beta)$ picked uniformly at random from the disk $x^2 +y^2 \leq 1$ satisfies $\alpha + \beta \leq 1$? $\frac{1}{\pi}$ $\frac{3}{4} + \frac{1}{4} \cdot \frac{1}{\pi}$ $\frac{3}{4}+ \frac{1}{4} \cdot \frac{2}{\pi}$ $1$ $\frac{2}{\pi}$
asked
Dec 18, 2018
in
Probability
by
Arjun
Veteran
(
425k
points)

389
views
tifr2019
engineeringmathematics
discretemathematics
probability
+2
votes
1
answer
5
TIFR2019A5
Asha and Lata play a game in which Lata first thinks of a natural number between $1$ and $1000$. Asha must find out that number by asking Lata questions, but Lata can only reply by saying Yes or no . Assume that Lata always tells the truth. What is the least ... within which she can always find out the number Lata has thought of? $10$ $32$ $100$ $999$ $\text{None of the above}$
asked
Dec 18, 2018
in
Algorithms
by
Arjun
Veteran
(
425k
points)

475
views
tifr2019
algorithmdesign
binarysearch
+1
vote
1
answer
6
TIFR2019A6
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is said to be $\textit{convex}$ if for all $x,y \in \mathbb{R}$ and $\lambda$ such that $0 \leq \lambda \leq1,$ $f(\lambda x+ (1\lambda)y) \leq \lambda f (x) + (1\lambda) f(y)$. Let $f:$\mathbb{R}$ $→$ $\mathbb ... $p,q$ and $r$ must be convex? Only $p$ Only $q$ Only $r$ Only $p$ and $r$ Only $q$ and $r$
asked
Dec 18, 2018
in
Set Theory & Algebra
by
Arjun
Veteran
(
425k
points)

351
views
tifr2019
engineeringmathematics
discretemathematics
settheory&algebra
functions
convexsetsfunctions
nongate
+5
votes
2
answers
7
TIFR2019A7
What are the last two digits of $1! + 2! + \dots +100!$? $00$ $13$ $30$ $33$ $73$
asked
Dec 18, 2018
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

321
views
tifr2019
modulararithmetic
numericalability
0
votes
1
answer
8
TIFR2019A8
Consider the following toy model of traffic on a straight , single lane, highway. We think of cars as points, which move at the maximum speed $v$ that satisfies the following constraints: The speed is no more than the speed limit $v_{max}$ mandated ... Which of the following graphs most accurately captures the relationship between the speed $v$ and the density $\rho$ in this model ?
asked
Dec 18, 2018
in
Others
by
Arjun
Veteran
(
425k
points)

313
views
tifr2019
generalaptitude
numericalability
+2
votes
1
answer
9
TIFR2019A9
Let $A$ and $B$ be two containers. Container $A$ contains $50$ litres of liquid $X$ and container $B$ contains $100$ litres of liquid $Y$. Liquids $X$ and $Y$ are soluble in each other. We now take $30$ ml of liquid $X$ from container $A$ and put it into container $B$. The mixture in ... $V_{AY} > V_{BX}$ $V_{AY} = V_{BX}$ $V_{AY} + V_{BX}=30$ $V_{AY} + V_{BX}=20$
asked
Dec 18, 2018
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

256
views
tifr2019
generalaptitude
numericalability
numericalcomputation
+2
votes
1
answer
10
TIFR2019A10
Avni and Badal alternately choose numbers from the set $\{1,2,3,4,5,6,7,8,9\}$ without replacement (starting with Avni). The first person to choose numbers of which any $3$ sum to $15$ wins the game (for example, Avni wins if she chooses ... a winning strategy Both of them have a winning strategy Neither of them has a winning strategy The Player that picks $9$ has a winning strategy
asked
Dec 18, 2018
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

290
views
tifr2019
generalaptitude
numericalability
logicalreasoning
+3
votes
4
answers
11
TIFR2019A11
Suppose there are $n$ guests at a party (and no hosts). As the night progresses, the guests meet each other and shake hands. The same pair of guests might shake hands multiple times. for some parties stretch late into the night , and it is hard to keep track.Still, they don't shake ... $2 \mid \text{Even} \mid  \mid \text{Odd} \mid$ $2 \mid \text{Odd} \mid  \mid \text{Even} \mid$
asked
Dec 18, 2018
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

311
views
tifr2019
generalaptitude
numericalability
logicalreasoning
+1
vote
1
answer
12
TIFR2019A12
Let $f$ be a function with both input and output in the set $\{0,1,2, \dots ,9\}$, and let the function $g$ be defined as $g(x) = f(9x)$. The function $f$ is nondecreasing, so that $f(x) \geq f(y)$ for $x \geq y$. Consider the following statements: There ... must be TRUE for ALL such functions $f$ and $g$ ? Only $(i)$ Only $(i)$ and $(ii)$ Only $(iii)$ None of them All of them
asked
Dec 18, 2018
in
Set Theory & Algebra
by
Arjun
Veteran
(
425k
points)

512
views
tifr2019
engineeringmathematics
discretemathematics
settheory&algebra
functions
+3
votes
2
answers
13
TIFR2019A13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$ What is the value of this integral correct up to two decimal places? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$
asked
Dec 18, 2018
in
Calculus
by
Arjun
Veteran
(
425k
points)

322
views
tifr2019
engineeringmathematics
calculus
integration
+4
votes
1
answer
14
TIFR2019A14
A drawer contains $9$ pens, of which $3$ are red, $3$ are blue, and $3$ are green. The nine pens are drawn from the drawer one at at time (without replacement) such that each pen is drawn with equal probability from the remaining pens in the drawer. What is the probability that two red pens are drawn in succession ? $7/12$ $1/6$ $1/12$ $1/81$ $\text{None of the above}$
asked
Dec 18, 2018
in
Probability
by
Arjun
Veteran
(
425k
points)

399
views
tifr2019
engineeringmathematics
probability
+2
votes
5
answers
15
TIFR2019A15
Consider the matrix $A = \begin{bmatrix} \frac{1}{2} &\frac{1}{2} & 0\\ 0& \frac{3}{4} & \frac{1}{4}\\ 0& \frac{1}{4} & \frac{3}{4} \end{bmatrix}$ What is $\lim_{n→\infty}$A^n$ ? $\begin{bmatrix} \ 0 & 0 & 0\\ 0& 0 ... $\text{The limit exists, but it is none of the above}$
asked
Dec 18, 2018
in
Calculus
by
Arjun
Veteran
(
425k
points)

407
views
tifr2019
engineeringmathematics
calculus
limits
0
votes
1
answer
16
TIFR2019B1
Which of the following decimal numbers can be exactly represented in binary notation with a finite number of bits ? $0.1$ $0.2$ $0.4$ $0.5$ All the above
asked
Dec 18, 2018
in
Digital Logic
by
Arjun
Veteran
(
425k
points)

235
views
tifr2019
digitallogic
numberrepresentation
+4
votes
3
answers
17
TIFR2019B2
How many distinct minimum weight spanning trees does the following undirected, weighted graph have ? $8$ $16$ $32$ $64$ None of the above
asked
Dec 18, 2018
in
Algorithms
by
Arjun
Veteran
(
425k
points)

357
views
tifr2019
algorithms
minimumspanningtrees
+1
vote
1
answer
18
TIFR2019B3
A graph is $d$ – regular if every vertex has degree $d$. For a $d$ – regular graph on $n$ vertices, which of the following must be TRUE? $d$ divides $n$ Both $d$ and $n$ are even Both $d$ and $n$ are odd At least one of $d$ and $n$ is odd At least one of $d$ and $n$ is even
asked
Dec 18, 2018
in
Graph Theory
by
Arjun
Veteran
(
425k
points)

234
views
tifr2019
graphconnectivity
graphtheory
+1
vote
2
answers
19
TIFR2019B4
Let $\varphi$ be a propositional formula on a set of variables $A$ and $\varphi$ be a propositional formula on a set of variables $B$ , such that $\varphi$ $\Rightarrow$ $\psi$ . A $\textit{Craig interpolant}$ of $\varphi$ and $\psi$ is a propositional formula $\mu$ on ... Craig interpolant for $\varphi$ and $\psi$ ? $q$ $\varphi$ itself $q \vee s$ $q \vee r$ $\neg q \wedge s$
asked
Dec 18, 2018
in
Mathematical Logic
by
Arjun
Veteran
(
425k
points)

306
views
tifr2019
engineeringmathematics
discretemathematics
mathematicallogic
firstorderlogic
0
votes
2
answers
20
TIFR2019B5
Stirling's approximation for $n!$ states for some constants $c_1,c_2$ $c_1 n^{n+\frac{1}{2}}e^{n} \leq n! \leq c_2 n^{n+\frac{1}{2}}e^{n}.$ What are the tightest asymptotic bounds that can be placed on $n!$ $?$ ... $n! =\Theta((\frac{n}{e})^{n+\frac{1}{2}})$ $n! =\Theta(n^{n+\frac{1}{2}}2^{n})$
asked
Dec 18, 2018
in
Algorithms
by
Arjun
Veteran
(
425k
points)

339
views
tifr2019
algorithms
asymptoticnotations
+1
vote
2
answers
21
TIFR2019B6
Given the following pseudocode for function $\text{printx()}$ below, how many times is $x$ printed if we execute $\text{printx(5)}?$ void printx(int n) { if(n==0){ printf(“x”); } for(int i=0;i<=n1;++i){ printx(n1); } } $625$ $256$ $120$ $24$ $5$
asked
Dec 18, 2018
in
Programming
by
Arjun
Veteran
(
425k
points)

246
views
tifr2019
programming
programminginc
+1
vote
1
answer
22
TIFR2019B7
A formula is said to be a $3$CFformula if it is a conjunction (i.e., an AND) of clauses, and each clause has at most $3$ literals. Analogously, a formula is said to be a $3$DFformula if it is a disjunction (i.e., an OR) of clauses of at most $3$ literals each. ... $\text{3DFSAT}$ is NPcomplete Neither $\text{3CFSAT}$ nor $\text{3DFSAT}$ are in P
asked
Dec 18, 2018
in
Algorithms
by
Arjun
Veteran
(
425k
points)

200
views
tifr2019
algorithms
pnpnpcnph
+1
vote
2
answers
23
TIFR2019B8
Consider the following program fragment: var a,b : integer; procedure G(c,d: integer); begin c:=cd; d:=c+d; c:=dc end; a:=2; b:=3; G(a,b); If both parameters to $G$ are passed by reference, what are the values of $a$ and $b$ at the end of the above program fragment ? $a=0$ and $b=2$ $a=3$ and $b=2$ $a=2$ and $b=3$ $a=1$ and $b=5$ None of the above
asked
Dec 18, 2018
in
Programming
by
Arjun
Veteran
(
425k
points)

215
views
tifr2019
programming
parameterpassing
+3
votes
1
answer
24
TIFR2019B9
Consider the following program fragment: var x, y: integer; x := 1; y := 0; while y < x do begin x := 2*x; y := y+1 end; For the above fragment , which of the following is a loop invariant ? $x=y+1$ $x=(y+1)^2$ $x=(y+1)2^y$ $x=2^y$ None of the above, since the loop does not terminate
asked
Dec 18, 2018
in
Programming
by
Arjun
Veteran
(
425k
points)

455
views
tifr2019
programming
loopinvariants
+4
votes
2
answers
25
TIFR2019B10
Let the language $D$ be defined in the binary alphabet $\{0,1\}$ as follows: $D:= \{ w \in \{0,1\}^* \mid \text{ substrings 01 and 10 occur an equal number of times in w} \}$ For example , $101 \in D$ while $1010 \notin D$. Which of the ... ? $D$ is regular $D$ is contextfree but not regular $D$ is decidable but not contextfree $D$ is decidable but not in NP $D$ is undecidable
asked
Dec 18, 2018
in
Theory of Computation
by
Arjun
Veteran
(
425k
points)

287
views
tifr2019
theoryofcomputation
identifyclasslanguage
+8
votes
2
answers
26
TIFR2019B11
Consider the following nondeterministic automaton,where $s_1$ is the start state and $s_4$ is the final (accepting) state. The alphabet is $\{a,b\}$. A transition with label $\epsilon$ can be taken without consuming any symbol from the input. Which of the following regular expressions correspond to the language ... $(a+b)^*ba^*$ $(a+b)^*ba(aa)^*$ $(a+b)^*$ $(a+b)^*baa^*$
asked
Dec 18, 2018
in
Theory of Computation
by
Arjun
Veteran
(
425k
points)

234
views
tifr2019
theoryofcomputation
regularexpressions
+1
vote
1
answer
27
TIFR2019B12
Let $G=(V,E)$ be a directed graph with $n(\geq 2)$ vertices, including a special vertex $r$. Each edge $e \in E$ has a strictly positive edge weight $w(e)$. An arborescence in $G$ rooted at $r$ is a subgraph $H$ of $G$ in which every ... $w^*$ is less than the weight of the minimum weight directed Hamiltonian cycle in $G$, when $G$ has a directed Hamiltonian cycle
asked
Dec 18, 2018
in
Graph Theory
by
Arjun
Veteran
(
425k
points)

352
views
tifr2019
graphconnectivity
graphtheory
difficult
+7
votes
6
answers
28
TIFR2019B13
A row of $10$ houses has to be painted using the colours red, blue, and green so that each house is a single colour, and any house that is immediately to the right of a red or a blue house must be green. How many ways are there to paint the houses? $199$ $683$ $1365$ $3^{10}2^{10}$ $3^{10}$
asked
Dec 18, 2018
in
Combinatory
by
Arjun
Veteran
(
425k
points)

556
views
tifr2019
engineeringmathematics
discretemathematics
permutationandcombination
medium
+2
votes
2
answers
29
TIFR2019B14
Let $m$ and $n$ be two positive integers. Which of the following is NOT always true? If $m$ and $n$ are coprime, there exist integers $a$ and $b$ such that $am + bn=1$ $m^{n1} \equiv 1 (\text{ mod } n)$ ... $m+1$ is a factor of $m^{n(n+1)}1$ If $2^n 1$ is prime, then $n$ is prime
asked
Dec 18, 2018
in
Numerical Ability
by
Arjun
Veteran
(
425k
points)

304
views
tifr2019
generalaptitude
numericalability
modulararithmetic
+1
vote
1
answer
30
TIFR2019B15
Consider directed graphs on $n$ labelled vertices $\{1,2, \dots ,n\}$, where each vertex has exactly one edge coming in and exactly one edge going out. We allow selfloops. How many graphs have exactly two cycles ? $\sum_{k=1}^{n1} k!(nk)!$ $\frac{n!}{2}\bigg[\sum_{k=1}^{n1} \frac{1}{k(nk)}\bigg]$ $n!\bigg[\sum_{k=1}^{n1} \frac{1}{k}\bigg]$ $\frac{n!(n1)}{2}$ None of the above
asked
Dec 18, 2018
in
Graph Theory
by
Arjun
Veteran
(
425k
points)

361
views
tifr2019
graphconnectivity
graphtheory
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