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TIFRGS2021 Question
Lavanya and Ketak each flip a fair coin (i.e., both heads and tails have equal probability of appearing) $n$ times. What is the probability that Lavanya sees more heads than Ketak? In the following, the binomial conefficient $n\choose k$ counts the number of $k$element subsets of an $n$element ... $\sum_{i=0}^{n}\frac{{n\choose i}}{2^{2n}}$
asked
Mar 24
in
Probability

7
views
tifr2021
probability
0
votes
0
answers
TIFRGS2021 Question
Fix $n\geq6$. Consider the set $C$ of binary strings $x_1x_2...x_n$ of length n such that the bits satisfy the following set of equalities, all modulo 2: $x_i + x_{i+1} + x_i+2 = 0$ for all $1\leq i\leq n2, x_{n1} + x_n + x_1 = 0$, and $x_n + x_1 + x_2 = 0$. What ... $n \geq6$ is divisible by $3$ then $C = 4$. If $n\geq 6$ is not divisible by $3$ the $C =14$
asked
Mar 24
in
Set Theory & Algebra

6
views
tifr2021
sets
0
votes
0
answers
TIFRGS2021 Question
Consider the sequence $y_n = \frac{1}{\int_{1}^{n}\frac{1}{(1 + x/n)^3}dx}$ for $n = 2, 3, 4, ...$. Which of the following is TRUE? (A) The sequence $\{y_n\}$ does not have a limit as $n\rightarrow \infty$. (B) $y_n\leq 1$ ... $0$. (E) The sequence $\{y_n\}$ first increases and then decreases as $n$ takes values $2, 3, 4, ...$
asked
Mar 24
in
Calculus

3
views
tifr2021
limits
0
votes
0
answers
TIFRGS2021 Question
Let $d$ be the number of positive square integers (that is, it is a square of some integer) that are factors of $20^5\times21^5$. Which of the following is true about $d$? (A) $50 \leq d < 100$ (B) $100 \leq d < 150$ (C) $150 \leq d < 200$ (D) $200 \leq d < 300$ (E) $300 \leq d$
asked
Mar 24
in
Combinatory

5
views
tifr2021
factors
0
votes
0
answers
TIFRGS2021 Question
A matching in a graph is a set of edges such that no two edges in the set share a common vertex. Let $G$ be a graph on $n$ vertices in which there is a subset $M$ of $m$ ... $p^{2m}$ (D) $(1  p^2)^m$ (E) $1  (1  p(1  p))^m$
asked
Mar 24
in
Probability

7
views
tifr2021
probability
0
votes
0
answers
TIFRGS2021 Question
Let $n$, $m$ and $k$ be three positive integers such that $n \geq m \geq k$. Let $S$ be a subset of $\{1, 2, , n\}$ of size $k$. Consider sampling a function uniformly at random from the set of all functions mapping $\{1, , n\}$ to $\{1, , m\}$. What is the probability ... $1  \frac{k!{n\choose k}}{n^k}$ (E) $1  \frac{k!{n\choose k}}{m^k}$
asked
Mar 24
in
Combinatory

4
views
tifr2021
binomial
0
votes
0
answers
TIFRGS2021Question
What is the probability that at least two out of four people have their birthdays in the same month, assuming their birthdays are uniformly distributed over the twelve months? (A) $\frac{25}{48}$ (B) $\frac{5}{8}$ (C) $\frac{5}{12}$ (D) $\frac{41}{96}$ (E) $\frac{55}{96}$
asked
Mar 24
in
Probability

7
views
tifr2021
probability
0
votes
0
answers
TIFRGS2021 Question
Let $M$ be a $n\times m$ real matrix. Consider the following: Let $k_1$ be the smallest number such that $M$ can be factorized as $A.B$, where $A$ is an $n\times k_1$ matrix and $B$ is a $k_1\times m$ matrix. Let $k_2$ ... $k_2 = k_3 < k_1$ (D) $k_1 = k_2 = k_3$ (E) No general relationship exists among $k_1$, $k_2$ and $k_3$
asked
Mar 24
in
Linear Algebra

5
views
tifr2021
matrices
0
votes
1
answer
TIRFGS2021 Question
What is the area of a rectangle with the largest perimeter that can be inscribed in a unit circle (i.e., all the vertices of the rectangle are on the circle with radius 1)? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
asked
Mar 24
in
Calculus

41
views
tifr2021
area
0
votes
1
answer
TIFRGS2021 Question
A box contains 5 red marbles, 8 green marbles, 11 blue marbles, and 15 yellow marbles. We draw marbles uniformly at random without replacement from the box. What is the minimum number of marbles to be drawn to ensure that out of the marbles drawn, at least 7 are of the same colour? (A) 7 (B) 8 (C) 23 (D) 24 (E) 39
asked
Mar 24
in
Combinatory

10
views
tifr2021
0
votes
1
answer
TIFRGS2021 Question
Find the following sum $\frac{1}{2^2 – 1} + \frac{1}{4^2 – 1} + \frac{1}{6^2 – 1} + … + \frac{1}{40^2 – 1}$ (A) $\frac{20}{41}$ (B) $\frac{10}{41}$ (C) $\frac{10}{21}$ (D) $\frac{20}{21}$ (E) $1$
asked
Mar 24
in
Calculus

29
views
numberseries
sum
tifr2021
0
votes
0
answers
Made easy test series Discrete Mathematics2
The number of ways of splitting a set of n elements into two parts is Answer is $2^{n1} – 1$, explanation states this is because partitions can’t be empty, is this true?
asked
Jan 29
in
Set Theory & Algebra

39
views
sets
0
votes
1
answer
GATE2016232
I got this question by assuming the size of the block as $2^x$ and then solving, but in the comments here(https://gateoverflow.in/39622/gate2016232), someone mentioned it can be solved by assuming byteaddressable memory. My question is after taking the ... ? Because as far as I know byte addressable means the lowest addressable unit is 1 byte, it says nothing about the block size?
asked
Oct 31, 2020
in
CO & Architecture

28
views
0
votes
0
answers
#Doubt GATE199626
In this question access time is given as sec/bytes, does this mean the access is dependent on the size of the memory? But all the solutions here(https://gateoverflow.in/2778/gate199626), do not take this into account, so what does it mean?
asked
Oct 31, 2020
in
CO & Architecture

25
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