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Recent questions tagged tifr2021
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Is the result for TIFR 2021 entrance exam out?
There is no information available on the website. Are the results out for Computer Science?
asked
Apr 1
in
TIFR
by
AMIT ROY
(
5
points)

13
views
tifr2021
0
votes
0
answers
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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

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
by
zxy123
(
3.6k
points)

29
views
numberseries
sum
tifr2021
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