# Recent questions tagged tifr-2021

0 votes
1 answer 13 views
When switching the CPU between two processes.. which of the following applies A. The PCB is both, saved and reloaded, only for the interrupted process that is existing the CPU B. The PCB is saved for the process that is scheduled for the CPU C. The PCB is reloaded for the process that is scheduled for the CPU D. No PCB is saved or reloaded E. None of the above
0 votes
0 answers 22 views
There is no information available on the website. Are the results out for Computer Science?
0 votes
0 answers 14 views
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 $n$ ... $\sum_{i=0}^{n}\frac{{n\choose i}}{2^{2n}}$
0 votes
0 answers 12 views
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 $1\leq i\leq n-2, x_{n-1} + x_n + x_1 = 0$, and $x_n + x_1 + x_2 = 0$. What is the size of ... $|C| = 4$ (E) If $n \geq6$ is divisible by $3$ then $|C| = 4$. If $n\geq 6$ is not divisible by $3$ the $|C| =14$
0 votes
0 answers 8 views
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 $2, 3, 4, ...$
0 votes
0 answers 10 views
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) $300 \leq d$
0 votes
0 answers 11 views
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 $m$ edges which is a matching. Consider a random process where each vertex in the graph is independently selected with probability $0 < p < 1$ and let $B$ ... $1 - (1 - p^2)^m$ (C) $p^{2m}$ (D) $(1 - p^2)^m$ (E) $1 - (1 - p(1 - p))^m$
0 votes
0 answers 11 views
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 that $f$ is not ... $1 - \frac{k!{n\choose k}}{n^k}$ (E) $1 - \frac{k!{n\choose k}}{m^k}$
0 votes
0 answers 11 views
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) $\frac{55}{96}$
0 votes
0 answers 10 views
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 $k_3$
0 votes
1 answer 117 views
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
0 votes
1 answer 23 views
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
0 votes
1 answer 37 views
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) $1$
To see more, click for the full list of questions or popular tags.