discrete-mathematics

Set Theory & Algebra Preparation Resources for GATE CSE

June 21, 2015 by Arjun Suresh 5 Comments

GATE Materials for Set Theory & Algebra

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Answered: GATE CSE 2017 Set 2 | Question: GA-8

The product of numbers with m and n digits has either m+n−1 or m+n digits. https://math.stackexchange.com/questions/1295186/my-proof-that-an-n-digit-number-times-an-n-digit-number-can-be-expressed-as-a-2 So, X^3 can have atmost 90 digits, and there is no option less than 90 digits. [...]

Answered: OS Applied Test Series

Statement 1- It is correct because we have limited memory of 200Mb. As per options, we can figure out that both process are running concurrently and first p1 take 80Mb from 200, so 200-80=120MB remaining. After that, P2 demands 70Mb, so 120-70=50Mb reaming. And 50 Mb is not sufficient for either of the processes to complete. P1 will wait for P2 to complete and release captured memory, and p2 will wait for p1 to get complete and release captured memory. Here both process will get stuck and this is deadlock. Statement 2- Because of statement 1 is true, statement 2 is false. [...]

Answered: ACE Test Series

Answer will be max heap of size n. We can access first max element from max heap in O(1). After that just delete k max element from heap and after every delete heapify the tree make sure it is max heap, which will take O(logn). So for K element time complexity will be O(klogn). And K is constant so O(logn). [...]

Self-doubt

DFS and BFS are equal in expressive power??? I(Independent on performances)?? [...]

Applied Grand Test 10

The Netherlands is one of the world leaders in the production and sale of tulips. Suppose the heights of the tulips in the green house of rotterdams fantastic flora follow a continuous uniform distribution with lower bound of 7 inches and upper bound of 16 inches. You have come to the greenhouse to select a bouquet of tulips, but only tulips with a height greater than 10 inches may be selected. What is the probability that a randomly selected tulip is tall enough to pick ____ [...]

Answered: GATE CSE 2017 Set 2 | Question: 23

no of vertices =n min degree for each vertex =3 now total degree =3*n no of edge =25 now we know for undirected graph , 2*edge = sum of degree sum of degree =2*25 =50 now 3*n = 50 n= 16.67 now if someone confused which one to took ceil of floor now just think if we put n= 17 then 3*17 =51 which is not the sum of degree as it is 50 and we can’t say 16 vertex of degree 3 and one vertex of degree 2 as min degree should be 3. now if you choose 16… [...]

Answered: CAT2016: 90

Given that, $2x+3y-5=0 \longrightarrow(1)$ $5x-7y+2=0 \longrightarrow(2)$ $9x-5y-4=0 \longrightarrow(3)$ Take equation $(1)$ and $(2).$ $2x+3y-5=0 \longrightarrow(1)\times7$ $5x-7y+2=0 \longrightarrow(2)\times3$ $14x+21y-35=0$ $15x-21y+6=0$ ---------------------------------- $29x-29=0$ $\boxed{x=1}$ Put the value of $’x’$ in equation $(1)$,we get. $2(1)+3y-5=0$ $\Rightarrow 3y=3$ $\Rightarrow \boxed{y=1}$ Take equation $(1)$ and $(3).$ $2x+3y-5=0 \longrightarrow(1)\times5$ $9x-5y-4=0 \longrightarrow(3)\times3$ $10x+15y-25=0$ $27x-15y-12=0$… [...]

Answered: CAT2016: 71

First, we can draw the diagram. We know that area of circle$=π\times(radius)^{2}$ Four circles are cut from the circular sheet, each has a radius $=5 cm.$ Area of cut out portion$=4\timesπ\times(5)^{2}$ $=4\timesπ\times25$ $=100π$ Area of uncut portion$=$Area of circular sheet$-$Area of a cutout portion $=π\times(20)^{2}-100π$ $=400π-100π$ $=300π$ $\therefore$ The ratio of the uncut to the cut portion $=300π:100π$ $=3:1$ Correct Answer$:\text{C}$ [...]

CAT2021 Set 3 | Verbal Ability and Reading Comprehension Question: 1

Which one of the following sets of words is closest to mapping the main arguments of the passage? Language; Unconcious; Psychoanalysis. Imagination; Magnetism; Psychiatry. Literary language; Unconscous; Insanity. Unconscious; Latent conception; Dreams. [...]

CAT2021 Set 3 | Verbal Ability and Reading Comprehension Question: 2

All of the following statements may be considered valid inferences from the passage, $\text{EXCEPT}:$ Unrelated practices began to be treated as related to each other, as knowledge of the mind grew in the nineteenth century. Without linguistic developments of the nineteenth century, the growth of understanding to the soul and the mind may not have happened. Eighteenth century thinkers were the first to perceive a connection between creative genus and insanity. New conceptions in the nineteenth century could provide new knowledge because of the establishment of fields such as anaesthesiology. [...]

CAT2021 Set 3 | Verbal Ability and Reading Comprehension Question: 3

“The enrichments of literary and interectual language led to an altered understanding of the meanings that underlie time-honored expressions and traditional catchwords.” Which one of the following interpretations of this sentence would be closest in meaning to the original? The meanings of time-honored expressions were changed by innovations in literary and intellectual language. All of the options listed here. Literay and intellectual languages was altered by time-honored expressions and traditional catchwords. Time-honored expressions and traditional catchwords were enriched by literay and intellectual language. [...]

CAT2021 Set 3 | Verbal Ability and Reading Comprehension Question: 4

Which one of the following statements best describes what the passage is about? The discovery of the unconscious as a part of the human mind. The identification of the unconscious as an object of psychical research. The growing vocabulary of the soul and the mind, as diverse processes. The collating of diverse ideas under the single term unconscious. [...]

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