# Recent questions tagged jest

1 vote
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X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-one For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.
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What is the cut off rank in JEST called for Mtech Research in CSA and CDS in general category and EWS category?
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Three dice are rolled independently. Probability of obtaining the difference from largest and smallest number as exactly 4 :
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A directed graph with n vertices, in which each vertex has exactly 3 outgoing edges. Which one is true? A) All the vertices have indegree = 3 . B) Some vertices will have indegree exactly 3. C)Some vertices have indegree atleast 3. D) Some of the vertices have indegree atmost 3
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Let ${(0,1)}^n$ set of all binary string of length n. Hamming sphere of radius around a string C in ${(0,1)}^n$ is the set of all strings d$\epsilon$ ${(0,1)}^n$ that differ from C in at most r of n position, S(C,r) for n=2k+1 For C,C’ $\epsilon$ ${(0,1)}^n$ S(C,k) and S(C’,k) are disjoint couldn't remember rest of the options.
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Solve the recurrence relation given as: T(n)=2T(n-2)+n; where T(2)=2 and T(1)=0 What is the time complexity?
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Give an efficient algorithm for maximum size rectangle binary sub-matrix with all 1s . [Complexity should be O($n^c$)] (Memory based – Original question had a lot of added details)
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Given a sequence $a_1$, $a_2$ , $a_3$ ... $a_n$ of any different positive integers, exhibit an arrangement of integers between 1 and $n^2$ which has no increasing or decreasing subsequence of length n+1.
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Suppose that G contains a cycle C, and a path of length at least k between some two vertices of C. Show that G contains a cycle of length at least √k.
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Let a and b be positive integers such that a > b and a^ 2 − b^ 2 is a prime number. Then a^2 − b^ 2 is equal to (A) a − b (B) a + b (C) a × b (D) none of the above
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When is the following statement true? (A ∪ B) ∩ C = A ∩ C (A) If Ā ∩ B ∩ C = φ (B) If A ∩ B ∩ C = φ (C) always (D) never
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T (n) = T (n/2) + 2; T (1) = 1 When n is a power of 2, the correct expression for T (n) is: (A) 2(log n + 1) (B) 2 log n (C) log n + 1 (D)2 log n + 1
1 vote
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If a fair die (with 6 faces) is cast twice, what is the probability that the two numbers obtained differ by 2? (A) 1/12 (B) 1/6 (C) 2/9 (D) 1/2
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Consider the following function, defined by a recursive program: function AP(x,y: integer) returns integer; {if {x = 0 then return y+1} else if { y = 0 then return AP(x-1,1)} else return AP(x-1, AP(x,y-1)) } (a) Show that on all nonnegative arguments x and y, the function AP terminates. (b) Show that for any x, AP(x, y) > y.
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A tournament is a directed graph in which there is exactly one directed edge between every pair of vertices. Let Tn be a tournament on n vertices. (a) Use induction to prove the following statement: Tn has a directed hamiltonian path (a directed path that visits ... , or a simple description of the steps in the algorithm, will suffice. What is the worst case time complexity of your algorithm?
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Two gamblers have an argument. The first one claims that if a fair coin is tossed repeatedly, getting two consecutive heads is very unlikely. The second, naturally, is denying this. They decide to settle this by an actual trial; if, within n coin tosses, no two ... has been demonstrated. What happens for larger values of n? Is it true that P (n) only increases with n? Justify your answer.
1 vote
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Describe two different data structures to represent a graph. For each such representation, specify a simple property about the graph that can be more efficiently checked in that representation than in the other representation. Indicate the worst case time required for verifying both of your properties in either representation.
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Consider the following program: function mu(a,b:integer) returns integer; var i,y: integer; begin ---------P---------- i = 0; y = 0; while (i < a) do begin --------Q------------ y := y + b ; i = i + 1 end return y end Write a condition P such that the program terminates, and a condition Q which is true whenever program execution reaches the place marked Q above.
1 vote
19
How many subsets of even cardinality does an n-element set have ? Justify answer. Please give a proof if possible.This is part of subjective JEST paper.
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please give answer or name a book from where i can access Describe two different data structures to represent a graph. For each such representa- tion, specify a simple property about the graph that can be more efficiently checked in that representation than in the other representation. Indicate the worst case time required for verifying both of your properties in either representation.
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I want a link to sites or pdf repos which have list of mathematical puzzles or riddles which involve concepts of Discrete Math,Data Structure etc It should be relevant to the gate syllabus as I feel that I need to train my mind to solve problems with new approach rather than a fixed approach. Just want to improve my analytical skills when answering entrance tests.
1 vote