# Recent activity by Himanshu1

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If we define the functions $f$, $g$ and $h$ that map $R$ into $R$ by : $f(x)=x^{4}, g(x)= \sqrt{x^{2}+1}, h(x)=x^{2}+72$, then the value of the composite functions $ho(gof)$ and $(hog)of$ are given as $x^{8}-71$ and $x^{8}-71$ $x^{8}-73$ and $x^{8}-73$ $x^{8}+71$ and $x^{8}+71$ $x^{8}+73$ and $x^{8}+73$
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The truth value of the statements: $\exists ! xP(x) \rightarrow \exists xP(x) \text{ and } \exists ! x \rceil P(x) \rightarrow \rceil \forall xP(x)$, (where the notation $\exists ! x P(x)$ denotes the proposition “There exists a unique $x$ such that $P(x)$ is true”) are: True and False False and True False and False True and True
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If $A_i = \{-i, \dots , -2, -1, 0, 1, 2, \dots , i \}$ then $\cup_{i=1}^\infty A_i$ is Z Q R C
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Consider a hash table with $n$ buckets, where external (overflow) chaining is used to resolve collisions. The hash function is such that the probability that a key value is hashed to a particular bucket is $\frac{1}{n}$. The hash table is initially empty and $K$ ... has occurred in any of the $K$ insertions? What is the probability that the first collision occurs at the $K^{th}$ insertion?
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Find the 1000_th power of the matrix -
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In a hash table of size 6 currently the locations 0,2,4 and 5 are occupied. The probability of a new record going into location 1 with a hash function resolving collisions by linear probing is (assume uniform hashing) a)2/3 b)1/3 c)1 d) 1/6
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What are the Number of states in minimum DFA that accepts Binary strings when interpreted as decimal mod 12 give 0 as remainder.Also give DFA.
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It's a question from Cormen book Exercise 4.4-5 and is described like this: Use a recursion tree to determine a good asymptotic upper bound on the recurrence $T(n)=T(n-1)+T(\frac{n}{2})+n$
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Find the least significant digit of $2^{3 \times 10 ^ {100 }}$ 2 4 6 8
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Highest mark in GATE CSE 2016: 88, 2015: 85 and in previous years too it is mostly the same. In other branches like ME, EE etc 98, 99 marks are common. What's the reason for this? Difficult/ambiguous questions are for all streams and this won't count for more than 5 marks. Moreover aptitude/mathematics portion are same for all streams.
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void fun(int *p) { int q = 10; p = &q; } int main() { int r = 20; int *p = &r; fun(p); printf("%d", *p); return 0; }
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In a class of $300$ students in an M.Tech programme, each student is required to take at least one subject from the following three: M600: Advanced Engineering Mathematics C600: Computational Methods for Engineers E600: Experimental Techniques for Engineers The registration data for the ... possible number of students in the class who have taken all the above three subjects? $20$ $30$ $40$ $50$
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Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a &ne; 0 , b &ne; 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a &ne; b then x1y1 + x2y2 + x3y3 is a) a b) b c) ab d) 0
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Consider the following statements relating to the level of poker play of four players $P,Q,R \ and \ S$. $P$ always beats $Q$ $R$ always beats $S$ $S$ loses to $P$ only sometimes. $R$ always loses to $Q$ Which of the following can be logically inferred from the above statements ... other players $S$ is the absolute worst player in the set (i). only (ii) only (i) and (ii) only' neither (i) nor (ii)
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Q. What are the various areas , one can choose in IITs/IISc. for masters ? What is their respective future scope ? When this selection is to be made ?
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#IISc2012Research 1>Recurrence relation and worst case time complexity of Merge sort 2> Difference between D&C and Dynamic Programming ?
Let $G$ be a complete undirected graph on $4$ vertices, having $6$ edges with weights being $1, 2, 3, 4, 5,$ and $6$. The maximum possible weight that a minimum weight spanning tree of $G$ can have is __________
The data given in the following table summarizes the monthly budget of an average household. ... $10\%$ $14\%$ $81\%$ $86\%$
Consider a carry look ahead adder for adding two n-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is $\Theta (1)$ $\Theta (\log(n))$ $\Theta (\sqrt{n})$ $\Theta (n)$)
If $(1.001)$^{1259}$=$3.52$and$(1.001)$^{2062}$= $7.85$, then $(1.001)$^{3321}$=$2.234.3311.3727.64$3 answers 26 The width of the physical address on a machine is$40$bits. The width of the tag field in a$512$KB$8$-way set associative cache is ________ bits. 4 answers 27 Let$X$be a recursive language and$Y$be a recursively enumerable but not recursive language. Let$W$and$Z$be two languages such that$\overline{Y}$reduces to$W$, and$Z$reduces to$\overline{X}$(reduction means the standard many-one reduction) ... is recursively enumerable.$W$is not recursively enumerable and$Z$is recursive.$W$is not recursively enumerable and$Z$is not recursive. 6 answers 28 Consider a$3 \ \text{GHz}$(gigahertz) processor with a three stage pipeline and stage latencies$\large\tau_1,\tau_2$and$\large\tau_3$such that$\large\tau_1 =\dfrac{3 \tau_2}{4}=2\tau_3$. If the longest pipeline stage is split into two pipeline stages of equal latency , the new frequency is __________$\text{GHz}$, ignoring delays in the pipeline registers. 2 answers 29 The given diagram shows the flowchart for a recursive function$A(n)$. Assume that all statements, except for the recursive calls, have$O(1)$time complexity. If the worst case time complexity of this function is$O(n^{\alpha})$, then the least possible value (accurate up to two decimal positions) of$\alpha$is ________. Flow chart for Recursive Function$A(n)$. 12 answers 30 A file system uses an in-memory cache to cache disk blocks. The miss rate of the cache is shown in the figure. The latency to read a block from the cache is$1$ms and to read a block from the disk is$10$ms. Assume that the cost of checking whether a ... sizes are in multiples of$10$MB. The smallest cache size required to ensure an average read latency of less than$6\$ ms is _________ MB.