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GATE2019 form filling
Is there anyone who is not able to fill the GATE 2019 form from past 2 or 3 days....???
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Relations and functions
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ISI2017PCBB1
Consider an alphabet $\Sigma = \{1, 2, 3\}$.Design a deterministic finitestate automaton (DFA) that accepts all strings in $\Sigma^*$ in which the digits appear in nondecreasing sequence, from left to right. For example, the string 1123 and 222 would be ... E)$ with $n$ nodes can be partitioned into 2 trees, then there is at least one vertex of of degrees less than 4 in $G$.
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ISI2017PCBB2
Write a complete ANSI C code using recursion to calculate th sum(s) of the digits of an integer number (i) consisting of maximum 5 digits. For example, (1) = if i=12345, then your program should print s=15, (2) if i=457, then s= ... like "abc" has 6 possible permutations: "abc", "acb", "bca", "bac", "cab", "cba".
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ISI2017PCBB3
Let $R(A,B,C)$ be a relation with primary key $(A)$ and $S(A, D, E)$ a relation with primary key $(A, D)$. Each of the relations has n tuples. If the number of tuples in $R \: \text{ natural join } S$ is $m$, then ... the relational calculus expression to output the ID for all the students who have not been taught by the same teacher in more than one course across all semsters
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ISI2017PCBB4
A file $F$ holds the nonzero elements of two large $n \times n$ matrices, $a$ and $B$. The matrix entries are sorted as triplets $(i, j, value)$, where $value$ is the $(i,j)$th element of a matrix. The file first stores the element of $A$ ... give reasons. If yes, provide a solution. Clearly explain the data structure and how you are going to store, retrieve, and add the elements.
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ISI2017PCBB5
a. An operating system contains three resource classes. The number of resource units in these classes are 7, 7 and 10 respectively. The current resource allocation state is shown below: Process Allocated Resources Maximum Requirements R1 R2 R3 R1 R2 R3 $P_1$ 2 ... memory reference time? Assume that finding a pagetable entry in the TLB takes 20 nanoseconds, if the entry is present.
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ISI2017PCBB6
Let $A=(a_1, a_2, \dots , a_n)$ be an array of $n$ distinct numbers. The array may not be sorted. The $first$ element $a_1$ is said to be a $blip$ if $a_1 > a_2$. Similarly, the $last$ element $a_n$ is said to be a $blip$ if $a_n>a_{n1}$. Among ... 3, \dots , n1\}$. Design an $O(\log n)$ time algorithm for finding a $blip$ in $A$. Justify the complexity of your algorithm.
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ISI2017PCBB7
Show that $\{1,A \bar{B}\}$ is functionality complete, i.e., any Boolean function with variables $A$ and $B$ can be expressed using these two primitives. Define a Boolean function $F(X_1, X_2, X_3, X_4, X_5, X_6)$ of six variables such that $\\ \ ... \: & = & \text{0, otherwise} \end{matrix} $ How many essential prime implicants does $F$ have? Justify they are essential.
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ISI2017PCBB8
Write the number $(5)^{\frac{1}{2}}$ in single precision IEEE 754 floating point form. Consider a simple code C for error detection and correction. Each codeword in C consists of 2 data bits $[d_1, d_0]$ followed by check bits $[c_2, c_1, ... '+' is a modulo2 addition. Write down all the codewords for C Determine the minimum Hamming distance between any two distinct codewords of C
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General question
Where can I get the slides of standard text books for all the subjects ???
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ISI2017PCBA1
Suppose all the roots of the equation $x^3 +bx2017=0$ (where $b$ is a real number) are real. Prove that exactly one root is positive.
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ISI2017PCBA2
Let $a, b, c$ and $d$ be real numbers such that $a+b=c+d$ and $ab=cd$. Prove that $a^n+b^n=c^n+d^n$ for all positive integers $n$.
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ISI2017PCBA3
Let $B=\{1, 2, 3, 4\}$. A set $S \subseteq B \times B$ called a symmetric set of $B$ if for all $x, y \in B$, $$ (x, y) \in S \Rightarrow (y,x) \in S.$$ Find the number of symmetric sets of $B$.
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ISI2017PCBA4
Let $\lceil x \rfloor$ denote the integer nearest to $x$. For example, $\lceil 1.1 \rfloor =1, \lceil 1.5 \rfloor =1$ and $\lceil 1.6 \rfloor$ =2. Draw the graph of the function $y= \mid x  \lceil x \rfloor \mid$ for $0 \leq x \leq 4$. Find all the points $x, \: 0 \leq x \leq 4$, where the function is not differentiable. Justify your answer.
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Wooe Test Series
Is wooe online test series good for Gate ?
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Where we have to fill surname in GOAPS
WHERE WE HAVE TO WRITE SURNAME IN GOAPS AS IT HAVE TOBE IN LAST NAME OR FIRST NAME.AND IAM A SOUTH INDIAN
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#self
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#sets
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ISI2016PCBB1
Consider the array $A=[20,13,19,8,3,5,4] that represents a heap. Draw the heap after removing the element 20. List all the distinct integer keys $k$ such that, when $k$ is inserted in the Binary Search Tree of Figure 1, its height increases. Note that you are not allowed to insert an already existing key again. Justify your answer.
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ISI2016PCBB2
Consider sending a large file of 360,000 bits from Host A to Host B, connected through a router, as shown in the below figure. Assume that there is no queuing ans propagation delay, and the router has sufficient buffer space. Host A splits the ... transferring one byte involves 4 operations: instatus, checkstatus, branch and read/write in memory, each requiring one machine cycle.
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ISI2016PCBB3
Consider the following extract from a program, written in a Clike language, that computes the transpose of a matrix. for (i=0; i<N; i++) for (j=0; j<N; j++) B[i,j]=A[i,j]; $A$ and $B$ are $N \times N$ matrices with floating point ... 8 bytes Each of $A$ and $B$ is stored starting from the beginning of a page None of the pages allocated to $A$ and $B$ are initially in memory.
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ISI2016PCBB4
Commodity items have some positive or negative changes in their prices each week. Each trading company picks a portfolio of commodity items, that is, they have one or more items and they own some nonzero quantity of each one. The database table for this problem ... and there exists at least one company selling that item only. (i.e., not selling any other item) in that week.
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ISI2016PCBB5
What will be the output of the following C program? If you think it will give a runtime error, you need to mention it. In either case, your answer must include proper justifications without which no credit will be given. #include<stdio.h> main() { unsigned char i, j, a[]={1, 2, 3, 4, 5}; ... ;, i, j, n); while(j !=0) a[0]+=n; printf("j=%d, a[0]=%d\n", j, a[0]); }
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ISI2016PCBB6
Let L be a regular language over $\{0,1\}$. Define the reverse of the language $L$ to be the language $L^R = \{ w \in \{0,1\}^* \: \: : \: \: \text{ reverse }(w) \in L\}$, where $\text{reverse}(w)$ denotes the string $w$ in reverse. For example ... \: \: x \in \{0,1\}^*$, $x$ contains an odd number of 1's and 00 as a substring}. Construct a regular expression for the language $L$.
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ISI2016PCBB7
Let $A$ be a sorted array of $n$ positive integers, such that $A[1] \leq A[2] \leq \dots \leq A[n]$. Given an integer $x$ as input, the goal is to find two array indices $k$ and $l$ such that $A[k]+A[l] =x$, if such indices exist; otherwise, the goal is to report 'Failure". Design an algorithm for this problem, that works in $O(n)$ time.
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ISI2016PCBB8
Consider all possible trees with $n$ nodes. Let $k$ be the number of nodes with degree greater than 1 in a given tree. What is the maximum possible value of $k$? Justify your answer. Consider $2n$ committees, each having at least $2n$ persons, formed from a group of $4n$ persons. Prove that there exists at least one person who belongs to at least n committees.
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ISI2016PCBA1
If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+6x+1=0$, then prove that $\frac{\alpha}{\beta} + \frac{\beta}{\alpha} + \frac{\beta}{\gamma}+ \frac{\gamma}{\beta} + \frac{\gamma}{\alpha}+ \frac{\alpha}{\gamma}=3$
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ISI2016PCBA2
Let $n$ be a fixed positive integer. For any real number $x$, if for some integer $q$, $x=qn+r, \: \: \: 0 \leq r < n$, then we define $x \text{ mod } n=r$. Specify the points of discontinuity of the function $f(x)=x \text{ mod } 3$ with proper reasoning.
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ISI2016PCBA3
A bit string is called legitimate if it contains no consecutive zeros, e.g., 0101110 is legitimate, where as 10100111 is not. Let $a_n$ denote the number of legitimate bit strings of length $n$. Define $a_0=1$. Derive a recurrence relation for $a_n$ (i.e., express $a_n$ in terms of the preceding $a_i$').
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