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101
UGC NET CSE | December 2019 | Part 2 | Question: 40
Consider a weighted directed graph. The current shortest distance from source $S$ to node $x$ is represented by $d[x]$. Let $d[v] =29$, $d[u]=15$, $w[u,v]=12$. What is the updated value of $d[v]$ based on current information? $29$ $27$ $25$ $17$
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102
UGC NET CSE | December 2019 | Part 2 | Question: 47
Consider the following statements with respect to the language $L = \{ a^n b^n \mid n \geq 0 \}$ $S_1 : L^2$ is a context free language $S_2 : L^k$ is context free language for any given $k \geq 1$ $S_3 : \overline{L}$ and $L^\ast$ ... the following is correct? only $S_1$ and $S_2$ only $S_1$ and $S_3$ only $S_2$ and $S_3$ $S_1$, $S_2$ and $S_3$
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103
UGC NET CSE | December 2019 | Part 2 | Question: 49
Let $G= (V, T, S, P)$ be any context-free grammar without any $\lambda$-productions or unit productions. Let $K$ be the maximum number of symbols on the right of any production in $P$. The maximum number of production rules for any equivalent grammar ... $K \mid P \mid + \mid T \mid$ Where $\mid \cdot \mid$ denotes the cardinality of the set.
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104
UGC NET CSE | December 2019 | Part 2 | Question: 50
Consider the following language families: $L_1 \equiv$ The context-free languages $L_2 \equiv$ The context-sensitive languages $L_3 \equiv$ The recursively enumerable languages $L_4 \equiv$ The recursive languages Which one of the following ... $L_1 \subseteq L_2 \subseteq L_4 \subseteq L_3$ $L_2 \subseteq L_1 \subseteq L_4 \subseteq L_3$
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105
UGC NET CSE | December 2019 | Part 2 | Question: 52
Let $A= \{001, 0011, 11, 101\}$ and $B=\{01, 111, 111, 010\}$. Similarly, let $C= \{00, 001, 1000\}$ and $D=\{0, 11, 011\}$. Which of the following pairs have a post-correspondence solution? Only pair $(A, B)$ Only pair $(C, D)$ Both $(A, B)$ and $(C, D)$ Neither $(A, B)$ nor $(C, D)$
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106
UGC NET CSE | December 2019 | Part 2 | Question: 53
Which of the following class of $\text{IP}$ address has the last address as $223.255.255.255$? Class $A$ Class $B$ Class $C$ Class $D$
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107
UGC NET CSE | December 2019 | Part 2 | Question: 79
Consider the following statements with respect to network security: Message confidentiality means that the sender and the receiver expect privacy Message integrity means that the data must arrive at the receiver exactly as they were sent. Message authentication means the receiver ... (ii) Only (i) and (iii) Only (ii) and (iii) (i), (ii) and (iii)
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108
UGC NET CSE | December 2019 | Part 2 | Question: 87
Match $\text{List-I}$ and $\text{List-II}$ ... $\text{(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)}$
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109
UGC NET CSE | December 2019 | Part 2 | Question: 93
A flow graph $F$ with entry node $(1)$ and exit node $(11)$ is shown below: How many regions are there in flowgraph $F$? $2$ $3$ $4$ $5$
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110
UGC NET CSE | December 2019 | Part 2 | Question: 95
A flow graph $F$ with entry node $(1)$ and exit node $(11)$ is shown below: How many predicate nodes are there and what are their names? Three: $(1,(2,3),6)$ Three: $(1,4,6)$ Four: $((2,3), 6, 10, 11)$ Four: $((2,3), 6, 9, 10)$
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111
UGC NET CSE | December 2019 | Part 1 | Question: 32
The term one gigabyte refers to: $1024$ petabytes $1024$ megabytes $1024$ kilobytes $1024$ bytes
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112
CMI-2018-DataScience-A: 3
Let $x=\begin{bmatrix} 3& 1 & 2 \end{bmatrix}$. Which of the following statements are true? $x^Tx$ is a $3\times 3$ matrix $xx^T$ is a $3\times 3$ matrix $xx^T$ is a $1\times 1$ matrix $xx^T=x^Tx$
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113
CMI-2018-DataScience-A: 12
In an entrance examination with multiple choice questions, with each question having four options and a single correct answer, suppose that only $20\%$ candidates think they know the answer to one difficult question and only half of them know it ... same. If a candidate has correctly answered the question, what is the (conditional) probability that she knew the answer?
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114
CMI-2018-DataScience-B: 2
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. Suppose $A,B$ and $C$ are $m\times m$ matrices. What does the following algorithm compute? (Here $A(i,j)$ ... .) for i=1 to m for j=1 to m for k=1 to m C(i,j)=A(i,k)*B(k,j)+C(i,j) end end end
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115
CMI-2019-DataScience-A: 8
Consider the following Venn diagram. The universal set $U$ is the set of all natural numbers from $1$ to $1000.$ The sets $A,B,C$ contain integers in $U$ that are multiples of $6,7,8$ respectively. The number of elements in the shaded region is: $12$ $15$ $16$ $17$
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CMI-2019-DataScience-B: 7
Ani is training for the olympics with Usain Bolt. After a few days of training Usain challenges Ani to catch him. Usain sets off running very slowly with a view to encourage Ani. He covers $\text{70m}$ the first minute, $\text{100m}$ the ... at an integral multiple of a minute. How many minutes did Ani run before catching up with Usain. What were their respective speeds?
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CMI-2020-DataScience-A: 18
The sum and product of the roots of the polynomial $9x^2+171x-81$ are, respectively: $-19$ and $-9$ $19$ and $9$ $-9$ and $19$ $9$ and $-19$
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CMI-2020-DataScience-B: 8
Owing to a defect in a certain machine which makes $N95$ masks, there is a $0.1\%$ probability that a mask it makes is $\text{not}$ effective in preventing airbone viruses from being inhaled. What is the probability that the first $1000$ masks that ... among the first one crore $(10^7)$ masks that the machine produces, there is at least one mask which is not effective?
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119
CMI2020-A: 2
Consider the following regular expressions over alphabet$\{a,b\}$, where the notation $(a+b)^+$ means $(a+b)(a+b)^*$: $r_1=(a+b)^+a(a+b)^*$ $r_2=(a+b)^*b(a+b)^+$ Let $L_1$ and $L_2$ be the languages defined by $r_1$ and $r_2$, respectively. Which of the following regular expressions define $L_1\cap L_2$? ... $(a+b)^*a\;b(a+b)^*$ $(a+b)^*b(a+b)^*a(a+b)^*$ $(a+b)^*a(a+b)^*b(a+b)^*$
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120
CMI2020-A: 9
A fair coin is repeatedly tossed. Each time a head appears, $1$ rupee is added to the first bag. Each time a tail appears, $2$ rupees are put in the second bag. What is the probability that both the bags have the same amount of money after $6$ coin tosses? $\frac{1}{2^6}$ $\frac{6!}{2!\cdot 4!\cdot 2^6}$ $\frac{2^2}{2^6}$ $\frac{6!}{2^6}$
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