# Recent activity by focus _GATE

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"From where are they bringing their books? _______ bringing _______ books from ________" The words that best fill the blanks in the above sentence are $\text{Their, they're, there}$ $\text{They're, their, there}$ $\text{There, their, they're}$ $\text{They're, there,there}$
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Define the value of $r$ in the following: $\sqrt (41)_{r} = (7)_{10}$
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Consider the following regular expression (RE) RE = (a+b)*(a+b+ε)a Which of the following is equivalent to the above RE? a) (a* + b*)+ (aa + ba) b) (ε + a+b*)+ a c) (a + b)+ (a + b + ε)a d) None of these
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L={WX$W^{R}$ / W,X$\epsilon (a+b)^{*}$.} L={XW$W^{R}$ / W,X$\epsilon (a+b)^{*}$.} l={W$W^{R}$X /W,X $\epsilon (a+b)^{*}$.} which of the above are REGULAR LANGUAGES.? ------------------------------------------------------- ... I think all are regular I)w=$\epsilon$ then w^r=$\epsilon$ and x=$(a+b)^{*}$ // it accept complete language so it is regular. same as for remaining problems also.am i ryt???
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A box contains 4 red balls and 6 black balls .Three balls are selected randomly from the box one after another without replacement .The probability that the selected set contains one red ball and two black ball is A)1/20 B) 1/12 C) 3/10 D)1/2
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A computer system has 6 tape drives, with n processes competing for them. Each process may need 3 tape drives. What is the maximum value of n for which the system is guaranteed to be deadlock? Justify your answer.
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A fair coin is tossed till a head appears for the first time .The probability that the number of required tosses is odd. A) 1/3 B) 1/2 C)2/3 D)3/4
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a lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is chosen at random. The probability that this pencil is not defective is?
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What is the expected no. of heads that come up when fair coin is flipped five times?
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Number of words of 4 letters that can be formed with the letters of the word IITJEE is a) 42 b) 82 c)102 d) 142
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T(n) = T(n/4) + T(3n/4) + n if n>1 = 1 if n =1 T(n) = ??
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Question 1:- Consider a 32-bit microprocessor that has an on-chip 16-KByte four-way set-associative cache. Assume that the cache has a line size of four 32-bit words. Draw a block diagram of this cache showing its organization and how the different address fields are used ... and number of bits taken were 6 ? How can i identify whether we need to convert to byte addressable from word size or not?
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Consider file consists of 10,000 records. Block size 1024 bytes, record size 100 bytes. search key 9 bytes, pointer 7 byte. a) How many 1st level index blocks using dense indexing. b)How many 1st level index blocks using sparse indexing. please explain in detail diff bw sparse and dense.
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3 level memory has the following specifications:- Level AccessTime/Word Block Size in words Hit Ratio 1 20 ns - .7 2 100 ns 2 .9 3 200 ns 4 1 If the referenced block is not in L1,then transfer from L2 to L1,If not in L2,then transfer from L3 to L2 to L1.How long will it take to access a block?
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A relation R(ABCD) with FD set f = {AB ->CD , D -> A } and the decomposition d = { R1(ABC) , R2(AD) , R3(BCD) } Check whether the following decomposition is dependency preserving or not ?
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The number of states in a minimal deterministic finite automaton corresponding to the language L = { an | n≥4 } is
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A cache has a capacity of 16 kbits and a line length of 128 bytes.how many set does cache have if it is 8 way set associative? A)16 B)32 C)64 D)none of the above
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Choose the equivalent prefix form of the following expression (a+(b-c))*((d-e)/(f+g-h)) *+a-bc/-de-+fgh *+a-bc-/de-+fgh *+a-bc/-ed-+fgh *+ab-c/-de-+fgh
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The regular expression for the complement of the language $L=\{a^nb^m \mid n \geq 4, m \leq 3\}$ is: $(\lambda +a+aa+aaa)b^*+a^*bbbb^*+(a+b)^*ba(a+b)^*$ $(\lambda +a+aa+aaa)b^*+a^*bbbbb^*+(a+b)^*ab(a+b)^*$ $(\lambda +a+aa+aaa)+a^*bbbbb^*+(a+b)^*ab(a+b)^*$ $(\lambda +a+aa+aaa)b^*+a^*bbbbb^*+(a+b)^*ba(a+b)^*$
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How 11010 is -6 ? According to me it should be -10 . Please explain anyone.
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The number of positive numbers of not more than 10 digits formed using 0,1,2,3?
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a. 2 b. 4 c. 1 d. 3
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Consider the following three tables $R, S$ and $T.$ In this question, all the join operations are natural joins $(\bowtie )$. $(\pi )$ ... (a) (b) (c) (d)
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Consider the following context-free grammar over the alphabet $\Sigma = \{a,b,c\}$ with $S$ as the start symbol:$S \rightarrow abScT \mid abcT$$T \rightarrow bT \mid b$ ... $\{\left ( ab \right )^{n}\left ( cb^{n} \right )^{m} \mid m,n \geq 1 \}$
Let $T$ be a binary search tree with $15$ nodes. The minimum and maximum possible heights of $T$ are: Note: The height of a tree with a single node is $0$. $4$ and $15$ respectively. $3$ and $14$ respectively. $4$ and $14$ respectively. $3$ and $15$ respectively.
Let $T$ be a tree with $10$ vertices. The sum of the degrees of all the vertices in $T$ is ________