# Recent activity by Golam Murtuza

1
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant? Hint: Use modulo $2$ arithmetic. $20160$ $32767$ $49152$ $57343$ $65520$
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In the following $C$ program fragment, $j$, $k$, $n$ and TwoLog_n are integer variables, and $A$ is an array of integers. The variable $n$ is initialized to an integer $\geqslant 3$, and TwoLog_n is initialized to the value of $2^*\lceil \log_2(n) \rceil$ for (k = 3; k <= n; k++) A[k] ... $\left\{m \mid m \leq n, \text{m is prime} \right\}$ { }
3
Consider the set of strings on $\{0,1\}$ in which, every substring of $3$ symbols has at most two zeros. For example, $001110$ and $011001$ are in the language, but $100010$ is not. All strings of length less than $3$ are also in the language. A partially completed DFA that accepts this ...
4
Match the following: $\small{\begin{array}{|ll|ll|}\hline \text{E.} & \text{Checking that identifiers are declared before their use} & \text{P.} & \text{$ ... $\text{E-R, F-P, G-S, H-Q}$ $\text{E-R, F-P, G-Q, H-S}$ $\text{E-P, F-R, G-S, H-Q}$
5
Choose the correct alternatives (More than one may be correct). Recursive languages are: A proper superset of context free languages. Always recognizable by pushdown automata. Also called type $0$ languages. Recognizable by Turing machines.
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Consider the following statement: $\text{ For all languages }L \subseteq \{0, 1\}^*, \text{ if }L^* \text{ is regular then L is regular.}$ Is the above statement true? Justify your answer.
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Which of the following are regular sets? $\left\{a^nb^{2m} \mid n \geq 0, m \geq 0 \right\}$ $\left\{a^nb^m \mid n =2m \right\}$ $\left\{a^nb^m \mid n \neq m \right\}$ $\left\{xcy \mid x, y, \in \left\{a, b\right\} ^* \right\}$ I and IV only I and III only I only IV only
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Consider the following two statements: $S_1: \left\{ 0^{2n} \mid n \geq 1 \right\}$ is a regular language $S_2: \left\{0^m1^n0^{m+n} \mid m \geq 1 \text{ and } n \geq 1 \right\}$ is a regular language Which of the following statement is correct? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
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Which of the following three statements are true? Prove your answer. The union of two recursive languages is recursive. The language $\{O^n \mid n\text{ is a prime} \}$ is not regular. Regular languages are closed under infinite union.
10
Choose the correct alternatives (more than one may be correct) and write the corresponding letters only: For a context free grammar, FOLLOW(A) is the set of terminals that can appear immediately to the right of non-terminal $A$ in some "sentential" form. We define two ... be different. FOLLOW(A) and RFOLLOW(A) are always the same. All the three sets are identical. All the three sets are different.
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Which of the following correctly describes $LR(k)$ parsing? The input string is alternately scanned left to right and right to left with $k$ reversals. Input string is scanned once left to right with rightmost derivation and $k$ symbol look-ahead. $LR(k)$ grammers ... string. Input string is scanned from left to right once with $k$ symbol to the right as look-ahead to give left-most derivation.
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$\int_{0}^{1} \ln x\, \mathrm{d}x=$ $1$ $-1$ $\infty$ $-\infty$ None of the above.
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Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then $X< 1$ $X>\frac{3}{2}$ $1< X< \frac{3}{2}$ none of the above
14
Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[-1, 1]$ $f$ is not bounded in $[-1, 1]$ $A$ is nonzero and finite II only III only II and III only I, II and III
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The relational DBMS is constructed on relational principles which are based on  The matrix theory  Axiomatic principles  Primary key  Primary & foreign key relationship
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For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\phi \in 2^{A}$ $\phi \subseteq 2^{A}$ $\left\{5,\left\{6\right\}\right\} \in 2^{A}$ $\left\{5,\left\{6\right\}\right\} \subseteq 2^{A}$ I and III only II and III only I, II and III only I, II and IV only
17
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k\\$ $^{\left(\frac{n^2-n}{2}\right)}C_n\\$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
18
The following numbers are inserted into an empty binary search tree in the given order: $10, 1, 3, 5, 15, 12, 16$. What is the height of the binary search tree (the height is the maximum distance of a leaf node from the root)? $2$ $3$ $4$ $6$
19
Consider the following $2-3-4$ tree (i.e., B-tree with a minimum degree of two) in which each data item is a letter. The usual alphabetical ordering of letters is used in constructing the tree. What is the result of inserting $G$ in the above tree? None of the above
20
A database of research articles in a journal uses the following schema. $\text{(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)}$ The primary key is '$\text{(VOLUME, NUMBER, STARTPAGE, ENDPAGE)}$ ... the weakest normal form that the new database satisfies, but the old one does not? $1NF$ $2NF$ $3NF$ $\text{BCNF}$
21
Mola is a digital platform for taxis in a city. It offers three types of rides - Pool, Mini and Prime. The table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of the revenue contributed by Prime to the total revenues ... $16.24$ $23.97$ $25.86$ $38.74$
22
Consider the sequence $S_0, S_1, S_2, \dots$ defined as follows: $S_0=0, \: S_1=1 \:$ and $S_n=2S_{n-1} + S_{n-2}$ for $n \geq 2$. Which of the following statements is FALSE? for every $n \geq 1$, $S_{2n}$ is even for every $n \geq 1$, $S_{2n+1}$ is odd for every $n \geq 1$, $S_{3n}$ is multiple of $3$ for every $n \geq 1$, $S_{4n}$ is multiple of $6$ none of the above
23
Data transmitted on a link uses the following $2D$ parity scheme for error detection: Each sequence of $28$ bits is arranged in a $4\times 7$ matrix (rows $r_0$ through $r_3$, and columns $d_7$ through $d_1$) and is padded with a column $d_0$ and row $r_4$ of parity bits ... shows data received by a receiver and has $n$ corrupted bits. What is the mini­mum possible value of $n$? $1$ $2$ $3$ $4$
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Consider the following C program: #include<stdio.h> struct Ournode{ char x, y, z; }; int main() { struct Ournode p={'1', '0', 'a'+2}; struct Ournode *q=&p; printf("%c, %c", *((char*)q+1), *((char*)q+2)); return 0; } The output of this program is: 0, c 0, a+2 '0', 'a+2' '0', 'c'
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Let $P_{1},P_{2},\ldots,P_{n}$ be $n$ points in the $xy-$plane such that no three of them are collinear. For every pair of points $P_{i}$ and $P_{j}$, let $L_{ij}$ be the line passing through them. Let $L_{ab}$ be the line with the steepest ... the largest or the smallest $y$-coordinate among all the points The difference between $x$-coordinates $P_{a}$ and $P_{b}$ is minimum None of the above
Consider the following C functions: int f1 (int n) { if(n == 0 || n == 1) return n; else return (2 * f1(n-1) + 3 * f1(n-2)); } int f2(int n) { int i; int X[N], Y[N], Z[N]; X[0] = Y[0] = Z[0] = 0; X[1] = 1; Y[1] = 2; Z[1] = 3; for(i = 2; i <= n; i++){ ... X[i]; Z[i] = 3 * X[i]; } return X[n]; } $f1(8)$ and $f2(8)$ return the values $1661$ and $1640$ $59$ and $59$ $1640$ and $1640$ $1640$ and $1661$
A Boolean formula is said to be a $tautology$ if it evaluates to TRUE for all assignments to its variables. Which one of the following is NOT a tautology? $(( p \vee q) \wedge (r \vee s)) \Rightarrow (( p \wedge r) \vee q \vee s)$ ... $(( p \vee q ) \wedge ( r \vee s)) \Rightarrow ( p \vee q)$