# Recent activity by rajatmyname

1
In the IEEE floating point representation the hexadecimal value $0\text{x}00000000$ corresponds to The normalized value $2^{-127}$ The normalized value $2^{-126}$ The normalized value $+0$ The special value $+0$
2
For the synchronous counter shown in Fig.3, write the truth table of $Q_{0}, Q_{1}$,and $Q_{2}$ after each pulse, starting from $Q_{0}=Q_{1}=Q_{2}=0$ and determine the counting sequence and also the modulus of the counter.
3
Consider the following Boolean function of four variables $f(A, B, C, D) = Σ(2, 3, 6, 7, 8, 9, 10, 11, 12, 13)$ The function is independent of one variable independent of two variables independent of three variable dependent on all the variables
4
Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function? XOR gates, NOT gates $2$ to $1$ multiplexers AND gates, XOR gates Three-input gates that output $(A.B) + C$ for the inputs $A, B$ and $C$.
5
Find the minimum product of sums of the following expression $f=ABC + \bar{A}\bar{B}\bar{C}$
6
An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is ... one of the following options is closest to the probability that the face value exceeds $3$? $0.453$ $0.468$ $0.485$ $0.492$
7
Consider the following state diagram and its realization by a JK flip flop The combinational circuit generates J and K in terms of x, y and Q. The Boolean expressions for J and K are : $\overline {x \oplus y}$ and $\overline {x \oplus y}$ $\overline {x \oplus y}$ and ${x \oplus y}$ ${x \oplus y}$ and $\overline {x \oplus y}$ ${x \oplus y}$ and ${x \oplus y}$
8
Two eight bit bytes $1100 0011$ and $0100 1100$ are added. What are the values of the overflow, carry and zero flags respectively, if the arithmetic unit of the CPU uses $2$'s complement form? $0, 1, 1'$ $1, 1, 0$ $1, 0, 1$ $0, 1, 0$
9
How many distinct ways are there to split $50$ identical coins among three people so that each person gets at least $5$ coins? $3^{35}$ $3^{50}-2^{50}$ $\binom{35}{2}$ $\binom{50}{15} \cdot 3^{35}$ $\binom{37}{2}$
10
There are $n$ kingdoms and $2n$ champions. Each kingdom gets $2$ champions. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^{n} . n!}$ $\frac{n!}{2}$ None of the above.
11
It is required to divide the $2n$ members of a club into $n$ disjoint teams of $2$ members each. The teams are not labelled. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^n . n!}$ $\frac{n!}{2}$ None of the above.
12
Suppose a box contains 20 balls: each ball has a distinct number in $\left\{1,\ldots,20\right\}$ written on it. We pick 10 balls (without replacement) uniformly at random and throw them out of the box. Then we check if the ball with number $1"$ on it is present in the box. If it is ... that the ball with number $2"$ on it is present in the box? $9/20$ $9/19$ $1/2$ $10/19$ None of the above
13
A box contains $5$ fair and $5$ biased coins. Each biased coin has a probability of head $\frac{4}{5}$. A coin is drawn at random from the box and tossed. Then the second coin is drawn at random from the box ( without replacing the first one). Given that the first coin has shown head, the ... that the second coin is fair is $\frac{20}{39}\\$ $\frac{20}{37}\\$ $\frac{1}{2}\\$ $\frac{7}{13}$
14
A biased coin is tossed repeatedly. Assume that the outcomes of different tosses are independent and probability of heads is $\dfrac{2}{3}$ in each toss. What is the probability of obtaining an even number of heads in $5$ ... $\left(\dfrac{124}{243}\right)$ $\left(\dfrac{125}{243}\right)$ $\left(\dfrac{128}{243}\right)$
15
The probability of throwing six perfect dices and getting six different faces is $1 -\dfrac{ 6!} { 6^{6}}$ $\dfrac{6! }{ 6^{6}}$ $6^{-6}$ $1 - 6^{-6}$ None of the above.
16
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
17
Consider the sequence $\langle x_n \rangle , \: n \geq 0$ defined by the recurrence relation $x_{n+1} = c . x^2_n -2$, where $c > 0$. Suppose there exists a non-empty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges to a limit. The sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1-\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c-1}$
18
An FM radio channel has a repository of $10$ songs. Each day, the channel plays $3$ ...
19
Suppose that the expectation of a random variable $X$ is $5$. Which of the following statements is true? There is a sample point at which $X$ has the value $5$. There is a sample point at which $X$ has value greater than $5$. There is a sample point at which $X$ has a value greater than equal to $5$. None of the above
20
A fair dice (with faces numbered $1, . . . , 6$) is independently rolled repeatedly. Let $X$ denote the number of rolls till an even number is seen and let $Y$ denote the number of rolls till $3$ is seen. Evaluate $E(Y |X = 2)$. $6\frac{5}{6}$ $6$ $5\frac{1}{2}$ $6\frac{1}{3}$ $5\frac{2}{3}$
21
Assume that you are flipping a fair coin, i.e. probability of heads or tails is equal. Then the expected number of coin flips required to obtain two consecutive heads for the first time is. $4$ $3$ $6$ $10$ $5$
22
Can someone show how we can systematically come up with regular expression for language not containing string 101 on alphabet {0,1} by first creating DFA and then converting it to regular expression?
23
How many 7 length bit strings have atleast 3 consecutive ones?
24
Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives. 1)Nobody is writing gate can manage to write gate 2)Anyone is not writing gate can manage to write gate 3)Everybody writing gate can not manage to write gate
25
Given that B(x) means "x is a bear" F(x) means "x is a fish" and E(x,y) means "x eats y" What is the best English translation of $\forall x [F(x)\rightarrow \forall y(E(y,x)\rightarrow B(y))]$ A) All fish eat bears B) Every bears can eat fish C) Only bears eat fish D) Bears eat only fish