# Questions by ankitgupta.1729

1
Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$
1 vote
2
Let $a_{n−1}a_{n−2}...a_0$ and $b_{n−1}b_{n−2}...b_0$ denote the $2's$ complement representation of two integers $A$ and $B$ respectively. Addition of $A$ and $B$ yields a sum $S=s_{n−1}s_{n−2}...s_0.$ The outgoing carry generated at the most significant bit ... $\oplus$ denotes the Boolean XOR operation. You may use the Boolean identity: $X+Y=X⊕Y⊕(XY)$ to prove your result.
3
Consider three relations $R_1(\underline{X},Y,Z), R_2(\underline{M},N,P),$ and $R_3(\underline{N,X})$. The primary keys of the relations are underlined. The relations have $100,30,$ and $400$ ... during execution of the join. For, (a), Order could be anything and min. cost =$100*30*400*$total size of all the attributes.
4
A $64000$-byte message is to be transmitted over a $2$-hop path in a store-and-forward packet-switching network. The network limits packets toa maximum size of $2032$ bytes including a $32$-byte header. The trans-mission lines in the network are error free and have a speed of $50$ Mbps. ... getting answer as $1*3*(T_t+T_p) + \;31*T_t$ where $T_t=0.325\; ms$ and $T_p=3.333\; ms$. Please Confirm.
5
For $n \geq1$, Let $a_{n} = \frac{1}{2^{2}} + \frac{2}{3^{2}} +.....+ \frac{n}{(n+1)^{2}}$ and $b_{n} = c_{0} + c_{1}r + c_{2}r^{2}+.....+c_{n}r^{n},$ where$|c_{k}| \leq M$ for all integers $k$ and $|r| \leq 1.$ ... $\{a_n\}$ is not a Cauchy sequence but $\{b_n\}$ is a Cauchy sequence (D) neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
6
Consider the group $G \;=\; \begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{-1} \end{pmatrix}\;: a,b \in \mathbb{R},a>0 \end{Bmatrix}$ ... is of finite order (D) $N$ is a normal subgroup and the quotient group is isomorphic to $\mathbb{R}^{+}$(the group of positive reals with multiplication).
1 vote
7
Let $P_{1},P_{2},$ and $P_{3}$ denote, respectively, the planes defined by $a_{1}x + b_{1}y + c_{1}z = \alpha _{1}$ $a_{2}x + b_{2}y + c_{2}z = \alpha _{2}$ $a_{3}x + b_{3}y + c_{3}z = \alpha _{3}$ ... then the planes (A) do not have any common point of intersection (B) intersect at a unique point (C) intersect along a straight line (D) intersect along a plane
1 vote
8
Let, $a_{n} \;=\; \left ( 1-\frac{1}{\sqrt{2}} \right ) ... \left ( 1- \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$ (A) equals $1$ (B) does not exist (C) equals $\frac{1}{\sqrt{\pi }}$ (D) equals $0$
9
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\;(\geq2)$ and $n\;(\geq1)$ respectively, satisfy $f(x^{2}+1) = f(x)g(x)$ $,$ for every $x\in \mathbb{R}$ , then (A) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) \neq 0$ (B) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) = 0$ (C) $f$ has $m$ distinct real roots (D) $f$ has no real root.
1 vote
10
S = $\int_{0}^{2\Pi } \sqrt{4cos^{2}t +sin^{2}t} \, \, dt$ Please explain how to solve it.
11
Prove that :- For all real symmetric matrices , No. of positive Pivots = No . of positive eigenvalues Can anyone please give the formal mathematical proof for the above statement ?
12
According to Universality of Uniform , We can get from the uniform distribution to the other distributions and also from other distributions back to the uniform distribution. Please explain how we would simulate from one distribution to other distribution ?
1 vote
13
State whether the following statement is TRUE or FALSE and why ? In a microprocessor-based system, if a bus (DMA) request and an interrupt request arrive simultaneously, the microprocessor attends first to the bus request.
1 vote
14
Prove that :- Every infinite cyclic group is isomorphic to the infinite cyclic group of integers under addition.
1 vote
15
16
I am not getting the problem which is given below. Please help Matrix transposition must be a familiar task. This problem is a generalization of it. We can assume matrix transposition as a permutation of the two dimensions of the matrix. Suppose the matrix ... and get the dimension values of the input tensor and then again linearize and get the location in the output tensor. file1 transpose
17
How many total Homeomorphically Irreducible Trees are possible with 'n' nodes ?
According to this Hopcroft's algorithm , we can efficiently minimize a Finite automata in $O(nlogn)$ time (polynomial time algo) then why it is said that Minimizing Finite Automata is computationally hard according to this link ?