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1
For two n-bit strings x, y ∈ {0, 1}n, define z := x ⊕ y to be the bitwise XOR of the two strings (that is, if xi, yi, zi denote the i-th bits of x, y, z respectively, then zi = xi + yi mod 2). A function h : {0, 1}n → {0, 1}n is called linear if h(x ⊕ y) = h(x) ⊕ h(y), for every x, y ∈ {0, 1}n. The number of such linear functions for n ≥ 2: 2^n 2^2n 2^(n+1) n
asked Feb 15 in Combinatory vivek_mishra 40 views
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2
A $n\times n$ matrix $A$ is said to be $symmetric$ if $A^T=A$. Suppose $A$ is an arbitrary $2\times 2$ matrix. Then which of the following matrices are symmetric (here $0$ denotes the $2\times 2$ matrix consisting of zeros): $A^TA$ $\begin{bmatrix} 0&A^T \\ A & 0 \end{bmatrix}$ $AA^T$ $\begin{bmatrix} A & 0 \\ 0 & A^T \end{bmatrix}$
asked Jan 29 in Others soujanyareddy13 32 views
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3
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ where $\Phi(a=-2)=0.02,$ ... less than 0.02 $\int^{18} _{-\infty} \frac{1}{\sqrt{2\pi .2^2}}\exp\{-\frac{1}{2}(\frac{x-24}{2})^2\}dx$
asked Jan 29 in Others soujanyareddy13 29 views
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4
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ where $\Phi(a=-2)=0.02,$ ... more than 0.4 less than 0.5
asked Jan 29 in Others soujanyareddy13 21 views
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5
$\text{Description for the following question:}$ If $Z$ is a continuous random variable which follows normal distribution with mean=$0$ and standard deviation=$1$, then $\mathbb{P}(Z\leq a)=\int^a _{-\infty} \frac{\exp\{\frac{-z^2}{2}\}}{\sqrt{2\pi}}dz=\Phi(a), $ ... will last more than $26$ months approximately equals $16\%$ is more than $15\%$ is less than $14\%$ is between $10\%$ and $15\%$
asked Jan 29 in Others soujanyareddy13 20 views
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6
$\text{Description for the following question:}$ Given below is the time table for a transcontinental train cutting across several time zones. All times given below are local time in respective cities. It is given that the average speed between any two cities is the same for both ... Which of the following pairs of cities are in the same time zone? Zut and Yag Xum and Wip Vaq and Uap Tix and Sab
asked Jan 29 in Others soujanyareddy13 14 views
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7
$\text{Description for the following question:}$ Given below is the time table for a transcontinental train cutting across several time zones. All times given below are local time in respective cities. It is given that the average speed between any two cities is the same for both way ... Write down the total time taken in minutes by the train to go from Zut to Raz.
asked Jan 29 in Others soujanyareddy13 14 views
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10
There are $n$ songs segregated into $3$ play lists. Assume that each play list has at least one song.The number of ways of choosing three songs consisting of one song from each play list is: $>\frac{n^3}{27}$ for all $n$ $\leq \frac{n^3}{27}$ for all $n$ $\left( \begin{array}{c} n \\ 3 \end{array} \right)$ for all $n$ $n^3$ for all $n$
asked Jan 29 in Others soujanyareddy13 15 views
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11
Consider the following functions defined from the interval $(0,1)$ to real numbers. Which of these functions attain their maximum value in the interval $(0,1)?$ $f(x)=\frac{1}{x(1-x)}$ $g(x)=-(x-0.75)^2$ $u(x)=\sin(\frac{\pi x}{2})$ $v(x)=x^2+2x$
asked Jan 29 in Others soujanyareddy13 18 views
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12
A farmer owns $50$ papaya trees. Each tree produces $600$ papayas in a year. For each additional tree planted in the orchard, the output of each tree (including the pre-existing ones) drops by $5$ papayas. How many trees should be added to the existing orchard in order to maximize the total production of papayas?
asked Jan 29 in Others soujanyareddy13 20 views
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13
Let $a,b$ be numbers between $1$ and $2$ and let $c,d$ be numbers between $3$ and $4$. Let $u=a^{-1},v=b^{-1},w=c^{-1}$ and $x=d^{-1}$. Say which of the following inequalities are true: $(a+b+c+d)(u+v+w+x)>16$ $(a^4+b^4+c^4+d^4)\leq 4abcd$ $(a^2+b^2)wx\leq (c^2+d^2)uv$ $d(a^3+b^3+c^3)<3abc$
asked Jan 29 in Others soujanyareddy13 16 views
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14
In the code fragment below, $\text{start}$ and $\text{end}$ are integer values and $\text{square(x)}$ is a function that returns $\text{Ture}$ if $\text{x}$ is a perfect square and $\text{False}$ otherwise. i := 0; j := 0; k :=0; for m in [start,start+1,...,end] { if(square(m)=True) ... $\text{j = k-i if (end - start)}$ is even $\text{i = k-j if (end - start)}$ is odd
asked Jan 29 in Others soujanyareddy13 14 views
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15
Given the following definition of the function $foo$, what does $foo(1037,2)$ return? Note that $a//b$ denotes the quotient (integer part) of $a\div b$, for integers $a$ and $b$. For instance $7//3$ is $2$. function foo(n,d) { x:=0; while(n>=1) { x:=x+1; n:=n//d; } return(x); }
asked Jan 29 in Others soujanyareddy13 18 views
1 vote
0 answers
16
There are $7$ switches on a switchboard, some of which are $on$ and some of which are $off$. In one move, you pick any $2$ switches and toggle each of them-if the switch you pick is currently $off$, you turn it $on$, if it is $on$, you turn it $off$. Your aim is to execute a sequence ... $\text{(off,on,on,on,off,on,off)}$ $\text{(off,on,off,off,on,off,on)}$ $\text{(off,on,off,off,off,on,off)}$
asked Jan 29 in Others soujanyareddy13 15 views
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0 answers
17
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. Let $N=\{1,2,3,...\}$ be the set of natural integers and let $f:N\times N \mapsto N$ be defined by $f(m,n)=(2m-1)*2^n.$Is $f$ injective? Is $f$ surjective? Give reasons.
asked Jan 29 in Others soujanyareddy13 12 views
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18
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 $A(i,j)$ denotes the $(i.j)^{th}$ entry of matrix $A$.) 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
asked Jan 29 in Others soujanyareddy13 15 views
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0 answers
19
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. Find $A^{10}$ where $A$ is the matrix $\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$. Justify your answer.
asked Jan 29 in Others soujanyareddy13 9 views
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0 answers
20
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. In computing, a floating point operation (flop) is any one of the following operations performed by a computer ... $c_{ij}=\displaystyle\sum^5 _{k=1} a_{ik} b_{kj}$. How does this number change if both the matrices are upper triangular?
asked Jan 29 in Others soujanyareddy13 13 views
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0 answers
21
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. A function $f$ from the set $A$ to itself is said to have a fixed point if $f(i)=i$ for some $i$ in $A$. Suppose $A$ is the set $\{a,b,c,d\}$. Find the number of bijective functions from the set $A$ to itself having no fixed point.
asked Jan 29 in Others soujanyareddy13 11 views
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22
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. A $4$-digit number is represented as $abcd$ i.e. $a\times 10^3 +b\times 10^2 +c\times10+d,$ where $a\neq0.$ Suppose the number $dcba$, obtained by reversing the digits of $abcd$, is $9$ times $abcd$. Find the number $abcd$.
asked Jan 29 in Others soujanyareddy13 9 views
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0 answers
23
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. A computer password requires you to use exactly $1$ uppercase letter, $3$ lowercase letters, $3$ digits and $2$ special characters (there are $33$ special characters that can be used). In how many ways can you create such a password$?$
asked Jan 29 in Others soujanyareddy13 11 views
0 votes
0 answers
24
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. $\text{Description for the following question:}$ Suppose $X$ is the number of successes ... one credit default in a year. You can assume that whether a given debtor will default or not is independent of the behavior of other debtors.
asked Jan 29 in Others soujanyareddy13 14 views
0 votes
0 answers
25
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. $\text{Description for the following question:}$ Suppose $X$ is the number of successes out of ... $\mathbb{E}(X)=np$. For the situation in the previous problem, what is the expected number defaults?
asked Jan 29 in Others soujanyareddy13 11 views
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0 answers
26
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. $\text{Description for the following question:}$ Suppose $X$ is the number of successes out of $n$ ... on his/her credit than the bank loses the entire loan amount. What is the expected revenue of the bank from a loan of $Rs. 100,000?$
asked Jan 29 in Others soujanyareddy13 10 views
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27
$\text{Description for the following question:}$ An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (in percentages) for the ice cream company over the last summer. The bar chart shows the detail of breakdown for strawberry flavor by states in lakhs of rupees. What are the total sales of the strawberry flavor?
asked Jan 29 in Others soujanyareddy13 21 views
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0 answers
28
$\text{Description for the following question:}$ An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (in percentages) for the ice cream company over the last summer. The bar chart shows the detail of breakdown for strawberry flavor by states in lakhs of rupees. What is the total revenue of the ice cream company?
asked Jan 29 in Others soujanyareddy13 10 views
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0 answers
29
$\text{Description for the following question:}$ An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (in percentages) for the ice cream company over the last summer. The bar chart shows the detail of breakdown for strawberry flavor by states in lakhs of rupees. What are the total sales of the chocolate flavor?
asked Jan 29 in Others soujanyareddy13 13 views
0 votes
0 answers
30
$\text{Description for the following question:}$ An Ice-cream company mainly operates in the five southern states of India. The pie chart shows the breakdown of revenues (in percentages) for the ice cream company over the last summer. The bar charts shows the detail of ... sold in the same proportion across the five states, then what are the sales of chocolate in Tamil Nadu, in lakhs of rupees?
asked Jan 29 in Others soujanyareddy13 9 views
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