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Recent questions tagged engineering-mathematics

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421
Probability- Gravner-11
We have a bag that contains $100$ balls, $50$ of them red and $50$ blue. Select $5$ balls at random. What is the probability that $3$ are blue and $2$ are red?
We have a bag that contains $100$ balls, $50$ of them red and $50$ blue. Select $5$ balls at random. What is the probability that $3$ are blue and $2$ are red?
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422
Probability - Gravner-10
A fair coin is tossed 10 times. What is the probability that we get exactly 5 Heads?
A fair coin is tossed 10 times. What is the probability that we get exactly 5 Heads?
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423
Probability - Gravner-9
A group consists of $3$ Norwegians, $4$ Swedes, and $5$ Finns, and they sit at random around a table. What is the probability that all groups end up sitting together?
A group consists of $3$ Norwegians, $4$ Swedes, and $5$ Finns, and they sit at random around a table. What is the probability that all groups end up sitting together?
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424
Probability - Gravner-8
Sit $3$ men and $3$ women at random (1) in a row of chairs and (2) around a table. Compute Probability (all women sit together). In case (2), also compute Probability (men and women alternate).
Sit $3$ men and $3$ women at random (1) in a row of chairs and (2) around a table. Compute Probability (all women sit together). In case (2), also compute Probability (me...
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425
Probability - Gravner-7
A bag has $6$ pieces of paper, each with one of the letters, $E .E, P,P,P,$ and $R$, on it. Pull $6$ pieces at random out of the bag (1) without , and (2) with replacement. What is the probability that these pieces, in order, spell $PEPPER$?
A bag has $6$ pieces of paper, each with one of the letters, $E .E, P,P,P,$ and $R$, on it. Pull $6$ pieces at random out of the bag (1) without , and (2) with replaceme...
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426
Probability - Gravner-6.a
Shuffle a deck of cards. Compute the probability : Probability for(top card is an Ace)
Shuffle a deck of cards. Compute the probability :Probability for(top card is an Ace)
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427
Probability - Gravner-5
Roll a die $4$ times. What is the probability that you get different numbers?
Roll a die $4$ times. What is the probability that you get different numbers?
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428
Probability - Gravner-4
Roll Two dice. What is the most likely sum?
Roll Two dice. What is the most likely sum?
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429
Probability - Gravner-3
Toss three fair coins. What is the probability of exactly one Heads$(H)$ ?
Toss three fair coins. What is the probability of exactly one Heads$(H)$ ?
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430
Probability - Gravner-2
In a family with $4$ children, what is the probability of a $2:2$ boy-girl split?
In a family with $4$ children, what is the probability of a $2:2$ boy-girl split?
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431
Ace booklet questions no 07
If A∆B = (A intersection B) whole complement than the universal set is??
If A∆B = (A intersection B) whole complement than the universal set is??
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434
ISI2017-MMA-4
Let $S\subseteq \mathbb{R}$. Consider the statement “There exists a continuous function $f:S\rightarrow S$ such that $f(x) \neq x$ for all $x \in S.$ ” This statement is false if $S$ equals $[2,3]$ $(2,3]$ $[-3,-2] \cup [2,3]$ $(-\infty,\infty)$
Let $S\subseteq \mathbb{R}$. Consider the statement “There exists a continuous function $f:S\rightarrow S$ such that $f(x) \neq x$ for all $x \in S.$ ”This statement ...
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435
ISI2017-MMA-5
If $A$ is a $2 \times 2$ matrix such that $trace \: A = det \: A =3$, then what is the trace of $A^{-1}$? $1$ $1/3$ $1/6$ $1/2$
If $A$ is a $2 \times 2$ matrix such that $trace \: A = det \: A =3$, then what is the trace of $A^{-1}$?$1$$1/3$$1/6$$1/2$
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436
ISI2017-MMA-6
In a class of $80$ students, $40$ are girls and $40$ are boys. Also, exactly $50$ students wear glasses. Then the set of all possible numbers of boys without glasses is $\{0, \dots , 30\}$ $\{10, \dots , 30\}$ $\{0, \dots , 40\}$ none of these
In a class of $80$ students, $40$ are girls and $40$ are boys. Also, exactly $50$ students wear glasses. Then the set of all possible numbers of boys without glasses is$\...
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439
ISI2017-MMA-14
Let $(v_n)$ be a sequence defined by $v_1=1$ and $v_{n+1}=\sqrt{v_n^2 +(\frac{1}{5})^n}$ for $n\geq1$. Then $\lim _{n\rightarrow \infty} v_n$ is $\sqrt{5/3}$ $\sqrt{5/4}$ $1$ nonexistent
Let $(v_n)$ be a sequence defined by $v_1=1$ and $v_{n+1}=\sqrt{v_n^2 +(\frac{1}{5})^n}$ for $n\geq1$. Then $\lim _{n\rightarrow \infty} v_n$ is$\sqrt{5/3}$$\sqrt{5/4}$$1...
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440
ISI2017-MMA-15
The diagonal elements of a square matrix $M$ are odd integers while the off-diagonals are even integers. Then $M$ must be singular $M$ must be nonsingular there is not enough information to decide the singularity of $M$ $M$ must have a positive eigenvalue
The diagonal elements of a square matrix $M$ are odd integers while the off-diagonals are even integers. Then$M$ must be singular$M$ must be nonsingularthere is not enoug...
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443
ISI2017-MMA-19
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3-px+q=0$, then the value of the determinant $\begin{vmatrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{vmatrix}$ is $p$ $p^2$ $0$ $p^2+6q$
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3-px+q=0$, then the value of the determinant $\begin{vmatrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \g...
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444
ISI2017-MMA-20
The number of ordered pairs $(X, Y)$, where $X$ and $Y$ are $n \times n$ real, matrices such that $XY-YX=I$ is $0$ $1$ $n$ infinite
The number of ordered pairs $(X, Y)$, where $X$ and $Y$ are $n \times n$ real, matrices such that $XY-YX=I$ is$0$$1$$n$infinite
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447
ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix} 1 & 1 & 2 & 2 \\ 1 & 1 & 1 & 3 \\ a & b & b & 1 \end{pmatrix}$ is 2 for some real numbers $a$ and $b$. Then the $b$ equals $1$ $3$ $1/2$ $1/3$
Suppose the rank of the matrix $\begin{pmatrix} 1 & 1 & 2 & 2 \\ 1 & 1 & 1 & 3 \\ a & b & b & 1 \end{pmatrix}$ is 2 for some real numbers $a$ and $b$. Then the $b$ equals...
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1 votes
1 answer
449
Degree Sequence
$<2, 2, 2, 1, 1>$ degree sequence is NOT graphic for simple graphs$?$
$<2, 2, 2, 1, 1>$ degree sequence is NOT graphic for simple graphs$?$
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450
ace booklet
whats ans of this qn and please explain
whats ans of this qn and please explain
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