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Recent questions in Engineering Mathematics
42
votes
5
answers
8801
GATE IT 2007 | Question: 21
Which one of these first-order logic formulae is valid? $\forall x\left(P\left(x\right) \implies Q\left(x\right)\right) \implies \left(∀xP\left(x\right)\implies \forall xQ\left(x\right)\right)$ ... $\forall x \exists y P\left(x, y\right)\implies \exists y \forall x P\left(x, y\right)$
Which one of these first-order logic formulae is valid?$\forall x\left(P\left(x\right) \implies Q\left(x\right)\right) \implies \left(∀xP\left(x\right)\implies \forall ...
Ishrat Jahan
10.3k
views
Ishrat Jahan
asked
Oct 29, 2014
Mathematical Logic
gateit-2007
mathematical-logic
normal
first-order-logic
+
–
22
votes
3
answers
8802
GATE IT 2007 | Question: 16
The minimum positive integer $p$ such that $3^{p} \pmod {17} = 1$ is $5$ $8$ $12$ $16$
The minimum positive integer $p$ such that $3^{p} \pmod {17} = 1$ is$5$$8$$12$$16$
Ishrat Jahan
7.3k
views
Ishrat Jahan
asked
Oct 29, 2014
Set Theory & Algebra
gateit-2007
set-theory&algebra
normal
number-theory
+
–
61
votes
8
answers
8803
GATE IT 2007 | Question: 2
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvectors of $A?$ $5$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5 - √5)}{2}$
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvect...
Ishrat Jahan
16.0k
views
Ishrat Jahan
asked
Oct 29, 2014
Linear Algebra
gateit-2007
linear-algebra
eigen-value
normal
+
–
20
votes
4
answers
8804
GATE IT 2007 | Question: 1
Suppose there are two coins. The first coin gives heads with probability $\dfrac{5}{8}$ when tossed, while the second coin gives heads with probability $\dfrac{1}{4}.$ One of the two coins is picked up at random with equal probability and tossed. What is the probability of ... $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{7}{16}\right)$ $\left(\dfrac{5}{32}\right)$
Suppose there are two coins. The first coin gives heads with probability $\dfrac{5}{8}$ when tossed, while the second coin gives heads with probability $\dfrac{1}{4}.$ On...
Ishrat Jahan
4.3k
views
Ishrat Jahan
asked
Oct 29, 2014
Probability
gateit-2007
probability
normal
binomial-distribution
+
–
22
votes
5
answers
8805
GATE IT 2008 | Question: 31
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ? $f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \frac{1}{x} &\text { otherwise}\end{cases}$ $2$ $2 \frac{1}{12}$ $2\frac{1}{6}$ $2\frac{1}{2}$
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ?$$f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \fr...
Ishrat Jahan
7.6k
views
Ishrat Jahan
asked
Oct 28, 2014
Calculus
gateit-2008
calculus
maxima-minima
normal
+
–
38
votes
7
answers
8806
GATE IT 2008 | Question: 29
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the other columns S3 ... solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?S1: Each row of $M$ can be represented as a linear combination of...
Ishrat Jahan
9.4k
views
Ishrat Jahan
asked
Oct 28, 2014
Linear Algebra
gateit-2008
linear-algebra
normal
matrix
+
–
33
votes
8
answers
8807
GATE IT 2008 | Question: 28
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only
Consider the following Hasse diagrams. Which all of the above represent a lattice?(i) and (iv) only(ii) and (iii) only(iii) only(i), (ii) and (iv) only
Ishrat Jahan
14.9k
views
Ishrat Jahan
asked
Oct 28, 2014
Set Theory & Algebra
gateit-2008
set-theory&algebra
lattice
normal
+
–
43
votes
6
answers
8808
GATE IT 2008 | Question: 27
$G$ is a simple undirected graph. Some vertices of $G$ are of odd degree. Add a node $v$ to $G$ and make it adjacent to each odd degree vertex of $G$. The resultant graph is sure to be regular complete Hamiltonian Euler
$G$ is a simple undirected graph. Some vertices of $G$ are of odd degree. Add a node $v$ to $G$ and make it adjacent to each odd degree vertex of $G$. The resultant graph...
Ishrat Jahan
13.9k
views
Ishrat Jahan
asked
Oct 28, 2014
Graph Theory
gateit-2008
graph-theory
graph-connectivity
normal
+
–
23
votes
1
answer
8809
GATE IT 2008 | Question: 26
Consider the field $C$ of complex numbers with addition and multiplication. Which of the following form(s) a subfield of $C$ with addition and multiplication? S1: the set of real numbers S2: $\{(a + ib) \mid a$ and $b$ are rational numbers$\}$ S3: $\{a + ib \mid (a^2 + b^2) \leq 1\}$ S4: $\{ia \mid a \text{ is real}\}$ only S1 S1 and S3 S2 and S3 S1 and S2
Consider the field $C$ of complex numbers with addition and multiplication. Which of the following form(s) a subfield of $C$ with addition and multiplication?S1: the set...
Ishrat Jahan
3.9k
views
Ishrat Jahan
asked
Oct 28, 2014
Set Theory & Algebra
gateit-2008
set-theory&algebra
normal
fields
non-gate
+
–
38
votes
3
answers
8810
GATE IT 2008 | Question: 25
In how many ways can $b$ blue balls and $r$ red balls be distributed in $n$ distinct boxes? $\frac{(n+b-1)!\,(n+r-1)!}{(n-1)!\,b!\,(n-1)!\,r!}$ $\frac{(n+(b+r)-1)!}{(n-1)!\,(n-1)!\,(b+r)!}$ $\frac{n!}{b!\,r!}$ $\frac{(n + (b + r) - 1)!} {n!\,(b + r - 1)}$
In how many ways can $b$ blue balls and $r$ red balls be distributed in $n$ distinct boxes?$\frac{(n+b-1)!\,(n+r-1)!}{(n-1)!\,b!\,(n-1)!\,r!}$$\frac{(n+(b+r)-1)!}{(n-1)!\...
Ishrat Jahan
8.3k
views
Ishrat Jahan
asked
Oct 27, 2014
Combinatory
gateit-2008
combinatory
normal
+
–
14
votes
3
answers
8811
GATE IT 2008 | Question: 24
The exponent of $11$ in the prime factorization of $300!$ is $27$ $28$ $29$ $30$
The exponent of $11$ in the prime factorization of $300!$ is$27$$28$$29$$30$
Ishrat Jahan
8.0k
views
Ishrat Jahan
asked
Oct 27, 2014
Set Theory & Algebra
gateit-2008
set-theory&algebra
normal
number-theory
+
–
34
votes
5
answers
8812
GATE IT 2008 | Question: 23
What is the probability that in a randomly chosen group of $r$ people at least three people have the same birthday? $1-\dfrac{365-364 \dots (365-r+1)}{365^{r}}$ ... $\dfrac{365 \cdot 364 \dots (365-r+1)}{365^{r}}$
What is the probability that in a randomly chosen group of $r$ people at least three people have the same birthday?$1-\dfrac{365-364 \dots (365-r+1)}{365^{r}}$$\dfrac{365...
Ishrat Jahan
8.5k
views
Ishrat Jahan
asked
Oct 27, 2014
Probability
gateit-2008
probability
normal
+
–
43
votes
2
answers
8813
GATE IT 2008 | Question: 22
Which of the following is the negation of $[∀ x, α → (∃y, β → (∀ u, ∃v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, y))]$ $[∃ x, α → (∀y, β → (∃u, ∀ v, ¬y))]$ $[∀ x, ¬α → (∃y, ¬β → (∀u, ∃ v, ¬y))]$ $[∃ x, α \wedge (∀y, β \wedge (∃u, ∀ v, ¬y))]$
Which of the following is the negation of $[∀ x, α → (∃y, β → (∀ u, ∃v, y))]$$[∃ x, α → (∀y, β → (∃u, ∀ v, y))]$$[∃ x, α → (∀y, β → ...
Ishrat Jahan
7.7k
views
Ishrat Jahan
asked
Oct 27, 2014
Mathematical Logic
gateit-2008
mathematical-logic
normal
first-order-logic
+
–
68
votes
9
answers
8814
GATE IT 2008 | Question: 21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ is a first order formul...
Ishrat Jahan
14.8k
views
Ishrat Jahan
asked
Oct 27, 2014
Mathematical Logic
gateit-2008
first-order-logic
normal
+
–
58
votes
7
answers
8815
GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?$5$$4$$3$$2$
Ishrat Jahan
51.4k
views
Ishrat Jahan
asked
Oct 27, 2014
Graph Theory
gateit-2008
normal
graph-connectivity
+
–
34
votes
4
answers
8816
GATE IT 2008 | Question: 3
What is the chromatic number of the following graph? $2$ $3$ $4$ $5$
What is the chromatic number of the following graph? $2$$3$$4$$5$
Ishrat Jahan
8.2k
views
Ishrat Jahan
asked
Oct 27, 2014
Graph Theory
gateit-2008
graph-theory
graph-coloring
normal
+
–
21
votes
2
answers
8817
GATE IT 2008 | Question: 2
A sample space has two events $A$ and $B$ such that probabilities $P(A\cap B) = \dfrac{1}{2}, P(A') = \dfrac{1}{3}, P(B') =\dfrac{1}{3}$. What is $P(A\cup B)$ ? $\left(\dfrac{11}{12}\right)$ $\left(\dfrac{10}{12}\right)$ $\left(\dfrac{9}{12}\right)$ $\left(\dfrac{8}{12}\right)$
A sample space has two events $A$ and $B$ such that probabilities $P(A\cap B) = \dfrac{1}{2}, P(A') = \dfrac{1}{3}, P(B') =\dfrac{1}{3}$. What is $P(A\cup B)$ ?$\left(\df...
Ishrat Jahan
4.3k
views
Ishrat Jahan
asked
Oct 27, 2014
Probability
gateit-2008
probability
easy
+
–
19
votes
2
answers
8818
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric? Please explain how to calculate .
On a set of n elements, how many relations are there that are both irreflexive and antisymmetric?Please explain how to calculate .
shree
25.9k
views
shree
asked
Oct 24, 2014
Set Theory & Algebra
set-theory&algebra
relations
+
–
14
votes
4
answers
8819
GATE CSE 1996 | Question: 10
Let $A = \begin{bmatrix} a_{11} && a_{12} \\ a_{21} && a_{22} \end{bmatrix} \text { and } B = \begin{bmatrix} b_{11} && b_{12} \\ b_{21} && b_{22} \end{bmatrix}$ be two matrices such that $AB=I$ ... $CD =I$. Express the elements of $D$ in terms of the elements of $B$.
Let $A = \begin{bmatrix} a_{11} && a_{12} \\ a_{21} && a_{22} \end{bmatrix} \text { and } B = \begin{bmatrix} b_{11} && b_{12} \\ b_{21} && b_{22} \end{bmatrix}$ be two m...
Kathleen
4.0k
views
Kathleen
asked
Oct 9, 2014
Linear Algebra
gate1996
linear-algebra
matrix
normal
descriptive
+
–
6
votes
1
answer
8820
GATE CSE 1996 | Question: 9
The Fibonacci sequence $\{f_1, f_2, f_3 \ldots f_n\}$ is defined by the following recurrence:$f_{n+2} = f_{n+1} + f_n, n \geq 1; f_2 =1:f_1=1$Prove by induction that every third element of the sequence is even.
The Fibonacci sequence $\{f_1, f_2, f_3 \ldots f_n\}$ is defined by the following recurrence:$$f_{n+2} = f_{n+1} + f_n, n \geq 1; f_2 =1:f_1=1$$Prove by induction that ev...
Kathleen
1.3k
views
Kathleen
asked
Oct 9, 2014
Combinatory
gate1996
recurrence-relation
proof
descriptive
+
–
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