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Highest voted questions in Engineering Mathematics
43
votes
5
answers
151
GATE CSE 2003 | Question: 5
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The nu...
Kathleen
10.5k
views
Kathleen
asked
Sep 16, 2014
Combinatory
gatecse-2003
combinatory
normal
+
–
43
votes
10
answers
152
GATE CSE 2003 | Question: 3
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right),{1}$ ${1},\left(\dfrac{1}{2}\right)$
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are$\left(\dfrac{1}{4...
Kathleen
11.8k
views
Kathleen
asked
Sep 16, 2014
Probability
gatecse-2003
probability
easy
conditional-probability
+
–
43
votes
5
answers
153
GATE CSE 2006 | Question: 3
The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false? It is not closed $2$ does not have an inverse $3$ does not have an inverse $8$ does not have an inverse
The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false?It is not closed$2$ does no...
Rucha Shelke
9.9k
views
Rucha Shelke
asked
Sep 16, 2014
Set Theory & Algebra
gatecse-2006
set-theory&algebra
group-theory
normal
+
–
43
votes
4
answers
154
GATE CSE 1991 | Question: 02-iv
Match the pairs in the following questions by writing the corresponding letters only. ...
Match the pairs in the following questions by writing the corresponding letters only.$$\begin{array}{|c|l|c|l|} \hline A. & \text{The number of distinct binary tree} & P....
Kathleen
5.0k
views
Kathleen
asked
Sep 12, 2014
Combinatory
gate1991
combinatory
normal
match-the-following
+
–
42
votes
9
answers
155
GATE CSE 2020 | Question: 39
Which one of the following predicate formulae is NOT logically valid? Note that $W$ is a predicate formula without any free occurrence of $x$. $\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W$ ... $\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W$
Which one of the following predicate formulae is NOT logically valid?Note that $W$ is a predicate formula without any free occurrence of $x$.$\forall x (p(x) \vee W) \equ...
Arjun
17.2k
views
Arjun
asked
Feb 12, 2020
Mathematical Logic
gatecse-2020
first-order-logic
mathematical-logic
2-marks
+
–
42
votes
11
answers
156
GATE CSE 2018 | Question: 1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$?$\frac...
gatecse
22.7k
views
gatecse
asked
Feb 14, 2018
Combinatory
gatecse-2018
generating-functions
normal
combinatory
1-mark
+
–
42
votes
1
answer
157
GATE CSE 2015 Set 3 | Question: 45
If for non-zero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25$ where $a \neq b \text{ then } \int\limits_1^2 f(x)dx$ is $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) + \frac{47b}{2} \end{bmatrix}$ ... $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) - \frac{47b}{2} \end{bmatrix}$
If for non-zero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25$ where $a \neq b \text{ then } \int\limits_1^2 f(x)dx$ is$\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - ...
go_editor
8.1k
views
go_editor
asked
Feb 15, 2015
Calculus
gatecse-2015-set3
calculus
integration
normal
+
–
42
votes
5
answers
158
GATE CSE 1996 | Question: 8
Let $F$ be the collection of all functions $f: \{1, 2, 3\} \to \{1, 2, 3\}$. If $f$ and $g \in F$, define an equivalence relation $\sim$ by $f\sim g$ if and only if $f(3) = g(3)$. Find the number of equivalence classes defined by $\sim$. Find the number of elements in each equivalence class.
Let $F$ be the collection of all functions $f: \{1, 2, 3\} \to \{1, 2, 3\}$. If $f$ and $g \in F$, define an equivalence relation $\sim$ by $f\sim g$ if and only if $f(3)...
Kathleen
6.0k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
relations
functions
normal
descriptive
+
–
42
votes
4
answers
159
GATE CSE 1995 | Question: 2.19
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is True Multiple Values False Cannot be determined
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusiv...
Kathleen
8.6k
views
Kathleen
asked
Oct 8, 2014
Mathematical Logic
gate1995
mathematical-logic
normal
propositional-logic
+
–
42
votes
4
answers
160
GATE CSE 1993 | Question: 17
Out of a group of $21$ persons, $9$ eat vegetables, $10$ eat fish and $7$ eat eggs. $5$ persons eat all three. How many persons eat at least two out of the three dishes?
Out of a group of $21$ persons, $9$ eat vegetables, $10$ eat fish and $7$ eat eggs. $5$ persons eat all three. How many persons eat at least two out of the three dishes?
Kathleen
8.2k
views
Kathleen
asked
Sep 29, 2014
Set Theory & Algebra
gate1993
set-theory&algebra
easy
set-theory
descriptive
+
–
42
votes
2
answers
161
GATE CSE 1997 | Question: 6.1
A partial order $≤$ is defined on the set $S=\left \{ x, a_1, a_2, \ldots, a_n, y \right \}$ as $x$ $\leq _{i}$ $a_{i}$ for all $i$ and $a_{i}\leq y$ for all $i$, where $n ≥ 1$. The number of total orders on the set S which contain the partial order $≤$ is $n!$ $n+2$ $n$ $1$
A partial order $≤$ is defined on the set $S=\left \{ x, a_1, a_2, \ldots, a_n, y \right \}$ as $x$ $\leq _{i}$ $a_{i}$ for all $i$ and $a_{i}\leq y$ for all $i$, where...
Kathleen
8.9k
views
Kathleen
asked
Sep 29, 2014
Set Theory & Algebra
gate1997
set-theory&algebra
partial-order
normal
+
–
42
votes
6
answers
162
GATE CSE 2014 Set 2 | Question: 51
A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.
A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.
go_editor
17.5k
views
go_editor
asked
Sep 28, 2014
Graph Theory
gatecse-2014-set2
graph-theory
numerical-answers
normal
graph-isomorphism
non-gate
+
–
42
votes
8
answers
163
GATE CSE 2004 | Question: 73
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
The inclusion of which of the following sets into$S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3,...
Kathleen
12.9k
views
Kathleen
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2004
set-theory&algebra
partial-order
normal
+
–
42
votes
5
answers
164
GATE CSE 2003 | Question: 60, ISRO2007-45
A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ ... $\int_0^t f_1(x)f_2(t-x)dx$ $\max\{f_1(t),f_2(t)\}$
A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ respectively denote the probability density functions of time taken to execute the two ...
Kathleen
9.1k
views
Kathleen
asked
Sep 17, 2014
Probability
gatecse-2003
probability
normal
isro2007
probability-density-function
+
–
41
votes
4
answers
165
GATE CSE 2018 | Question: 44
Consider Guwahati, $(G)$ and Delhi $(D)$ whose temperatures can be classified as high $(H)$, medium $(M)$ and low $(L)$. Let $P(H_G)$ denote the probability that Guwahati has high temperature. Similarly, $P(M_G)$ ... , then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is ________.
Consider Guwahati, $(G)$ and Delhi $(D)$ whose temperatures can be classified as high $(H)$, medium $(M)$ and low $(L)$. Let $P(H_G)$ denote the probability that Guwahati...
gatecse
13.8k
views
gatecse
asked
Feb 14, 2018
Probability
gatecse-2018
probability
conditional-probability
numerical-answers
2-marks
+
–
41
votes
4
answers
166
GATE CSE 1991 | Question: 15,b
Consider the following first order formula: ... Does it have finite models? Is it satisfiable? If so, give a countable model for it.
Consider the following first order formula:$\left ( \matrix{ \forall x \exists y : R(x,y) \\[1em] \Large \land \\[1em] \forall x \forall y : \left ( R(x,y) \impl...
ibia
6.3k
views
ibia
asked
Nov 16, 2015
Mathematical Logic
gate1991
mathematical-logic
first-order-logic
descriptive
+
–
41
votes
1
answer
167
GATE IT 2004 | Question: 34
Let $H_1, H_2, H_3,$ ... be harmonic numbers. Then, for $n \in Z^+$, $\sum_{j=1}^{n} H_j$ can be expressed as $nH_{n+1} - (n + 1)$ $(n + 1)H_n - n$ $nH_n - n$ $(n + 1) H_{n+1} - (n + 1)$
Let $H_1, H_2, H_3,$ ... be harmonic numbers. Then, for $n \in Z^+$, $\sum_{j=1}^{n} H_j$ can be expressed as$nH_{n+1} - (n + 1)$$(n + 1)H_n - n$$nH_n - n$$(n + 1) H_{n+...
Ishrat Jahan
5.6k
views
Ishrat Jahan
asked
Nov 2, 2014
Combinatory
gateit-2004
recurrence-relation
combinatory
normal
+
–
41
votes
9
answers
168
GATE IT 2004 | Question: 31
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments: $P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$ $Q: [(¬p ∧q) ∧ [q → (p → r)]] → ¬r$ $R: [[(q ∧ r) → p] ∧ (¬q \vee p)] → r$ $S: [p ∧ (p → r) ∧ (q \vee ¬ r)] → q$ Which of the above arguments are valid? $P$ and $Q$ only $P$ and $R$ only $P$ and $S$ only $P, Q, R$ and $S$
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments:$P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$$Q: [(¬p ∧q) �...
Ishrat Jahan
11.8k
views
Ishrat Jahan
asked
Nov 2, 2014
Mathematical Logic
gateit-2004
mathematical-logic
normal
propositional-logic
+
–
41
votes
3
answers
169
GATE CSE 1994 | Question: 1.10
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$? $g=g^{-1} \text{ for every } g \in G$ $g=g^2 \text{ for every }g \in G$ $(goh)^2 = g^2oh^2 \text{ for every } g, h \in G$ $G$ is of finite order
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$?$g=g^{-1} \text{ for every } g \in G$$g=g^2 \text{ for every }g \in G$$(goh)...
Kathleen
10.6k
views
Kathleen
asked
Oct 4, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
group-theory
normal
+
–
41
votes
3
answers
170
GATE CSE 2014 Set 3 | Question: 4
Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues? If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is ... eigenvalues are positive. If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues?If the trace of the matrix is positive and the determinant of the...
go_editor
11.3k
views
go_editor
asked
Sep 28, 2014
Linear Algebra
gatecse-2014-set3
linear-algebra
eigen-value
normal
+
–
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