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8
answers
1
GATE CSE 2008 | Question: 27
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is $0.6$. If she studies mathematics on a day, then the probability that she studies computer ... what is the probability that she studies computer science on Wednesday? $0.24$ $0.36$ $0.4$ $0.6$
answered
in
Probability
Apr 23, 2023
7.6k
views
gatecse-2008
probability
normal
conditional-probability
2
answers
2
GATE ECE 2020 | GA Question: 8
A circle with centre $\text{O}$ is shown in the figure. A rectangle $\text{PQRS}$ of maximum possible area is inscribed in the circle. If the radius of the circle is $a$, then the area of the shaded portion is _______. $\pi a^{2}-a^{2}$ $\pi a^{2}-\sqrt{2}a^{2}$ $\pi a^{2}-2a^{2}$ $\pi a^{2}-3a^{2}$
commented
in
Quantitative Aptitude
Sep 13, 2021
2.2k
views
gate2020-ec
quantitative-aptitude
geometry
circle
area
7
answers
3
GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.
answered
in
Mathematical Logic
Aug 21, 2021
12.9k
views
gatecse-2016-set1
mathematical-logic
normal
numerical-answers
propositional-logic
5
answers
4
GATE CSE 2003 | Question: 9
Assuming all numbers are in $2’s$ complement representation, which of the following numbers is divisible by $11111011$? $11100111$ $11100100$ $11010111$ $11011011$
answered
in
Digital Logic
Aug 5, 2021
10.3k
views
gatecse-2003
digital-logic
number-representation
normal
6
answers
5
GATE CSE 2002 | Question: 1.15
The $2's$ complement representation of the decimal value $-15$ is $1111$ $11111$ $111111$ $10001$
answered
in
Digital Logic
Aug 5, 2021
9.9k
views
gatecse-2002
digital-logic
number-representation
easy
2
answers
6
GATE CSE 1990 | Question: 3-ix
The number of ways in which $5\; A's, 5\; B's$ and $5\; C's$ can be arranged in a row is: $15!/(5!)^{3}$ $15!$ $\left(\frac{15}{5}\right)$ $15!(5!3!)$.
answer reshown
in
Combinatory
Jul 24, 2021
3.1k
views
gate1990
normal
combinatory
10
answers
7
GATE CSE 2002 | Question: 1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
commented
in
Mathematical Logic
Jul 10, 2021
14.7k
views
gatecse-2002
mathematical-logic
normal
propositional-logic
6
answers
8
GATE CSE 1995 | Question: 1.19
Let $R$ be a symmetric and transitive relation on a set $A$. Then $R$ is reflexive and hence an equivalence relation $R$ is reflexive and hence a partial order $R$ is reflexive and hence not an equivalence relation None of the above
comment edited
in
Set Theory & Algebra
Jul 1, 2021
14.3k
views
gate1995
set-theory&algebra
relations
normal
3
answers
9
GATE CSE 1998 | Question: 1.7
Let $R_1$ and $R_2$ be two equivalence relations on a set. Consider the following assertions: $R_1 \cup R_2$ is an equivalence relation $R_1 \cap R_2$ is an equivalence relation Which of the following is correct? Both assertions are true Assertions (i) is true ... (ii) is not true Assertions (ii) is true but assertions (i) is not true Neither (i) nor (ii) is true
commented
in
Set Theory & Algebra
Jun 30, 2021
12.4k
views
gate1998
set-theory&algebra
relations
normal
4
answers
10
GATE CSE 2001 | Question: 4
Consider the function $h: N \times N \rightarrow N$ so that $h(a,b) = (2a +1)2^b - 1$, where $N=\{0,1,2,3,\dots\}$ is the set of natural numbers. Prove that the function $h$ is an injection (one-one). Prove that it is also a Surjection (onto)
commented
in
Set Theory & Algebra
Jun 30, 2021
3.2k
views
gatecse-2001
functions
set-theory&algebra
normal
descriptive
5
answers
11
GATE CSE 2004 | Question: 70
The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not valid valid a contradiction None of the above
commented
in
Mathematical Logic
Jun 28, 2021
7.4k
views
gatecse-2004
mathematical-logic
normal
propositional-logic
5
answers
12
GATE CSE 1996 | Question: 2.2
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric
commented
in
Set Theory & Algebra
Jun 27, 2021
13.9k
views
gate1996
set-theory&algebra
relations
normal
4
answers
13
Associativity of implication?
a + b->c means (a + b)-> c or a + (b->c)?
commented
in
Mathematical Logic
Jun 27, 2021
2.1k
views
3
answers
14
GATE CSE 1994 | Question: 2.3
Amongst the properties $\left\{\text{reflexivity, symmetry, anti-symmetry, transitivity}\right\}$ the relation $R=\{(x, y) \in N^2|x \neq y\}$ satisfies _________
answered
in
Set Theory & Algebra
Jun 27, 2021
5.1k
views
gate1994
set-theory&algebra
normal
relations
fill-in-the-blanks
9
answers
15
GATE CSE 1996 | Question: 2.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is given by $f^{-1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{x-y}\right)$ ... $f^{-1}(x,y)=\left [ 2\left(x-y\right),2\left(x+y\right) \right ]$
answered
in
Set Theory & Algebra
Jun 26, 2021
9.7k
views
gate1996
set-theory&algebra
functions
normal
4
answers
16
GATE CSE 1989 | Question: 13c
Find the number of single valued functions from set $A$ to another set $B,$ given that the cardinalities of the sets $A$ and $B$ are $m$ and $n$ respectively.
answered
in
Set Theory & Algebra
Jun 26, 2021
2.8k
views
gate1989
descriptive
functions
set-theory&algebra
7
answers
17
GATE Civil 2020 Set 1 | GA Question: 8
Insert seven numbers between $2$ and $34$, such that the resulting sequence including $2$ and $34$ is an arithmetic progression. The sum of these inserted seven numbers is ______. $120$ $124$ $126$ $130$
answered
in
Quantitative Aptitude
Jun 21, 2021
2.0k
views
gate2020-ce-1
quantitative-aptitude
arithmetic-series
2
answers
18
GATE Chemical 2020 | GA Question: 5
The difference between the sum of the first $2n$ natural numbers and the sum of the first $n$ odd natural numbers is ______ $n^2-n$ $n^2+n$ $2n^2-n$ $2n^2+n$
answered
in
Quantitative Aptitude
Jun 18, 2021
3.7k
views
gate2020-ch
quantitative-aptitude
arithmetic-series
7
answers
19
GATE2011 MN: GA-61
If $\dfrac{(2y+1)}{(y+2)} < 1,$ then which of the following alternatives gives the CORRECT range of $y$ ? $- 2 < y < 2$ $- 2 < y < 1$ $- 3 < y < 1$ $- 4 < y < 1$
answer edited
in
Quantitative Aptitude
Jun 13, 2021
3.3k
views
quantitative-aptitude
gate2011-mn
algebra
6
answers
20
GATE CSE 2015 Set 1 | Question: 16
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\varnothing \in 2^{A}$ $\varnothing \subseteq 2^{A}$ ... I and III only II and III only I, II and III only I, II and IV only
commented
in
Set Theory & Algebra
May 29, 2021
15.5k
views
gatecse-2015-set1
set-theory&algebra
set-theory
normal
7
answers
21
GATE CSE 2006 | Question: 22
Let $E, F$ and $G$ be finite sets. Let $X = (E ∩ F) - (F ∩ G)$ and $Y = (E - (E ∩ G)) - (E - F)$. Which one of the following is true? $X ⊂ Y$ $X ⊃ Y$ $X = Y$ $X - Y ≠ \emptyset$ and $Y - X ≠ \emptyset$
commented
in
Set Theory & Algebra
May 27, 2021
6.5k
views
gatecse-2006
set-theory&algebra
normal
set-theory
3
answers
22
TIFR CSE 2013 | Part A | Question: 3
Three candidates, Amar, Birendra and Chanchal stand for the local election. Opinion polls are conducted and show that fraction $a$ of the voters prefer Amar to Birendra, fraction $b$ prefer Birendra to Chanchal and fraction $c$ ... $(a, b, c) = (0.49, 0.49, 0.49);$ None of the above.
answered
in
Mathematical Logic
May 24, 2021
2.5k
views
tifr2013
set-theory&algebra
set-theory
2
answers
23
Kenneth Rosen Edition 7 Exercise 2.3 Question 27 (Page No. 153)
Prove that a strictly decreasing function from $R$ to it-self is one-to-one. Give an example of an decreasing function from $R$ to itself that is not one-to-one
commented
in
Set Theory & Algebra
May 19, 2021
2.4k
views
kenneth-rosen
discrete-mathematics
set-theory&algebra
8
answers
24
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
answered
in
Combinatory
May 17, 2021
5.5k
views
gatecse-2008
combinatory
easy
summation
3
answers
25
TIFR CSE 2011 | Part A | Question: 12
The action for this problem takes place in an island of Knights and Knaves, where Knights always make true statements and Knaves always make false statements and everybody is either a Knight or a Knave. Two friends A and B lives in a house. The census ... a Knave. A is a Knave and B is a Knight. Both are Knaves. Both are Knights. No conclusion can be drawn.
answered
in
Mathematical Logic
May 16, 2021
2.0k
views
tifr2011
mathematical-logic
propositional-logic
5
answers
26
TIFR CSE 2011 | Part A | Question: 1
If either wages or prices are raised, there will be inflation. If there is inflation, then either the government must regulate it or the people will suffer. If the people suffer, the government will be unpopular. Government will not be ... raised Prices are not raised If the inflation is not regulated, then the prices are not raised Wages are not raised
answer edited
in
Mathematical Logic
May 16, 2021
2.9k
views
tifr2011
mathematical-logic
propositional-logic
normal
12
answers
27
GATE CSE 2015 Set 3 | Question: 24
In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type ... person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail
answered
in
Mathematical Logic
May 16, 2021
17.7k
views
gatecse-2015-set3
mathematical-logic
difficult
logical-reasoning
10
answers
28
GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE
answered
in
Mathematical Logic
Apr 12, 2021
10.5k
views
gatecse-2017-set1
mathematical-logic
propositional-logic
11
answers
29
GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
commented
in
Mathematical Logic
Apr 12, 2021
19.8k
views
gatecse-2016-set2
mathematical-logic
normal
numerical-answers
propositional-logic
5
answers
30
GATE CSE 2014 Set 3 | Question: 1
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? Only L is TRUE. Only M is TRUE. Only N is TRUE. L, M and N are TRUE.
answered
in
Mathematical Logic
Apr 12, 2021
10.6k
views
gatecse-2014-set3
mathematical-logic
easy
propositional-logic
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