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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? $0.24$ $0.36$ $0.4$ $0.6$
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 da...
7.8k
views
answered
Apr 23, 2023
Probability
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 _______. $\pi a^{2}-a^{2}$ $\pi a^{2}-\sqrt{2}a^{2}$ $\pi a^{2}-2a^{2}$ $\pi a^{2}-3a^{2}$
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 $a$,...
2.2k
views
commented
Sep 13, 2021
Quantitative Aptitude
gate2020-ec
quantitative-aptitude
geometry
circle
area
+
–
8
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 ____________.
Let $p, q, r, s$ represents the following propositions.$p:x\in\left\{8, 9, 10, 11, 12\right\}$$q:$ $x$ is a composite number.$r:$ $x$ is a perfect square.$s:$ $x$ is a pr...
13.1k
views
answered
Aug 21, 2021
Mathematical Logic
gatecse-2016-set1
mathematical-logic
normal
numerical-answers
propositional-logic
+
–
5
answers
4
GATE CSE 2003 | Question: 9
Assuming all numbers are in $2’s$ complement representation, which of the following numbers is divisible by $11111011$? $11100111$ $11100100$ $11010111$ $11011011$
Assuming all numbers are in $2’s$ complement representation, which of the following numbers is divisible by $11111011$?$11100111$$11100100$$11010111$$11011011$
10.5k
views
answered
Aug 5, 2021
Digital Logic
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 $1111$ $11111$ $111111$ $10001$
The $2's$ complement representation of the decimal value $-15$ is$1111$$11111$$111111$$10001$
10.0k
views
answered
Aug 5, 2021
Digital Logic
gatecse-2002
digital-logic
number-representation
easy
+
–
2
answers
6
GATE CSE 1990 | Question: 3-ix
The number of ways in which $5\; A's, 5\; B's$ and $5\; C's$ can be arranged in a row is: $15!/(5!)^{3}$ $15!$ $\left(\frac{15}{5}\right)$ $15!(5!3!)$.
The number of ways in which $5\; A's, 5\; B's$ and $5\; C's$ can be arranged in a row is:$15!/(5!)^{3}$$15!$$\left(\frac{15}{5}\right)$$15!(5!3!)$.
3.1k
views
answer reshown
Jul 24, 2021
Combinatory
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) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$...
14.9k
views
commented
Jul 10, 2021
Mathematical Logic
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
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 reflex...
14.4k
views
comment edited
Jul 1, 2021
Set Theory & Algebra
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
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 rel...
12.5k
views
commented
Jun 30, 2021
Set Theory & Algebra
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)
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 $...
3.2k
views
commented
Jun 30, 2021
Set Theory & Algebra
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
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 v...
7.6k
views
commented
Jun 28, 2021
Mathematical Logic
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
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 transi...
14.0k
views
commented
Jun 27, 2021
Set Theory & Algebra
gate1996
set-theory&algebra
relations
normal
+
–
4
answers
13
Associativity of implication?
a + b->c means (a + b)-> c or a + (b->c)?
a + b->c means(a + b)- c or a + (b->c)?
2.1k
views
commented
Jun 27, 2021
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 _________
Amongst the properties $\left\{\text{reflexivity, symmetry, anti-symmetry, transitivity}\right\}$ the relation $R=\{(x, y) \in N^2|x \neq y\}$ satisfies _________
5.2k
views
answered
Jun 27, 2021
Set Theory & Algebra
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 $f^{-1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{x-y}\right)$ ... $f^{-1}(x,y)=\left [ 2\left(x-y\right),2\left(x+y\right) \right ]$
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 ...
9.8k
views
answered
Jun 26, 2021
Set Theory & Algebra
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.
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.
2.9k
views
answered
Jun 26, 2021
Set Theory & Algebra
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 ______. $120$ $124$ $126$ $130$
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...
2.1k
views
answered
Jun 21, 2021
Quantitative Aptitude
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 ______ $n^2-n$ $n^2+n$ $2n^2-n$ $2n^2+n$
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$$2n^2+n$
3.8k
views
answered
Jun 18, 2021
Quantitative Aptitude
gate2020-ch
quantitative-aptitude
arithmetic-series
+
–
7
answers
19
GATE2011 MN: GA-61
If $\dfrac{(2y+1)}{(y+2)} < 1,$ then which of the following alternatives gives the CORRECT range of $y$ ? $- 2 < y < 2$ $- 2 < y < 1$ $- 3 < y < 1$ $- 4 < y < 1$
If $\dfrac{(2y+1)}{(y+2)} < 1,$ then which of the following alternatives gives the CORRECT range of $y$ ?$- 2 < y < 2$$- 2 < y < 1$$- 3 < y < 1$$- 4 < y < 1$
3.3k
views
answer edited
Jun 13, 2021
Quantitative Aptitude
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
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?$\varnoth...
15.6k
views
commented
May 29, 2021
Set Theory & Algebra
gatecse-2015-set1
set-theory&algebra
set-theory
normal
+
–
8
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 $Y - X ≠ \emptyset$
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$$X - Y �...
6.7k
views
commented
May 27, 2021
Set Theory & Algebra
gatecse-2006
set-theory&algebra
normal
set-theory
+
–
3
answers
22
TIFR CSE 2013 | Part A | Question: 3
Three candidates, Amar, Birendra and Chanchal stand for the local election. Opinion polls are conducted and show that fraction $a$ of the voters prefer Amar to Birendra, fraction $b$ prefer Birendra to Chanchal and fraction $c$ ... $(a, b, c) = (0.49, 0.49, 0.49);$ None of the above.
Three candidates, Amar, Birendra and Chanchal stand for the local election. Opinion polls are conducted and show that fraction $a$ of the voters prefer Amar to Birendra, ...
2.5k
views
answered
May 24, 2021
Mathematical Logic
tifr2013
set-theory&algebra
set-theory
+
–
2
answers
23
Kenneth Rosen Edition 7 Exercise 2.3 Question 27 (Page No. 153)
Prove that a strictly decreasing function from $R$ to it-self is one-to-one. Give an example of an decreasing function from $R$ to itself that is not one-to-one
Prove that a strictly decreasing function from $R$ to it-self is one-to-one.Give an example of an decreasing function from $R$ to itself that is not one-to-one
2.5k
views
commented
May 19, 2021
Set Theory & Algebra
kenneth-rosen
discrete-mathematics
set-theory&algebra
+
–
8
answers
24
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then$P = Q - k$$P = Q...
6.0k
views
answered
May 17, 2021
Combinatory
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.
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 everybod...
2.1k
views
answered
May 16, 2021
Mathematical Logic
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
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 s...
3.0k
views
answer edited
May 16, 2021
Mathematical Logic
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
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 l...
17.9k
views
answered
May 16, 2021
Mathematical Logic
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
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 \r...
10.7k
views
answered
Apr 12, 2021
Mathematical Logic
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 ___________.
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 $P \wedge (P \Rightarrow Q)$...
20.1k
views
commented
Apr 12, 2021
Mathematical Logic
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.
Consider the following statements:P: Good mobile phones are not cheapQ: Cheap mobile phones are not goodL: P implies QM: Q implies PN: P is equivalent to QWhich one of th...
10.7k
views
answered
Apr 12, 2021
Mathematical Logic
gatecse-2014-set3
mathematical-logic
easy
propositional-logic
+
–
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