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0
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1
GATE200827
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 ... on Monday, what is the probability that she studies computer science on Wednesday? 0.24 0.36 0.4 0.6
answered
36 minutes
ago
in
Probability

625
views
gate2008
probability
normal
+2
votes
2
query on exams
what are all the PSUs for CS undergrads which conduct their own exams for recruitment.when will be the exam registration dates for them? Does IIT kanpur,IIIT hyderabad conducts a separate exam for M.tech admissions? is there any other exam other than Gate ,that I could get an M.tech admission in IITs or IISc? please let me know.
answered
1 day
ago
in
GATE

21
views
psu
gate
0
votes
3
GATE 2016129
Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If the outcomes are (TAILS, HEADS) then output $Y$ and stop. Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $N$ and stop. ... , then go to Step 1. The probability that the output of the experiment is $Y$ is (up to two decimal places) ____________.
answered
1 day
ago
in
Probability

1.7k
views
gate20161
probability
normal
numericalanswers
+1
vote
4
TIFR2011A3
The probability of three consecutive heads in four tosses of a fair coin is. $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$ $\frac{3}{16}$ None of the above.
answered
1 day
ago
in
Probability

141
views
tifr2011
probability
0
votes
5
TIFR2013A14
An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is $1/(2n)$ $1/[(6n)!]$ $1  6^{n}$ $6^{n}$ None of the above.
answered
1 day
ago
in
Probability

159
views
tifr2013
probability
0
votes
6
TIFR2013A13
Doctors $A$ and $B$ perform surgery on patients in stages $III$ and $IV$ of a disease. Doctor $A$ has performed a $100$ surgeries (on $80$ stage $III$ and $20$ stage $IV$ patients) and $80$ out of her $100$ patients have survived ( ... successful There is not enough data since the choice depends on the stage of the disease the patient is suffering from.
answered
1 day
ago
in
Probability

125
views
tifr2013
probability
0
votes
7
TIFR2013A6
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise twothirds of the population the park, and give a correct answer to requests for directions with probability $3/4$. The air of Kabrastan ... is again East. What is the probability of East being correct? $1/4$ $1/3$ $1/2$ $2/3$ $3/4$
answered
1 day
ago
in
Probability

226
views
tifr2013
probability
+1
vote
8
TIFR2012A20
There are $1000$ balls in a bag, of which $900$ are black and $100$ are white. I randomly draw $100$ balls from the bag. What is the probability that the $101$st ball will be black? $9/10$ More than $9/10$ but less than $1$. Less than $9/10$ but more than $0$. $0$ $1$
answered
1 day
ago
in
Probability

238
views
tifr2012
probability
0
votes
9
TIFR2011A19
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by 4? $\frac{1}{3}$ $\frac{1}{6}$ $\frac{1}{9}$ $\frac{5}{18}$ $\frac{2}{9}$
answered
Sep 16
in
Probability

282
views
tifr2011
probability
0
votes
10
EC,GATE2007
An examination consists of two papers , paper1 and paper2 . the probability of failing in paper 1 is 0.3 and that in paper 2 is 0.2 . Given that a student has failed in paper2 , the probability of failing in paper1 is 0.6 .The ... creat sample space and then try to find probability, what's wrong here ? Someone verify pls ...M getting different ans ...
answered
Sep 9
in
Probability

76
views
engineeringmathematics
+1
vote
11
TIFR2014A3
The Fibonacci sequence is defined as follows: $F_{0} = 0, F_{1} = 1,$ and for all integers $n \geq 2, F_{n} = F_{n−1} + F_{n−2}$. Then which of the following statements is FALSE? $F_{n+2} = 1 + \sum ^{n}_{i=0} ... . $F_{4n}$ is a multiple of $3$, for every integer $n \geq 0$. $F_{5n}$ is a multiple of $4$, for every integer $n \geq 0$.
answered
Sep 5
in
Combinatory

135
views
tifr2014
recurrence
easy
–1
vote
12
GATE2004IT34
Let H1, H2, H3, ... be harmonic numbers. Then, for n ∊ Z+, $\sum_{j=1}^{n} H_j$ can be expressed as nHn+1  (n + 1) (n + 1)Hn  n nHn  n (n + 1) Hn+1  (n + 1)
answered
Sep 5
in
Combinatory

555
views
gate2004it
recurrence
permutationsandcombinations
normal
+1
vote
13
application form
i missed uploading thumb impression in gate application form its not given in brochure i got the copy of application form should i worry? I am giving gate 2nd time
answered
Sep 4
in
Others

62
views
gateapplication
–1
vote
14
GATE2008IT25
In how many ways can b blue balls and r red balls be distributed in n distinct boxes? $\frac{(n+b1)!\,(n+r1)!}{(n1)!\,b!\,(n1)!\,r!}$ $\frac{(n+(b+r)1)!}{(n1)!\,(n1)!\,(b+r)!}$ $\frac{n!}{b!\,r!}$ $\frac{(n + (b + r)  1)!} {n!\,(b + r  1)}$
answered
Aug 31
in
Combinatory

773
views
gate2008it
permutationsandcombinations
normal
0
votes
15
GATE1994_1.15
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is $n$ $n^2$ $\frac{n(n1)}{2}$ $\frac{n(n+1)}{2}$
answered
Aug 31
in
Combinatory

767
views
gate1994
permutationsandcombinations
normal
0
votes
16
GATE1999_1.3
The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is $^{n1}C_k$ $^nC_k$ $^nC_{k+1}$ None of the above
answered
Aug 31
in
Combinatory

597
views
gate1999
permutationsandcombinations
normal
0
votes
17
GATE20035
$n$ 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 \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)
answered
Aug 31
in
Combinatory

709
views
gate2003
permutationsandcombinations
normal
0
votes
18
GATE200213
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of 2 positive integers (which are not necessarily distinct). For example, for $n=3$ the number of ways is 2, i.e., 1+2, 2+1. Give only ... $n \geq k$ be expressed as the sum of k positive integers (which are not necessarily distinct). Give only the answer without explanation.
answered
Aug 31
in
Combinatory

402
views
gate2002
permutationsandcombinations
normal
descriptive
0
votes
19
GATE1998_1.23
How many sub strings of different lengths (nonzero) can be found formed from a character string of length $n$? $n$ $n^2$ $2^n$ $\frac{n(n+1)}{2}$
answered
Aug 31
in
Combinatory

1.1k
views
gate1998
permutationsandcombinations
normal
0
votes
20
TIFR2011A2
In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together? $\displaystyle\frac{(6+3)!}{2!}$ $\displaystyle\frac{6!}{2!}$ $\displaystyle\frac{3!3!}{2!}$ $\displaystyle\frac{4!3!}{2!}$ None of the above.
answered
Aug 31
in
Combinatory

175
views
tifr2011
permutationsandcombinations
+1
vote
21
group theory
Which book to follow for Group Theory ?
answered
Aug 31
in
Set Theory & Algebra

40
views
0
votes
22
TIFR2012A7
It is required to divide the $2n$ members of a club into $n$ disjoint teams of 2 members each. The teams are not labelled. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^n . n!}$ $n! / 2$ None of the above.
answered
Aug 31
in
Combinatory

426
views
tifr2012
permutationsandcombinations
+4
votes
23
ISI 2004 MIII
Q.3 A subset S of set of numbers {2,3,4,5,6,7,8,9,10} is said to be good if has exactly 4 elements and their gcd=1, Then number of good subset is A) 126 B) 125 C)123 D)121
answered
Aug 30
in
Combinatory

177
views
permutationsandcombinations
isi2004
0
votes
24
ISI 2004 MIII
answered
Aug 30
in
Combinatory

124
views
permutationsandcombinations
isi2004
0
votes
25
TIFR2017A6
How many disctict words can be formed by permuting the letters of the word ABRACADABRA? $\frac{11!}{5! \: 2! \: 2!}$ $\frac{11!}{5! \: 4! }$ $11! \: 5! \: 2! \: 2!\:$ $11! \: 5! \: 4!$ $11! $
answered
Aug 30
in
Combinatory

139
views
tifr2017
permutationsandcombinations
+1
vote
26
TIFR2017A5
How many distinct ways are there to split 50 identical coins among three people so that each person gets at least 5 coins? $3^{35}$ $3^{50}2^{50}$ $\begin{pmatrix} 35 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 50 \\ 15 \end{pmatrix}. 3^{35}$ $\begin{pmatrix} 37 \\ 2 \end{pmatrix}$
answered
Aug 28
in
Combinatory

217
views
tifr2017
permutationsandcombinations
+1
vote
27
GATE19894i
Provide short answers to the following questions: How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
answered
Aug 28
in
Combinatory

232
views
gate1989
descriptive
permutationsandcombinations
+1
vote
28
ISI 2017
For each positive intefer $n$ consider the set $S_n$ defined as follows: $S_1 = \{1\}, \: S_2 = \{2, 3\}, \: S_3 = \{4,5,6\}, \: \dots $ and, in general, $S_{n+1}$ consists of $n+1$ consecutinve integers the smallest of which is one more than the largest integer in $S_n$. Ten the sum of all the integers in $S_{21}$ equals 1113; 53361; 5082; 4641
answered
Aug 28
in
Combinatory

117
views
engineeringmathematics
isi2017
permutationsandcombinations
0
votes
29
ISI 2016
A palindrome is a sequence of digits which reads the same backward or forward. For example, 7447, 1001 are palindromes, but 7455, 1201 are not palindromes. How many 8 digit prime palindromes are there?
answered
Aug 28
in
Combinatory

209
views
isi2016
permutationsandcombinations
+1
vote
30
TIFR2012A10
In how many different ways can $r$ elements be picked from a set of $n$ elements if (i) Repetition is not allowed and the order of picking matters? (ii) Repetition is allowed and the order of picking does not matter? $\frac{n!}{\left(n  r\right)!}$ and $\ ... \frac{n!}{\left(n  r\right)!}$, respectively. $\frac{n!}{r!}$ and $\frac{r!}{n!}$, respectively.
answered
Aug 27
in
Combinatory

210
views
tifr2012
permutationsandcombinations
+1
vote
31
Engineering mathematics
Standard books required for linear algebra and calculus for gate syllabus ?
answered
Aug 23
in
Linear Algebra

42
views
linear
algebra
and
calculus
0
votes
32
GATE20104
Consider the set S = $\{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms A Group A Ring An integral domain A field
answered
Aug 20
in
Set Theory & Algebra

697
views
gate2010
settheory&algebra
normal
ring
groups
0
votes
33
GATE19902x
Match the pairs in the following questions: (a) Groups (p) Associativity (b) Semigroups (q) Identity (c) Monoids (r) Commutativity (d) Albelian groups (s) Left inverse
answered
Aug 20
in
Set Theory & Algebra

155
views
gate1990
matchthefollowing
settheory&algebra
groups
0
votes
34
GATE1996_1.4
Which of the following statements is false? The set of rational numbers is an abelian group under addition The set of integers in an abelian group under addition The set of rational numbers form an abelian group under multiplication The set of real numbers excluding zero is an abelian group under multiplication
answered
Aug 20
in
Set Theory & Algebra

538
views
gate1996
settheory&algebra
groups
normal
0
votes
35
GATE200513
The set \(\{1, 2, 4, 7, 8, 11, 13, 14\}\) is a group under multiplication modulo 15. the inverses of 4 and 7 are respectively: 3 and 13 2 and 11 4 and 13 8 and 14
answered
Aug 20
in
Set Theory & Algebra

382
views
gate2005
settheory&algebra
normal
groups
0
votes
36
GATE1995_21
Let $G_1$ and $G_2$ be subgroups of a group $G$. Show that $G_1 \cap G_2$ is also a subgroup of $G$. Is $G_1 \cup G_2$ always a subgroup of $G$?.
answered
Aug 19
in
Set Theory & Algebra

307
views
gate1995
settheory&algebra
groups
normal
0
votes
37
GATE19879b
How many onetoone functions are there from a set $A$ with $n$ elements onto itself?
answered
Aug 14
in
Set Theory & Algebra

168
views
gate1987
settheory&algebra
functions
+1
vote
38
GATE20062
Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is $z^{2^{xy}}$ $z \times 2^{xy}$ $z^{2^{x+y}}$ $2^{xyz}$
answered
Aug 14
in
Set Theory & Algebra

442
views
gate2006
settheory&algebra
normal
functions
+1
vote
39
GATE198913c
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
Aug 14
in
Set Theory & Algebra

131
views
gate1989
descriptive
functions
+2
votes
40
GATE200337
Let \(f : A \to B\) be an injective (onetoone) function. Define \(g : 2^A \to 2^B\) as: \(g(C) = \left \{f(x) \mid x \in C\right\} \), for all subsets $C$ of $A$. Define \(h : 2^B \to 2^A\) as: \(h(D) = \{x \mid x \in A, f(x) \in D\}\), for ... ? \(g(h(D)) \subseteq D\) \(g(h(D)) \supseteq D\) \(g(h(D)) \cap D = \phi\) \(g(h(D)) \cap (B  D) \ne \phi\)
answered
Aug 14
in
Set Theory & Algebra

749
views
gate2003
settheory&algebra
functions
normal
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