GATE Overflow - Recent questions in Combinatory
http://gateoverflow.in/questions/mathematics/discrete-mathematics/combinatory
Powered by Question2AnswerCombinatory
http://gateoverflow.in/134611/combinatory
How many ordered quadruples $\left ( x_{1},x_{2},x_{3},x_{4} \right )$ of odd positive integers satisfy<br />
<br />
$$x_{1}+x_{2}+x_{3}+x_{4}=98?$$Combinatoryhttp://gateoverflow.in/134611/combinatorySat, 24 Jun 2017 13:41:31 +0000Recurrence Relation
http://gateoverflow.in/134583/recurrence-relation
<p>The solution of <strong>a<sub>n</sub> = 2a<sub>n-1</sub><sub> </sub>+ 1</strong> where <strong>a<sub>0 </sub>= 1</strong> is ? </p>
<p>Please use the <strong>substitution method</strong> because I seem to have problem understanding it.</p>Combinatoryhttp://gateoverflow.in/134583/recurrence-relationSat, 24 Jun 2017 07:51:08 +0000Combinatorics : Multinomial Coefficients
http://gateoverflow.in/134546/combinatorics-multinomial-coefficients
<p>What's the relationship between combination and polynomial equation? I mean, I am not able to grasp certain points here or let's say connect them into a whole:
<br>
<br>
1. Take a question where it's asked that we have to arrange 10 books : 4 of A, 3 of B, 2 of C, and 1 of D in such a way that each book of similar type remain with its own type so like AAAABBBDCCC, etc. Here we are doing 4!*4!*3!*2!*1!.
<br>
<br>
2. When we take a question of dividing 10 police officers into 3 groups: 10 -> 5,3,2. Here we use 10!/*5!*3!*2!).
<br>
<br>
3. How many solutions of $x1+x2+x3+...+xn=300$ are possible?
<br>
<br>
Doubt: What's the difference between 1 & 2? Isn't two equivalent to saying arrange 10 officers like manner of AAAAABBBCC? If we are grouping 10 distinct elements into 3 groups where each group is of same type, then what's the catch here?
<br>
<br>
Second is what's the similarity between 2 and 3? Isn't three equivalent to saying group 300 distinct element into 3 bags/groups?
<br>
<br>
I am totally confuse here and I think I cannot move ahead with my GATE preparation if I cannot clear my doubt on combinatorics which in turn would mean no way of doing probability's tricky questions.</p>
<p> </p>
<p>EDIT: Here's the images of different questions. How do I differentiate between them?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9083059680419989013"><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14165371670004274780"></p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11854156684812671111"></p>Combinatoryhttp://gateoverflow.in/134546/combinatorics-multinomial-coefficientsSat, 24 Jun 2017 01:58:38 +0000Derangements
http://gateoverflow.in/134403/derangements
How many ways we can put 5 letters L1, L2, L3, L4, L5 in 5 envelopes e1, e2, e3, e4 and e5 (at 1 letter per envelope) so that<br />
<br />
i. no letter is correctly placed?<br />
<br />
ii. at least 1 letter is correctly placed?<br />
<br />
iii. exactly 2 letters are correctly placed?<br />
<br />
iv. at most 1 letter is correctly placed?<br />
<br />
v. at least 1 letter is wrongly placed?<br />
<br />
vi. exactly 1 letter is wrongly placed?Combinatoryhttp://gateoverflow.in/134403/derangementsFri, 23 Jun 2017 03:31:20 +0000#combinatory
http://gateoverflow.in/133790/%23combinatory
<p><strong>Determine the number of factors of 3<sup>4</sup> * 5<sup>2</sup> * * 11<sup>7</sup> * 13<sup>8</sup>.</strong></p>Combinatoryhttp://gateoverflow.in/133790/%23combinatoryMon, 19 Jun 2017 05:32:07 +0000#Discrete #Combinatorics
http://gateoverflow.in/132665/%23discrete-%23combinatorics
The number of ways in which n distinct objects can be put into two identical boxes so that no box remains empty, is<br />
<br />
a) 2^n - 1<br />
<br />
b) 2^n - 2<br />
<br />
c) 2^(n-1) - 1<br />
<br />
d) None of these<br />
<br />
Please explain your answer.Combinatoryhttp://gateoverflow.in/132665/%23discrete-%23combinatoricsSun, 11 Jun 2017 12:33:15 +0000[Discrete Maths] Counting ,Number of solutions to the equation
http://gateoverflow.in/132586/discrete-maths-counting-number-of-solutions-to-the-equation
How many solutions are there to the equation<br />
x1 + x2 + x3 + x4 + x5 = 21,<br />
where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that:<br />
<br />
0 ≤ x1 ≤ 3 , 1 ≤ x2 < 4 and 15≤x3 ?Combinatoryhttp://gateoverflow.in/132586/discrete-maths-counting-number-of-solutions-to-the-equationSat, 10 Jun 2017 17:55:46 +0000recurrence relation (rosen )
http://gateoverflow.in/131797/recurrence-relation-rosen
<p>solve the given recurrence relation ?</p>
<p> </p>
<hr>
<hr>
<p>$a_{n}=3a_{n/2}+n$</p>
<p>n=2^k , $a_{1}$=1</p>
<p>by changing the variables $b_{k}=3b_{k-1}+2^{k}$</p>
<p>after solving this i got c1.$3^{k}-2.2^{k}$</p>
<p>now i am facing difficulty to find the value of c1 ... might be silly can some one help me </p>Combinatoryhttp://gateoverflow.in/131797/recurrence-relation-rosenSun, 04 Jun 2017 06:56:22 +0000Generating function , closed form
http://gateoverflow.in/131674/generating-function-closed-form
Find a closed form for the generating function for the given sequence<br />
<br />
1) 1,1,0,1,1,1,1,1.....<br />
<br />
2) 1,2,1,1,1,1,1.....<br />
<br />
Do manually ..Combinatoryhttp://gateoverflow.in/131674/generating-function-closed-formSat, 03 Jun 2017 01:53:33 +0000Rosen example ( generating function)
http://gateoverflow.in/131673/rosen-example-generating-function
Let the alphabet consist of {0,1,2} find the number of r digit binary sequence that contain an even number of 0's.Combinatoryhttp://gateoverflow.in/131673/rosen-example-generating-functionSat, 03 Jun 2017 01:03:44 +0000Generalised permutation and combination
http://gateoverflow.in/131559/generalised-permutation-and-combination
Suppose that a basketball league has 32 teams ,split into 2 conference of 16 teams each . Each conference is splits into 3 division .suppose that north central Division plays 4 games against each of other teams in this division , 3 games against each of the 11 remaining teams in the conference , and 2 games against each of the 16 teams in the other conference ,in how many different order can the games of one of the teams in the north central Division scheduled ? <br />
<br />
I am unable to approach , little bit confusion in question statement ... please reply in detail ..Combinatoryhttp://gateoverflow.in/131559/generalised-permutation-and-combinationFri, 02 Jun 2017 03:52:56 +0000Permutation
http://gateoverflow.in/131551/permutation
How many strings with 5 or more characters can be formed from the letter SEERESS ? <br />
<br />
Verify the answer ...Combinatoryhttp://gateoverflow.in/131551/permutationFri, 02 Jun 2017 00:53:40 +0000Kenneth rosen exercise 6.3 Q.29
http://gateoverflow.in/131467/kenneth-rosen-exercise-6-3-q-29
How many 4-permutations of the positive integers not exceeding 100 contain three consecutive integers k,k+1,k+2, in the correct order<br />
<br />
A.) Where these consecutive integers can perhaps be separated by other integerd in the permutation ?<br />
<br />
B.) Whre they are in consecutive positions in the permutation ?Combinatoryhttp://gateoverflow.in/131467/kenneth-rosen-exercise-6-3-q-29Thu, 01 Jun 2017 11:30:00 +0000Cominatroics
http://gateoverflow.in/131345/cominatroics
There are 12 copies of Mathematics, 7 copies of Engineering, 3 different books on Medicine and 2 different books on Economics. Find the number of ways in which one or more than one book can be selected?<br />
A. 3421 B. 3111<br />
C. 3327 D. 3201Combinatoryhttp://gateoverflow.in/131345/cominatroicsWed, 31 May 2017 06:23:35 +0000#combinatroics
http://gateoverflow.in/131310/%23combinatroics
An elevator starts at the basement with 8 people (not including the elevator operator) and discharges them all by the time it reaches the top floor, number 6. In how many ways could the operator have perceived the people leaving the elevator if all people look alike to him? What if the 8<br />
people consisted of 5 men and 3 women and the operator could tell a man from a woman?Combinatoryhttp://gateoverflow.in/131310/%23combinatroicsTue, 30 May 2017 13:45:41 +0000#seldom_ross_chapter1_problems_23
http://gateoverflow.in/131182/%23seldom_ross_chapter1_problems_23
A psychology laboratory conducting dream research contains 3 rooms, with 2 beds in each room. If 3 sets of identical twins are to be assigned to these 6 beds so that each set of twins sleeps in different beds in the same room, how many assignments are possible?<br />
<br />
each set of twins sleeps in different beds in the same room hence each twin assigned one room, here 3 twins and we arrange them into 3 rooms so 3! ways <br />
twins are identical so no need of arranging them <br />
so answer is only 3!=6 <br />
<br />
but given answer is 48Combinatoryhttp://gateoverflow.in/131182/%23seldom_ross_chapter1_problems_23Mon, 29 May 2017 01:18:51 +0000Discrete Mathematics and its applications - Kenneth Rosen, Counting - Basics of Counting - Exercise 51
http://gateoverflow.in/130886/discrete-mathematics-applications-counting-counting-exercise
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?Combinatoryhttp://gateoverflow.in/130886/discrete-mathematics-applications-counting-counting-exerciseFri, 26 May 2017 07:57:41 +0000Kenneth rosen chp 6 question 39 counting
http://gateoverflow.in/130005/kenneth-rosen-chp-6-question-39-counting
How many partial functions are there from a set with m elements to a set with n elements, where m and n are positive integers.<br />
<br />
Answer : (n+1)^m <br />
<br />
How . Can anyone please help?Combinatoryhttp://gateoverflow.in/130005/kenneth-rosen-chp-6-question-39-countingWed, 17 May 2017 14:54:04 +0000Kenneth rosen chapter 6 question 41 counting
http://gateoverflow.in/129991/kenneth-rosen-chapter-6-question-41-counting
A palindrome is a string whose reversal is identical to the string. how many bit strings of length n are palindromes ?Combinatoryhttp://gateoverflow.in/129991/kenneth-rosen-chapter-6-question-41-countingWed, 17 May 2017 13:00:29 +0000Kenneth rosen chapter 6 question 17 counting
http://gateoverflow.in/129976/kenneth-rosen-chapter-6-question-17-counting
How many strings of 5 ASCII characters contain the character @ atleast once ? [ NOTE : there are 128 ascii characters ] <br />
<br />
<br />
<br />
Answer is : 1,321,368,961<br />
<br />
Can anyone explain how ?Combinatoryhttp://gateoverflow.in/129976/kenneth-rosen-chapter-6-question-17-countingWed, 17 May 2017 11:15:26 +0000basic aptitude
http://gateoverflow.in/129883/basic-aptitude
<table>
<tbody>
<tr>
<td>
<p>12 chairs are arranged in a row and are numbered 1 to 12 4 men have to be seated in these chairs so that the chairs numbered 1 and 8 should be occupied and no two men occupy adjacent chairs.</p>
<p>Find the number of ways the task can be done.</p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td> </td>
<td><strong>A.</strong></td>
<td>
<p>360</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>B.</strong></td>
<td>
<p>384</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>C.</strong></td>
<td>
<p>432</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>D.</strong></td>
<td>
<p>470</p>
</td>
</tr>
</tbody>
</table>Combinatoryhttp://gateoverflow.in/129883/basic-aptitudeMon, 15 May 2017 14:03:54 +0000basic aptitude
http://gateoverflow.in/129878/basic-aptitude
<table>
<tbody>
<tr>
<td>
<p>The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?</p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td> </td>
<td><strong>A.</strong></td>
<td>
<p>275</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>B.</strong></td>
<td>
<p>251</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>C.</strong></td>
<td>
<p>240</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>D.</strong></td>
<td>
<p>242</p>
</td>
</tr>
</tbody>
</table>
<p> can someone give me proper way to solve ?</p>Combinatoryhttp://gateoverflow.in/129878/basic-aptitudeMon, 15 May 2017 13:48:10 +0000Subsequence Theorem From Rosen.
http://gateoverflow.in/129834/subsequence-theorem-from-rosen
There is a theorem<br />
<br />
Every sequence of n^2 + 1 distinct real numbers contains a subsequence of length n + 1 that<br />
is either strictly increasing or strictly decreasing.<br />
<br />
Proof: Let a1, a2,...,an2+1 be a sequence of n^2 + 1 distinct real numbers.Associate an ordered<br />
pair with each term of the sequence, namely, associate (ik, dk) to the term ak, where ik is the<br />
length of the longest increasing subsequence starting at ak, and dk is the length of the longest<br />
decreasing subsequence starting at ak.<br />
Suppose that there are no increasing or decreasing subsequences of length n + 1. Then ik<br />
and dk are both positive integers less than or equal to n, for k = 1, 2,...,n^2 + 1. Hence, by the<br />
product rule there are n2 possible ordered pairs for (ik, dk). By the pigeonhole principle, two of<br />
these n^2 + 1 ordered pairs are equal. In other words, there exist terms as and at , with s<t<br />
such that is = it and ds = dt . We will show that this is impossible. Because the terms of the<br />
sequence are distinct, either as < at or as > at . If as < at , then, because is = it , an increasing<br />
subsequence of length it + 1 can be built starting at as, by taking as followed by an increasing<br />
subsequence of length it beginning at at . This is a contradiction. Similarly, if as > at , the same<br />
reasoning shows that ds must be greater than dt , which is a contradiction.<br />
<br />
<br />
<br />
<br />
<br />
My question is how n^2 ordered pair possible for (ik,dk) ??Combinatoryhttp://gateoverflow.in/129834/subsequence-theorem-from-rosenMon, 15 May 2017 03:12:13 +0000maths
http://gateoverflow.in/129379/maths
In how many ways three girls and nine boys can be seated int two vans each having numbered seats ,3 in the front and and 4 at the back ?<br />
<br />
How many arrangements are possible if 3 girls sit together in back row on adjacent seats?Combinatoryhttp://gateoverflow.in/129379/mathsFri, 12 May 2017 10:58:33 +0000basic aptitude
http://gateoverflow.in/129131/basic-aptitude
<table>
<tbody>
<tr>
<td>
<p>Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:</p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td> </td>
<td><strong>A.</strong></td>
<td>
<p>69760</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>B.</strong></td>
<td>
<p>30240</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>C.</strong></td>
<td>
<p>99748</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>D.</strong></td>
<td>
<p>42386</p>
</td>
</tr>
</tbody>
</table>
<p> </p>
<p>i got ans from the method totol words - no word repeated , but if i want to do with general method means 10*10*9*8*7 *5!/2! + 10*10*10*9*8*5!/3! + 10*10*10*10*9*5!/4! + 10*10*10*10*!0 from this getting different ans where is going wrong ? someone verify pls </p>Combinatoryhttp://gateoverflow.in/129131/basic-aptitudeWed, 10 May 2017 06:22:38 +0000#rosen , #counting , #5.1 , 41(a)
http://gateoverflow.in/128608/%23rosen-%23counting-%235-1-41-a
in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people , if<br />
<br />
a) the bride must next to the groom<br />
<br />
my solution is since given that bride and groom must be next to each other then now we have to select 4 person from 8 that is 8c4 now we have to arrange these people since bride and groom next to each other then take BG as one block and rest four __ , __ , __ , __ ,<br />
<br />
now arranging BG , __ , __ ,__, __ will take 5! , and arranging BG mutually is 2! ,<br />
<br />
so total ways is 8c4*5!*2!<br />
<br />
but answer is given 240 (rosen )Combinatoryhttp://gateoverflow.in/128608/%23rosen-%23counting-%235-1-41-aSun, 07 May 2017 17:51:30 +0000Discrete Mathematics Thegatebook
http://gateoverflow.in/128449/discrete-mathematics-thegatebook
how many positive integers between 50 and 100,<br />
<br />
(a) divisible by 7<br />
(b) divisible by 11<br />
(c) divisible by 7 and 11?Combinatoryhttp://gateoverflow.in/128449/discrete-mathematics-thegatebookSun, 07 May 2017 10:25:10 +0000combinatorics
http://gateoverflow.in/127196/combinatorics
In how many ways 8 different shirts can be distributed to 4 different people so that each will get 2 shirts?Combinatoryhttp://gateoverflow.in/127196/combinatoricsFri, 28 Apr 2017 09:40:08 +0000combinatorics
http://gateoverflow.in/127195/combinatorics
Number of 5 digit number having there digits in non decreasing order (from left to right) constructed by using the digits belonging to the set {1, 2, 3, 4, 5, 6, 7, 8, 9} ?Combinatoryhttp://gateoverflow.in/127195/combinatoricsFri, 28 Apr 2017 09:38:19 +0000Generalised permutation combinations
http://gateoverflow.in/126603/generalised-permutation-combinations
In how many ways can a dozen books be placed on four distinguishable shelves<br />
<br />
if no two books are the same, and the positions of the books on the shelves matter?<br />
<br />
(Hint: Break this into 12 tasks, placing each book separately. Start with the sequence 1,2,3,4 to<br />
<br />
represent the shelves. Represent the books by bi, i = 1, 2, ..., 12. Place b1 to the right of one of<br />
<br />
the terms in 1, 2, 3, 4. Then successively place b2, b3, ..., and b12.)Combinatoryhttp://gateoverflow.in/126603/generalised-permutation-combinationsSat, 22 Apr 2017 21:58:10 +0000rosen
http://gateoverflow.in/126428/rosen
<p><big>A shelf holds 12 books in a row. How many ways are there to choose five books so that no two adjacent books are chosen?</big></p>Combinatoryhttp://gateoverflow.in/126428/rosenFri, 21 Apr 2017 15:46:38 +0000Combinatorics
http://gateoverflow.in/126365/combinatorics
A bagel shop has onion bagels, poppy seed bagels, egg bagels, salty bagels, pumpernickel bagels, sesame seed bagels, raisin bagels, and plain bagels. <br />
<br />
How many ways are there to choose<br />
<br />
a dozen bagels with at least three egg bagels and no more than two salty bagels?Combinatoryhttp://gateoverflow.in/126365/combinatoricsFri, 21 Apr 2017 00:26:11 +0000rosen discrete
http://gateoverflow.in/126217/rosen-discrete
How many strings of six lowercase letters of the<br />
English alphabet contain exactly two vowel?Combinatoryhttp://gateoverflow.in/126217/rosen-discreteWed, 19 Apr 2017 18:04:50 +0000Fibonacci series
http://gateoverflow.in/125565/fibonacci-series
Let a,b,c,d are 4 consecutive numbers of Fibonacci series.<br />
<br />
Prove or dis-approve:<br />
<br />
ad-bc= ±1Combinatoryhttp://gateoverflow.in/125565/fibonacci-seriesFri, 14 Apr 2017 22:15:20 +0000Rosen chapter-6 (counting)
http://gateoverflow.in/125539/rosen-chapter-6-counting
How many solutions are there to the equation<br />
x1 + x2 + x3 + x4 + x5 = 21,<br />
where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0$\leq$ x1$\leq$10 ?Combinatoryhttp://gateoverflow.in/125539/rosen-chapter-6-countingFri, 14 Apr 2017 16:31:03 +0000How to approach?
http://gateoverflow.in/125197/how-to-approach
A spider is at the bottom of a cliff, and is n inches from the top. Every step it takes brings it one inch closer to the top with probability 1/3, and one inch away from the top with probability 2/3, unless it is at the bottom in which case, it always gets one inch closer. What is the expected number of steps for the spider to reach the top as a function of n?<br />
<br />
a)Never reach to the top<br />
<br />
b)Linear to n<br />
<br />
c)Polynomial to n<br />
<br />
d)Exponential to nCombinatoryhttp://gateoverflow.in/125197/how-to-approachWed, 12 Apr 2017 10:23:36 +0000Rosen, Discrete Mathematics
http://gateoverflow.in/125117/rosen-discrete-mathematics
How many bit strings of length eight contain either three<br />
consecutive 0s or four consecutive 1s?Combinatoryhttp://gateoverflow.in/125117/rosen-discrete-mathematicsTue, 11 Apr 2017 15:15:08 +0000Rosen, Discrete Mathematics ,counting
http://gateoverflow.in/125099/rosen-discrete-mathematics-counting
How many partial functions are there from a set with m elements to a set with n<br />
elements, where m and n are positive integers?Combinatoryhttp://gateoverflow.in/125099/rosen-discrete-mathematics-countingTue, 11 Apr 2017 14:15:26 +0000ISI 2017
http://gateoverflow.in/124372/isi-2017
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14005501081496295567"></p>Combinatoryhttp://gateoverflow.in/124372/isi-2017Thu, 06 Apr 2017 01:20:21 +0000ISI 2004 MIII
http://gateoverflow.in/123727/isi-2004-miii
Q 4) In how many ways can three person, each throwing a single die once, make a score of 11<br />
<br />
A) 22 B)27 C)24 D)38Combinatoryhttp://gateoverflow.in/123727/isi-2004-miiiMon, 03 Apr 2017 14:57:07 +0000ISI 2004 MIII
http://gateoverflow.in/123721/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<br />
<br />
A) 126 B) 125 C)123 D)121Combinatoryhttp://gateoverflow.in/123721/isi-2004-miiiMon, 03 Apr 2017 14:27:44 +0000ISI 2004 MIII
http://gateoverflow.in/123718/isi-2004-miii
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13954498214722884749"></p>Combinatoryhttp://gateoverflow.in/123718/isi-2004-miiiMon, 03 Apr 2017 14:17:03 +0000ISI 2004 MIII
http://gateoverflow.in/123714/isi-2004-miii
Q 1. The number of permutation of {1,2,3,4,5} that keep at least one integer fixed is.<br />
<br />
A) 81 B)76 C)120 D)60Combinatoryhttp://gateoverflow.in/123714/isi-2004-miiiMon, 03 Apr 2017 13:58:33 +0000A bit string is called legitimate if it contains no consecutive zeros, e.g., 0101110 is legitimate,
http://gateoverflow.in/122640/string-legitimate-contains-consecutive-0101110-legitimate
<p>A bit string is called legitimate if it contains no consecutive zeros, e.g., 0101110 is legitimate, whereas 10100111 is not. Let an denote
<br>
the number of legitimate bit strings of length n. Dene a0 = 1. Derive a recurrence relation for an (i.e., express an in terms of the preceding a<sub>i</sub>'s).</p>Combinatoryhttp://gateoverflow.in/122640/string-legitimate-contains-consecutive-0101110-legitimateSun, 26 Mar 2017 23:38:44 +0000Suppose there are n positive real numbers such that their sum is 20
http://gateoverflow.in/122636/suppose-there-are-positive-real-numbers-such-that-their-sum
Suppose there are n positive real numbers such that their sum is 20<br />
and the product is strictly greater than 1. What is the maximum possible<br />
value of n?<br />
<br />
(A) 18 (B) 19 (C) 20 (D) 21Combinatoryhttp://gateoverflow.in/122636/suppose-there-are-positive-real-numbers-such-that-their-sumSun, 26 Mar 2017 23:12:55 +0000The number of terms independent of x in the binomial expansion of
http://gateoverflow.in/122635/the-number-of-terms-independent-of-in-the-binomial-expansion
The number of terms independent of x in the binomial expansion of <br />
<br />
(A) 0 (B) 1 (C) 2 (D) 5Combinatoryhttp://gateoverflow.in/122635/the-number-of-terms-independent-of-in-the-binomial-expansionSun, 26 Mar 2017 23:09:06 +0000Suppose a 6 digit number N is formed by rearranging the digits of the number 123456
http://gateoverflow.in/122634/suppose-digit-number-formed-rearranging-digits-number-123456
Suppose a 6 digit number N is formed by rearranging the digits of the number 123456. If N is divisible by 5, then the set of all possible<br />
remainders when N is divided by 45 is<br />
(A) {30} (B) {15, 30} (C) {0,15,30} (D) {0, 5, 15, 30}Combinatoryhttp://gateoverflow.in/122634/suppose-digit-number-formed-rearranging-digits-number-123456Sun, 26 Mar 2017 23:00:33 +0000A club with n members is organized into four committees so that each member
http://gateoverflow.in/122622/club-with-members-organized-into-four-committees-that-member
A club with n members is organized into four committees so that each<br />
member belongs to exactly two committees and each pair of committees<br />
has exactly one member in common. Then<br />
(A) n = 4<br />
(B) n = 6<br />
(C) n = 8<br />
(D) n cannot be determined from the given informationCombinatoryhttp://gateoverflow.in/122622/club-with-members-organized-into-four-committees-that-memberSun, 26 Mar 2017 21:19:37 +0000What is the highest power of 18 contained
http://gateoverflow.in/122544/what-is-the-highest-power-of-18-contained
What is the highest power of $18$ contained in $50C25$?Combinatoryhttp://gateoverflow.in/122544/what-is-the-highest-power-of-18-containedSat, 25 Mar 2017 18:49:55 +0000MadeEasy Workbook [2016] Q1
http://gateoverflow.in/122518/madeeasy-workbook-2016-q1
In how many ways can seven girls be seated at a round table so that two particular girls are separated?<br />
<br />
(a) 260<br />
<br />
(b) 320<br />
<br />
(c) 480<br />
<br />
(d) 560Combinatoryhttp://gateoverflow.in/122518/madeeasy-workbook-2016-q1Sat, 25 Mar 2017 13:17:51 +0000