GATE Overflow - Recent questions in Engineering Mathematics
http://gateoverflow.in/questions/mathematics
Powered by Question2AnswerMADE EASY TEST SERIES
http://gateoverflow.in/106729/made-easy-test-series
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8856951113969376819"></p>Graph Theoryhttp://gateoverflow.in/106729/made-easy-test-seriesTue, 17 Jan 2017 07:01:48 +0000Gate-2006, CE
http://gateoverflow.in/106695/gate-2006-ce
There are 25 calculators in a box. Two of them are defective. Suppose 5 calculators are randomly picked for inspection (i.e., each has the same chance of being selected), what is the probability that only one of the defective calculators will be included in the inspection?<br />
<br />
can we do it by both hypergeometric as well as by binomial distribution?Probabilityhttp://gateoverflow.in/106695/gate-2006-ceTue, 17 Jan 2017 06:19:23 +0000Probability
http://gateoverflow.in/106656/probability
The probability that when 12 balls are distributed naming three boxes the first will contain three balls is My doubt is to select 3 balls in first box is 1 since all ball s must be identical but given is 12C3 whyMathematical Logichttp://gateoverflow.in/106656/probabilityTue, 17 Jan 2017 04:31:06 +0000VIRTUAL - Gate-2017
http://gateoverflow.in/106470/virtual-gate-2017
<p>Two matrices A and B are called similar if there exists another matrix S such that S<sup>−1</sup>AS = B. Consider the statements:
<br>
(I) If A and B are similar then they have identical rank.
<br>
(I) If A and B are similar then they have identical trace.
<br>
(III) <img alt="" height="36" src="http://www.techtud.com/sites/default/files/public/user_files/tud6911/v1.png" width="262">
<br>
Which of the following is TRUE. </p>
<table>
<thead>
<tr>
<th> </th>
<th> </th>
</tr>
</thead>
</table>
<table>
<thead>
<tr>
<th> </th>
<th> </th>
</tr>
</thead>
<tbody>
<tr>
<td> </td>
<td>
<p>(A) Only I and III </p>
</td>
</tr>
<tr>
<td> </td>
<td>
<p>(B) Only II </p>
</td>
</tr>
<tr>
<td> </td>
<td>
<p>(C) Both I and II but not III </p>
</td>
</tr>
<tr>
<td> </td>
<td>
<p>(D) All of I, II and III</p>
</td>
</tr>
</tbody>
</table>Mathematical Logichttp://gateoverflow.in/106470/virtual-gate-2017Mon, 16 Jan 2017 14:10:05 +0000What is the expected length of the cycle containing vertex 1?
http://gateoverflow.in/106462/what-is-the-expected-length-of-the-cycle-containing-vertex-1
<p>A random permutation π of set[n] = {1, 2, …, n} can be represent by a directed graph on n vertices with directed arc (i, π<sub>i</sub>) where π<sub>i</sub> is the i<sup>th</sup> entry in the permutation. Observe that the resulting graph is just a collection of disjoint cycles.
<br>
What is the expected length of the cycle containing vertex 1?</p>
<ol>
<li> n(n-1)/2n</li>
<li> (n+1)/2n</li>
<li> ((n-1))/2</li>
<li> ((n+1))/2</li>
</ol>
<p> </p>
<p>/pls explain the question </p>Graph Theoryhttp://gateoverflow.in/106462/what-is-the-expected-length-of-the-cycle-containing-vertex-1Mon, 16 Jan 2017 13:54:25 +0000made easy 5
http://gateoverflow.in/106438/made-easy-5
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6871799121104883068"></p>Mathematical Logichttp://gateoverflow.in/106438/made-easy-5Mon, 16 Jan 2017 13:15:55 +0000Testbook
http://gateoverflow.in/106414/testbook
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9826512353065079146"></p>Graph Theoryhttp://gateoverflow.in/106414/testbookMon, 16 Jan 2017 12:30:45 +0000answer 90 or 444?
http://gateoverflow.in/106281/answer-90-or-444
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6347837754231132418"></p>Combinatoryhttp://gateoverflow.in/106281/answer-90-or-444Mon, 16 Jan 2017 08:25:15 +0000how to Solve Any 3rd Degree Polynomial Equation
http://gateoverflow.in/106274/how-to-solve-any-3rd-degree-polynomial-equation
<p>how to Solve Any 3rd Degree Polynomial Equation</p>
<p> ax<sup>3</sup> + bx<sup>2</sup> + cx + d = 0 </p>Mathematical Logichttp://gateoverflow.in/106274/how-to-solve-any-3rd-degree-polynomial-equationMon, 16 Jan 2017 08:16:48 +0000Ace Pre Gate 2017
http://gateoverflow.in/106253/ace-pre-gate-2017
<p> </p>
<p> </p>
<p><big>All elements of a 2x2 matrix "A" can have values either 0 or 1. The probability that any element gets a value (0 or 1) is 1/2. If all elements of this matrix are chosen at random, what is the probability that the determinant of this matrix is positive?</big></p>Probabilityhttp://gateoverflow.in/106253/ace-pre-gate-2017Mon, 16 Jan 2017 07:24:59 +0000Integration
http://gateoverflow.in/106245/integration
Solve the following $\int_{0}^{\infty}e^{-x^2}x^4dx$Mathematical Logichttp://gateoverflow.in/106245/integrationMon, 16 Jan 2017 06:56:40 +0000rosen
http://gateoverflow.in/106117/rosen
Find a recurrence relation for the number of bit strings<br />
of length n that contain the string 01.<br />
<br />
I am getting a recurrence like An = 2^(n-2) + 2A(n-1) - A (N-2) .Answer is not given for this question.Please help and explain your steps.Combinatoryhttp://gateoverflow.in/106117/rosenMon, 16 Jan 2017 05:22:02 +0000Discrete Maths # Counting
http://gateoverflow.in/106105/discrete-maths-%23-counting
How many ways we can distribut 12 similar items into 5 different boxes so that first two box will contain only even number of items and next three must contain more than 2 and less than 6 items ??Mathematical Logichttp://gateoverflow.in/106105/discrete-maths-%23-countingMon, 16 Jan 2017 04:16:52 +0000Graph theory
http://gateoverflow.in/106088/graph-theory
Is isomorphism of graph in syllabus?Mathematical Logichttp://gateoverflow.in/106088/graph-theoryMon, 16 Jan 2017 02:51:54 +0000Recurrence
http://gateoverflow.in/106020/recurrence
An organism is born on day K=1 with 1 cell. During day K=2,3,...... the organism produces $\frac{K^{2}}{K-1}$ times more new cells than it produced on day K-1. Number of cells in the organism at the end of 9th day if no cell dies is ___________<br />
<br />
My Issue: Unable to solve the recurrence relation.Combinatoryhttp://gateoverflow.in/106020/recurrenceSun, 15 Jan 2017 16:58:36 +0000Non-isomorphic graphs
http://gateoverflow.in/105987/non-isomorphic-graphs
<p>How many <em><strong>non-isomorphic</strong></em> simple graph are there with <strong>N</strong> vertices, where <strong>N = 4 ?</strong></p>Graph Theoryhttp://gateoverflow.in/105987/non-isomorphic-graphsSun, 15 Jan 2017 15:37:27 +0000#nlc payment
http://gateoverflow.in/105975/%23nlc-payment
@ arjun sir for nlc application i have done sbi collect payment 2 days before but still nlc is showing fee paid status as not paid what to do nowGraph Theoryhttp://gateoverflow.in/105975/%23nlc-paymentSun, 15 Jan 2017 15:27:44 +0000logic
http://gateoverflow.in/105950/logic
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9943592195343228718"></p>
<p>Which of above three are valid. I know A3 is valid.</p>Mathematical Logichttp://gateoverflow.in/105950/logicSun, 15 Jan 2017 14:43:34 +0000Discrete Maths
http://gateoverflow.in/105941/discrete-maths
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6628154107736757451"></p>
<p>I have solved it by some legacy method ! i want to know how to solve using combinatorics ??</p>Mathematical Logichttp://gateoverflow.in/105941/discrete-mathsSun, 15 Jan 2017 14:27:42 +0000Number of Sums
http://gateoverflow.in/105861/number-of-sums
<table style="width:100%">
</table>
<table style="width:100%">
<tbody>
<tr>
<td> </td>
<td>The function for finding the fibonacci series is given as follows :
<br>
<br>
<img alt="Image not present" src="http://s3-ap-southeast-1.amazonaws.com/gate-content-images/data/images/common/papers/partners/34/580/image033.png">
<br>
<br>
The number of additions taken in evaluating fib(5) is.</td>
</tr>
</tbody>
</table>
<p>Your Answer:
<br>
<br>
4
<br>
<br>
Correct Answer: 7 Status: incorrect</p>Graph Theoryhttp://gateoverflow.in/105861/number-of-sumsSun, 15 Jan 2017 11:51:57 +0000Perfect Matching for a graph
http://gateoverflow.in/105858/perfect-matching-for-a-graph
<table style="width:100%">
<tbody>
<tr>
<td>Find the number of perfect matching of the graph
<br>
<img alt="Image not present" src="http://s3-ap-southeast-1.amazonaws.com/gate-content-images/data/images/common/papers/partners/34/580/image031.png"></td>
</tr>
</tbody>
</table>
<p>Your Answer:
<br>
<br>
105
<br>
<br>
Correct Answer: 9 Status: incorrect</p>Mathematical Logichttp://gateoverflow.in/105858/perfect-matching-for-a-graphSun, 15 Jan 2017 11:49:48 +0000ACE MOCK I
http://gateoverflow.in/105821/ace-mock-i
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9875917990569254297"></p>Mathematical Logichttp://gateoverflow.in/105821/ace-mock-iSun, 15 Jan 2017 11:08:42 +0000Discrete Maths
http://gateoverflow.in/105554/discrete-maths
<p>How many one to one functions are possible from A to B where |A| =4 and |B| = 6 such that i<sup>th</sup> element of A can not match with i<sup>th</sup> element of B.??</p>Set Theory & Algebrahttp://gateoverflow.in/105554/discrete-mathsSat, 14 Jan 2017 17:06:01 +0000GROUP THEORY
http://gateoverflow.in/105538/group-theory
Can someone tell whether these topics are important in GROUP THEORY?<br />
<br />
ISOMORPHIC GROUPS<br />
<br />
NORMAL GROUPS<br />
<br />
COSETS.Set Theory & Algebrahttp://gateoverflow.in/105538/group-theorySat, 14 Jan 2017 15:46:36 +0000Test Series
http://gateoverflow.in/105525/test-series
<p><a rel="nofollow" href="http://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003">http://gateoverflow.in/?qa=blob&qa_blobid=4549376166631720003</a></p>Calculushttp://gateoverflow.in/105525/test-seriesSat, 14 Jan 2017 14:57:54 +0000discrete
http://gateoverflow.in/105500/discrete
How many solutions are there to the equation: $X_1+X_2+X_3+X_4+X_5=21$ ?<br />
<br />
If $0 \leq X1 \leq 3 , 1 \leq X2 < 4 , X3 \geq 15$Combinatoryhttp://gateoverflow.in/105500/discreteSat, 14 Jan 2017 13:56:10 +0000Recurrence relation for total no of n length English letter words, with even no of a’s
http://gateoverflow.in/105371/recurrence-relation-total-length-english-letter-words-with
<p>The recurrence relation for total no of n length English letter words, with even no of a’s.</p>
<p>Below is some parts I could build -</p>
<p>Assumptions - 26 english letters and no epsilon</p>
<p>Let us assume a string of length n and positions from (1 to n)</p>
<p>Let T(n) denote the number of strings with length 'n' containing even number of a's</p>
<p>Now, <strong>T(n) = Number of String of length 'n' that do not with 'a' + Number of String of length 'n' ending with 'a' </strong></p>
<p>Let T(n) = Part1 + Part2 </p>
<p>Part1 :</p>
<p>If a strings does not end with 'a' then it means string of length (n-1) has even number of a's and can be permuted in T(n-1) ways.</p>
<p>Thus the n<sup>th </sup>position can be filled only with the remaining 25 letters except 'a' then below is the conclusion -</p>
<p><strong>Number of String of length 'n' that do not with 'a' = 25* T(n-1) </strong></p>
<p>Part2 :</p>
<p>If a string ends with 'a' then the string of length (n-1) that is except position n<sup>th </sup>should contain odd number of a<sup>'</sup>s so that end result will be even number of a<sup>'</sup>s</p>
<p>There is only 1 possibility for n<sup>th </sup>position and for upto length (n-1) we should have odd 'a's</p>
<p>Could someone please guide how to proceed further and if things are correct till here?</p>Combinatoryhttp://gateoverflow.in/105371/recurrence-relation-total-length-english-letter-words-withSat, 14 Jan 2017 08:44:36 +0000Which is maximum Planar graph whose Line Graph is Planar?(Check the answer)
http://gateoverflow.in/105345/which-maximum-planar-graph-whose-graph-planar-check-answer
Graph Theoryhttp://gateoverflow.in/105345/which-maximum-planar-graph-whose-graph-planar-check-answerSat, 14 Jan 2017 06:26:19 +0000How many maximum cycles possible in any Complete graph? (Check the Answer)
http://gateoverflow.in/105343/how-many-maximum-cycles-possible-complete-graph-check-answer
Graph Theoryhttp://gateoverflow.in/105343/how-many-maximum-cycles-possible-complete-graph-check-answerSat, 14 Jan 2017 06:20:45 +0000discrete math
http://gateoverflow.in/105303/discrete-math
how many bit strings of lenght 8 contain either three consecutive 0s or four consecutive 1s ?Combinatoryhttp://gateoverflow.in/105303/discrete-mathSat, 14 Jan 2017 04:14:38 +0000test series 2
http://gateoverflow.in/105164/test-series-2
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=1611856507685042360"></p>Mathematical Logichttp://gateoverflow.in/105164/test-series-2Fri, 13 Jan 2017 15:05:33 +0000Geeks for Geeks
http://gateoverflow.in/105062/geeks-for-geeks
<p>A and B are two sets. If |A| = 5 , |B| = 3 , then, the number of onto functions from A to B are ___ ?</p>
<p><strong>(A)</strong> 35
<br>
<strong>(B)</strong> 150
<br>
<strong>(C)</strong> 29
<br>
<strong>(D)</strong> 27</p>Mathematical Logichttp://gateoverflow.in/105062/geeks-for-geeksFri, 13 Jan 2017 12:15:13 +0000geek mock 2017 #38
http://gateoverflow.in/104995/geek-mock-2017-%2338
Let A = { 1,2,3,4,…….∞ } and a binary operation ‘+’ is defined by a + b = ab ∀ a,b ∈ A. Which of the following is true ?<br />
<br />
( A, + ) is a semi group but not monoid<br />
<br />
( A, + ) is a monoid but not group<br />
<br />
( A, + ) is a group<br />
<br />
( A, + ) is not a semi grou<br />
<br />
<br />
<br />
i think it should be semigroup because we dont have an identity elementSet Theory & Algebrahttp://gateoverflow.in/104995/geek-mock-2017-%2338Fri, 13 Jan 2017 10:17:35 +0000hoe many different choices for classes does we have? ________
http://gateoverflow.in/104940/hoe-many-different-choices-for-classes-does-we-have-________
<p>Tom Riddle must choose 4 classes for his final semester at school. He must take at least 1 science class and at least 1 art class. In his school offers 4 (distinct) science classes, 3 (distinct) art classes and three other (distinct) classes, hoe many different choices for classes does we have? ________</p>
<ol>
<li> 195</li>
<li> 175</li>
<li> 210</li>
<li> 160</li>
</ol>Combinatoryhttp://gateoverflow.in/104940/hoe-many-different-choices-for-classes-does-we-have-________Fri, 13 Jan 2017 07:53:17 +0000i m confused over thiz concept . need help.
http://gateoverflow.in/104808/i-m-confused-over-thiz-concept-need-help
when we say we are applying brute force to solve any problem then solution b 2^n or n^n<br />
<br />
Note: i know what is brute force , it is try all possible combination to solve the problemMathematical Logichttp://gateoverflow.in/104808/i-m-confused-over-thiz-concept-need-helpFri, 13 Jan 2017 02:28:42 +0000matrix groups
http://gateoverflow.in/104793/matrix-groups
<p>Which of the following is true?</p>
<ul>
<li>Every lower triangular matrix is group under multiplication operation where all elements of diagonal are non zero numbers.</li>
<li>Every diagonal matrix is group under multiplication operation, where all elements of diagonal are non zero numbers.</li>
<li>Every matrix is Abelian under addition operation where all elements are real numbers.</li>
<li>Both (a) and b)</li>
</ul>
<p>isn't a b c all are correct?</p>Linear Algebrahttp://gateoverflow.in/104793/matrix-groupsThu, 12 Jan 2017 23:17:28 +0000LINEAR ALGEBRA
http://gateoverflow.in/104762/linear-algebra
<p><strong>IS ZERO THE ONLY EIGEN VALUE OF SINGULAR MATRICES??</strong></p>Mathematical Logichttp://gateoverflow.in/104762/linear-algebraThu, 12 Jan 2017 19:50:32 +0000ace maths
http://gateoverflow.in/104690/ace-maths
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13318814493719879487"></p>Mathematical Logichttp://gateoverflow.in/104690/ace-mathsThu, 12 Jan 2017 17:12:11 +0000Maths : what is meant by square free ?
http://gateoverflow.in/104689/maths-what-is-meant-by-square-free
<p>D<sub>30</sub>={1,2,3,5,6,10,15,30}</p>
<p>because D<sub>30</sub> is square free so it is boolean algebra and every boolean algebra is distributed and complemented also</p>
<p>here square free means no divisor of 30 is square ?</p>Set Theory & Algebrahttp://gateoverflow.in/104689/maths-what-is-meant-by-square-freeThu, 12 Jan 2017 17:09:36 +0000what is the probability that the mother could have had the very long or very short pregnancy
http://gateoverflow.in/104579/what-probability-mother-could-very-long-very-short-pregnancy
<p>An expert witness in a paternity suit testifies that the length (in days) of distributed with parameters μ=270 and σ^2=100. The defendant in the suit is able to prove that he was out of the country during a period that began 290 days before the birth of the child and ended 240 days before birth.
<br>
If the defendant was in fact, the father of the child, what is the probability that the mother could have had the very long or very short pregnancy indicated by the testimony?</p>
<ol>
<li> 0.241</li>
<li> 0.0241</li>
</ol>
<p> </p>
<p>how to solve such questions??</p>Probabilityhttp://gateoverflow.in/104579/what-probability-mother-could-very-long-very-short-pregnancyThu, 12 Jan 2017 13:54:30 +0000made easy Test 3
http://gateoverflow.in/104570/made-easy-test-3
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8237913175401946966"></p>
<p>#plz explain 1st and 2nd ???</p>Mathematical Logichttp://gateoverflow.in/104570/made-easy-test-3Thu, 12 Jan 2017 13:42:43 +0000findthe probability that all the customers that arrive at the shop within the first 10 minutes, all bought product A?
http://gateoverflow.in/104543/findthe-probability-customers-arrive-minutes-bought-product
<p>Customers arrive at a shop according to a Poisson process at rate λ (/min), where they choose to buy either product A (with probability P) or product B (with probability 1 – P), independently. Given that during the first hour 5 customers chose product B, what is the probability that all the customers that arrive at the shop within the first 10 minutes, all bought product A?</p>
<ol>
<li> 60%</li>
<li> 70%</li>
<li> 30%</li>
<li> 40%</li>
</ol>Probabilityhttp://gateoverflow.in/104543/findthe-probability-customers-arrive-minutes-bought-productThu, 12 Jan 2017 13:10:51 +0000Probability
http://gateoverflow.in/104445/probability
2 friends Alice and Bob have found an unfair coin,It has 72% chance of coming up heads.Alice and Bob plays a game with this coin.If coin comes up head then tails,Alice wins.If it's reverse(tails,then heas),Bob wins.And if neither of those two things happens,the game restarts and continues untill there is a winner <br />
<br />
What is Bob's probability of winning?Mathematical Logichttp://gateoverflow.in/104445/probabilityThu, 12 Jan 2017 09:52:48 +0000Maths: Probability Distribution Que01
http://gateoverflow.in/104418/maths-probability-distribution-que01
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=15533185615533012495"></p>Probabilityhttp://gateoverflow.in/104418/maths-probability-distribution-que01Thu, 12 Jan 2017 08:14:34 +0000gate cs 2005
http://gateoverflow.in/104337/gate-cs-2005
<p><strong>What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs (a, b) and (c, d) in the chosen set such that "a ≡ c mod 3" and "b ≡ d mod 5"</strong></p>
<p>-------------------------------------------------------------------------------------------------------------------------------------------</p>
<p><strong>Solution given is like this : </strong></p>
<p>a = c mod 3 (given) Thus, ‘a’ can be any one of these values : 0, 1, 2
<br>
b = d mod 5 (given) Thus, ‘b’ can be any one of these values : 0, 1, 2, 3, 4
<br>
Thus, ordered pair for (a, b) are : (0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4)
<br>
Therefore, ordered pair (a, b) has 15 combinations and ordered pair (c, d) has 1 combination. Total combinations = 15 + 1 = 16
<br>
</p>
<p>-------------------------------------------------------------------------------------------------------------------------------------------</p>
<p><strong>My doubt is cant it be acheived by having just two ordered pairs??</strong> for example: (2,1) and (8,6) ...so we can have </p>
<p>a=2,b=1,c=8,d=6 ....and </p>
<p>"2 ≡ 8 mod 3" and "1 ≡ 6 mod 5"</p>Set Theory & Algebrahttp://gateoverflow.in/104337/gate-cs-2005Thu, 12 Jan 2017 06:09:00 +0000Maths: Group Theorey
http://gateoverflow.in/104241/maths-group-theorey
<p>A group G in which (ab)<sup>2</sup> = a<sup>2</sup>b<sup>2</sup> for all a,b in G is neccessarily</p>
<p>A. finite
<br>
B. cyclic
<br>
C. of order two
<br>
D. Abelian</p>
<p>please prove it
<br>
ands: D </p>Set Theory & Algebrahttp://gateoverflow.in/104241/maths-group-theoreyWed, 11 Jan 2017 19:47:06 +0000Maths: Group Theorey
http://gateoverflow.in/104236/maths-group-theorey
<p>Let * be the binary operation on the rational number given by a*b=a+b+2ab. which of the following are true?
<br>
i. * is commutative
<br>
ii. there is a rational number that is an identity with * operation
<br>
iii. every rational numebr has an inverse with * operation</p>
<p><span class="marker">I know that i is true and iii is false but why is ii false?</span>
<br>
<br>
Ans: (i) is only true</p>Set Theory & Algebrahttp://gateoverflow.in/104236/maths-group-theoreyWed, 11 Jan 2017 19:34:06 +0000Maths:
http://gateoverflow.in/104232/maths
Combinatoryhttp://gateoverflow.in/104232/mathsWed, 11 Jan 2017 19:32:59 +0000#Chromatic number , Planarity
http://gateoverflow.in/104130/%23chromatic-number-planarity
Let G be a planar graph such that every face is bordered by exactly 3 edges.Which of the following can never be the value for χ(G) ? (where χ(G) is the chromatic number of G)<br />
<br />
a) 2<br />
<br />
b) 3<br />
<br />
c) 4<br />
<br />
d) None of these<br />
<br />
PS : (Explain: "every face is bordered by exactly 3 edges. ")Graph Theoryhttp://gateoverflow.in/104130/%23chromatic-number-planarityWed, 11 Jan 2017 15:09:19 +0000Generating Function
http://gateoverflow.in/104105/generating-function
<p>Find the coefficient of <strong>x<sup>83</sup></strong> in<strong> (x<sup>5</sup>+ x<sup>8</sup>+ x<sup>11</sup>+ x<sup>14</sup>+ x<sup>17</sup>)<sup>10 </sup></strong>?</p>Combinatoryhttp://gateoverflow.in/104105/generating-functionWed, 11 Jan 2017 14:16:05 +0000