GATE CSE Doubts - Recent questions and answers
https://csedoubts.gateoverflow.in/qa
Powered by Question2Answerhttps://www.cs.utexas.edu/~lorenzo/corsi/cs372/06F/hw/3sol.html
https://csedoubts.gateoverflow.in/28997/https-www-cs-utexas-edu-lorenzo-corsi-cs372-06f-hw-3sol-html
<p>source: <a rel="nofollow" href="https://www.cs.utexas.edu/~lorenzo/corsi/cs372/06F/hw/3sol.html">https://www.cs.utexas.edu/~lorenzo/corsi/cs372/06F/hw/3sol.html</a></p>
<p>The question :</p>
<p>In a 32-bit machine we subdivide the virtual address into 4 segments as follows:<br>
</p>
<table border="" style="width:40%">
<tbody>
<tr>
<td>
<p>10-bit</p>
</td>
<td>
<p>8-bit</p>
</td>
<td>
<p>6-bit</p>
</td>
<td>
<p>8 bit</p>
</td>
</tr>
</tbody>
</table>
<p>We use a 3-level page table, such that the first 10-bit are for the first level and so on.</p>
<ol>
<li><strong>What is the size of a page table for a process that has 256K of memory starting at address 0?</strong></li>
</ol>
<p> </p>
<p> </p>
<p>My approach at solving the question:</p>
<p>Since the size of the page is 256B, dividing the process size with the page size gives the number of pages == 2^10. Then the size of the page table of a process can be given as the number of pages in the process * Page Table Entry(PTE). Therefore the answer with my approach is 2^10*10 which is wrong. Can someone please correct me and say where I am wrong? Thanks in advance.</p>
<p>I understand that here multilevel paging is used and there are more than one page tables, however I believe that using my approach above I should get an answer that is at least close to the given answer. However that is not the case. Please help.</p>
<p> </p>Operating Systemhttps://csedoubts.gateoverflow.in/28997/https-www-cs-utexas-edu-lorenzo-corsi-cs372-06f-hw-3sol-htmlTue, 13 Apr 2021 08:43:12 +0000https://www.cs.utexas.edu/~lorenzo/corsi/cs372/06F/hw/3sol.html
https://csedoubts.gateoverflow.in/28998/https-www-cs-utexas-edu-lorenzo-corsi-cs372-06f-hw-3sol-html
<p>The question :</p>
<p>In a 32-bit machine we subdivide the virtual address into 4 segments as follows:<br>
</p>
<table border="" style="width:40%">
<tbody>
<tr>
<td>
<p>10-bit</p>
</td>
<td>
<p>8-bit</p>
</td>
<td>
<p>6-bit</p>
</td>
<td>
<p>8 bit</p>
</td>
</tr>
</tbody>
</table>
<p>We use a 3-level page table, such that the first 10-bit are for the first level and so on.</p>
<ol>
<li><strong>What is the size of a page table for a process that has 256K of memory starting at address 0?</strong></li>
</ol>
<p> </p>
<p> </p>
<p>My approach at solving the question:</p>
<p>Since the size of the page is 256B, dividing the process size with the page size gives the number of pages == 2^10. Then the size of the page table of a process can be given as the number of pages in the process * Page Table Entry(PTE). PTE contains the number of bits required to address a byte in the physical memory. From the above subdivision, we know that the number of bits required to access a byte from physical memory is 32 bits. Therefore number of pages = 2^10, PTE = 32 bits. I understand that we use multi level paging here but let us just assume that there is a single Page Table only(the size of single page table is slightly lower than the size of page tables in multi level paging), then the size of the single page table would be 2^10 * 32. Which is way more than expected. Can someone please point out where I am making the mistake? Also can someone please clarify what does PTE hold?</p>Operating Systemhttps://csedoubts.gateoverflow.in/28998/https-www-cs-utexas-edu-lorenzo-corsi-cs372-06f-hw-3sol-htmlTue, 13 Apr 2021 08:43:07 +0000college options with AIR 852 and Gate score 686
https://csedoubts.gateoverflow.in/29000/college-options-with-air-852-and-gate-score-686
Hi folks,<br />
<br />
could you please help me with college selection, <br />
my gate rank is 852<br />
gate score 686<br />
cgpa 8.65 <br />
<br />
What is your opinion on new IITs (except IIT hyderabad) , IITdhanbad over IIIT banglore and IIIT delhi in terms of academic and placement point of viewIISc/IITshttps://csedoubts.gateoverflow.in/29000/college-options-with-air-852-and-gate-score-686Tue, 13 Apr 2021 08:43:04 +0000Answered: #Career Guidance Help
https://csedoubts.gateoverflow.in/28990/%23career-guidance-help?show=29001#a29001
I think gap won't matter if you are joining mtech program, in case if you are planning for job/ research program in nits or iits then at the time of interview they might ask about the education gapOthershttps://csedoubts.gateoverflow.in/28990/%23career-guidance-help?show=29001#a29001Tue, 13 Apr 2021 08:43:01 +0000Memory Allocation for literal constants other than string
https://csedoubts.gateoverflow.in/28995/memory-allocation-for-literal-constants-other-than-string
<p><strong>Is Space Also Allocated In Memory For Other Literal Constants(<em>int/char/float </em>Etc)? Because For <em>String Literal Constants </em>Memory Is Allocated. </strong></p>Programminghttps://csedoubts.gateoverflow.in/28995/memory-allocation-for-literal-constants-other-than-stringSat, 10 Apr 2021 14:10:16 +0000#DFA Introduction, Formal Languages, DFA Construction examples
https://csedoubts.gateoverflow.in/28993/%23dfa-introduction-formal-languages-construction-examples
<p><img alt="" height="38" src="https://csedoubts.gateoverflow.in/?qa=blob&qa_blobid=8162367136186769903" width="765"></p>Theory of Computationhttps://csedoubts.gateoverflow.in/28993/%23dfa-introduction-formal-languages-construction-examplesSat, 10 Apr 2021 13:22:55 +0000IISC CDS admission test 2021
https://csedoubts.gateoverflow.in/28994/iisc-cds-admission-test-2021
Did anyone receive communication from IISC regarding CDS orientation and exam instructions regarding admission processes 2021 ?Written Examhttps://csedoubts.gateoverflow.in/28994/iisc-cds-admission-test-2021Sat, 10 Apr 2021 13:22:49 +0000AppliedGate lecture example
https://csedoubts.gateoverflow.in/28989/appliedgate-lecture-example
What is the NFA that does not accept strings ending “101” ?Theory of Computationhttps://csedoubts.gateoverflow.in/28989/appliedgate-lecture-exampleWed, 07 Apr 2021 15:23:49 +0000Kenneth H. Rosen 7th edition
https://csedoubts.gateoverflow.in/28988/kenneth-h-rosen-7th-edition
Show that ¬(p ⊕ q) and p ↔ q are logically equivalent.Mathematical Logichttps://csedoubts.gateoverflow.in/28988/kenneth-h-rosen-7th-editionWed, 07 Apr 2021 11:24:11 +0000complement(ww) |w ε {a,b)* is CFL or Not
https://csedoubts.gateoverflow.in/28983/complement-ww-w-%CE%B5-a-b-is-cfl-or-not
complement(ww) |w ε {a,b)* is CFL . BUt its Complement {ww|w ε {a,b}*} is not CFL ?HOW?Theory of Computationhttps://csedoubts.gateoverflow.in/28983/complement-ww-w-%CE%B5-a-b-is-cfl-or-notWed, 07 Apr 2021 02:13:56 +0000Please tell me when GO book order link will ve available, how to order ,tell me procedure 😇
https://csedoubts.gateoverflow.in/28985/please-when-book-order-link-will-available-order-procedure
Study Resourceshttps://csedoubts.gateoverflow.in/28985/please-when-book-order-link-will-available-order-procedureWed, 07 Apr 2021 02:13:26 +0000Data Structures
https://csedoubts.gateoverflow.in/28986/data-structures
<p><img alt="" src="https://csedoubts.gateoverflow.in/?qa=blob&qa_blobid=12733668055533731021"></p>DShttps://csedoubts.gateoverflow.in/28986/data-structuresWed, 07 Apr 2021 02:13:20 +0000#addmissions #iits
https://csedoubts.gateoverflow.in/28982/%23addmissions-%23iits
while filling form of mtech cse of iit guhwati i found that they are auto filling your marks as well as gate score based on your registration number.<br />
<br />
In my case my original marks is 60 but normalized is 58.7 but by default they fill it as 60(orignal marks) ,so i change it to 58.7 and then i submit form and pay fee but then i found in my marks column still 60 marks is showing.<br />
<br />
so is this problem occuring with someone else and how to resolve it ?IISc/IITshttps://csedoubts.gateoverflow.in/28982/%23addmissions-%23iitsTue, 06 Apr 2021 12:50:05 +0000Answered: MTech Admission Query
https://csedoubts.gateoverflow.in/28973/mtech-admission-query?show=28978#a28978
<p>May be the following links can help. </p>
<ol style="list-style-type:decimal" type="1">
<li>GATE cut off(w.r.t. rank & score) of top IITs/IISc/CMI/ISI : <a rel="nofollow" href="https://gatecse.in/cut-off-for-masters-admissions/">https://gatecse.in/cut-off-for-masters-admissions/</a></li>
<li>GATE 2019 admission response from GO(contains rank & score of students admitted into tier 1 institute) : <a rel="nofollow" href="https://gatecse.in/gate-cse-2019-admission-responses/">https://gatecse.in/gate-cse-2019-admission-responses/</a></li>
<li>Although you said you want to get into top IITs, if you need, you can take a look on cut off of top NITs as well : <a rel="nofollow" href="http://ccmt.gatecselastrank.com">http://ccmt.gatecselastrank.com</a></li>
<li>GO “Score to college predictor” : <a rel="nofollow" href="https://gateoverflow.in/mymarks/ScoreToColleges.php">https://gateoverflow.in/mymarks/ScoreToColleges.php</a></li>
</ol>
<p>Though this is not the official source of cut offs of various institutes, it is very accurate and it will give you good idea of what colleges you can get.</p>IISc/IITshttps://csedoubts.gateoverflow.in/28973/mtech-admission-query?show=28978#a28978Tue, 06 Apr 2021 05:54:24 +0000Answered: type conversion in c programming
https://csedoubts.gateoverflow.in/28965/type-conversion-in-c-programming?show=28975#a28975
All operands of type char and short are converted to int before any operation.<br />
<br />
That’s why sizeof(c+i) returns 4.<br />
<br />
In the assignment operator the value of the RHS operand is converted to the type of the LHS operand.<br />
<br />
That’s why sizeof(s) returns 2.Programminghttps://csedoubts.gateoverflow.in/28965/type-conversion-in-c-programming?show=28975#a28975Mon, 05 Apr 2021 13:06:06 +0000Average case analysis in Quicksort
https://csedoubts.gateoverflow.in/28969/average-case-analysis-in-quicksort
<p>In quick sort the time complexity equation is <strong> T(n)=T(k)+T(n-k-1)+⊝(n) </strong>in average case how does the equation comes out to be <strong>T(n)=T(n/9)+T(9n/10)+⊝(n) </strong>in <strong>Average case.</strong></p>
<p> </p>Algorithmshttps://csedoubts.gateoverflow.in/28969/average-case-analysis-in-quicksortSat, 03 Apr 2021 23:15:11 +0000Gate 2016 Set Theory
https://csedoubts.gateoverflow.in/28966/gate-2016-set-theory
<p>Consider a set U of 23 different compounds in a chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following statements:</p>
<ol>
<li>Each compound in U \ S reacts with an odd number of compounds.</li>
<li>At least one compound in U \ S reacts with an odd number of compounds.</li>
<li>Each compound in U \ S reacts with an even number of compounds.</li>
</ol>
<p>Which one of the above statements is <strong>ALWAYS TRUE</strong>? <strong>(Please Draw a graph Not Able to visualize)</strong></p>
<ol>
<li>Only I</li>
<li>Only II</li>
<li>Only III</li>
<li>None.</li>
</ol>Set Theory & Algebrahttps://csedoubts.gateoverflow.in/28966/gate-2016-set-theorySat, 03 Apr 2021 15:38:00 +0000Answered: Simple-paging
https://csedoubts.gateoverflow.in/28938/simple-paging?show=28967#a28967
Page size will always be equal to frame size. Otherwise there is no point of paging.Operating Systemhttps://csedoubts.gateoverflow.in/28938/simple-paging?show=28967#a28967Sat, 03 Apr 2021 15:37:54 +0000CollegeAssignment
https://csedoubts.gateoverflow.in/28968/collegeassignment
Draw the canonical collection of lr(0) item s-->da|ab a-->ba|c B-->bB|c. Find out whether the grammar is LR(0) or not and SLR(1) or not.Compiler Designhttps://csedoubts.gateoverflow.in/28968/collegeassignmentSat, 03 Apr 2021 15:37:50 +0000Help me with my interview preparation.
https://csedoubts.gateoverflow.in/28964/help-me-with-my-interview-preparation
I've secured a AIR of 800 in gate 2021 CS&IT with a score of 692. I'm currently searching for preparation guide for interviews. Any links to organized content for the same would be helpful.Interview Questionshttps://csedoubts.gateoverflow.in/28964/help-me-with-my-interview-preparationSat, 03 Apr 2021 08:47:56 +0000In a computer system, the cache memory uses two-way set associative mapping technique to do the address translation.
https://csedoubts.gateoverflow.in/28963/computer-associative-mapping-technique-address-translation
<p><img alt="" src="https://csedoubts.gateoverflow.in/?qa=blob&qa_blobid=9986442928202636692"></p>CO & Architecturehttps://csedoubts.gateoverflow.in/28963/computer-associative-mapping-technique-address-translationFri, 02 Apr 2021 09:39:01 +0000Is the result for TIFR 2021 entrance exam out?
https://csedoubts.gateoverflow.in/28961/is-the-result-for-tifr-2021-entrance-exam-out
There is no information available on the website. Are the results out for Computer Science?TIFRhttps://csedoubts.gateoverflow.in/28961/is-the-result-for-tifr-2021-entrance-exam-outThu, 01 Apr 2021 15:31:27 +0000Regarding making short notes
https://csedoubts.gateoverflow.in/28952/regarding-making-short-notes
hello, currently i am studying operating system and i am finding difficulty in making short notes in sense that what to and what not to include in short notes. please guide. also if u can share some sample of short note that would be of great help.Othershttps://csedoubts.gateoverflow.in/28952/regarding-making-short-notesTue, 30 Mar 2021 12:12:42 +0000c programing storage classes
https://csedoubts.gateoverflow.in/28949/c-programing-storage-classes
please explain the difference in extern and global variable both have global scope then what is the difference how they used as in programmeProgramminghttps://csedoubts.gateoverflow.in/28949/c-programing-storage-classesMon, 29 Mar 2021 17:18:52 +0000Query regarding admissions in IIT.
https://csedoubts.gateoverflow.in/28935/query-regarding-admissions-in-iit
I gave gate in CS this year and got Rank 291 (Gate Score : 773). I have done Mechanical Engineering . Recently I got to know that I am not eligible for IIT G and IIT R because my bachelors is not in CS. What are the best possible options for me at this rank . Please let me know there might be options I am not aware of.<br />
<br />
Thank youIISc/IITshttps://csedoubts.gateoverflow.in/28935/query-regarding-admissions-in-iitSun, 28 Mar 2021 07:04:24 +0000#self-doubt #Group-theory
https://csedoubts.gateoverflow.in/28939/%23self-doubt-%23group-theory
let S be a semigroup over an operation *, having p,q,e as it’s elements, such that p*e=p; q*e=q; e*e=e and also p*q=p. Then will this semi group be a monoid?Set Theory & Algebrahttps://csedoubts.gateoverflow.in/28939/%23self-doubt-%23group-theorySun, 28 Mar 2021 07:04:03 +0000Can I get any colleges with AIR -2560(gen) ?
https://csedoubts.gateoverflow.in/28941/can-i-get-any-colleges-with-air-2560-gen
My rank is 2560 with gate score of 571.<br />
<br />
I don’t really care whether the course is MTech or MS(3 years).<br />
<br />
Can I get admission even in any of the low-ranking IITs(Patna/Mandi)? What about MS/MTech at any IIITs ( hyd, bang,delhi) ? <br />
<br />
Please replyWritten Examhttps://csedoubts.gateoverflow.in/28941/can-i-get-any-colleges-with-air-2560-genSun, 28 Mar 2021 07:03:44 +0000#admissions #iits
https://csedoubts.gateoverflow.in/28943/%23admissions-%23iits
Can someone suggests best colleges that one should fill with rank 426 and gate score 746 in gate CSE 2021?IISc/IITshttps://csedoubts.gateoverflow.in/28943/%23admissions-%23iitsSat, 27 Mar 2021 17:53:50 +0000#self doubts
https://csedoubts.gateoverflow.in/28936/%23self-doubts
In Database normalization, I had a question.<br />
<br />
In the 3rd Normal form, we remove the transitive dependency, so due to this removal, we remove some of the redundant entries.<br />
<br />
My question is why we need BCNF. How re are removing more redundant entries by using BCNF. <br />
<br />
please explain this by using an example and compare with 3rd normal form.Databaseshttps://csedoubts.gateoverflow.in/28936/%23self-doubtsSat, 27 Mar 2021 09:19:25 +0000Answered: Gate CSE score 678 rank 943 what opportunities do I have ??
https://csedoubts.gateoverflow.in/28891/gate-cse-score-678-rank-943-what-opportunities-do-i-have?show=28933#a28933
I think u can get iiit bangalore easily (thats best option i think at this score) and Nit surathkal,calicut and lower Nit’s and Mtech (RA) at old iits and mtech at new iits.<br />
<br />
ALL THE BEST !GATEhttps://csedoubts.gateoverflow.in/28891/gate-cse-score-678-rank-943-what-opportunities-do-i-have?show=28933#a28933Sat, 27 Mar 2021 02:45:10 +0000made easy workbook
https://csedoubts.gateoverflow.in/28934/made-easy-workbook
<p><img alt="" src="https://csedoubts.gateoverflow.in/?qa=blob&qa_blobid=11288511833277435121"></p>
<p>in this question since they are asking function time so it depends on n and so that’s y time is O(1)?</p>Algorithmshttps://csedoubts.gateoverflow.in/28934/made-easy-workbookSat, 27 Mar 2021 02:45:05 +0000TIFR-2019 probabilty
https://csedoubts.gateoverflow.in/28928/tifr-2019-probabilty
consider an urn with ‘a’ red and ‘b’ blue ball . Balls are drawn out one by one without replacement uniformly at random until the first red ball is drawn .what is expected no of ball drawn?Probabilityhttps://csedoubts.gateoverflow.in/28928/tifr-2019-probabiltyThu, 25 Mar 2021 06:04:15 +0000Answered: GATE-2022 guidance
https://csedoubts.gateoverflow.in/28874/gate-2022-guidance?show=28932#a28932
<p>You could use <a rel="nofollow" href="https://gatecse.in/gate-subjects/">subjects.gatecse.in</a> – </p>
<ul>
<li>Subjectwise resources for GATE CSE – all materials are listed under each subject page</li>
</ul>
<p> </p>GATEhttps://csedoubts.gateoverflow.in/28874/gate-2022-guidance?show=28932#a28932Thu, 25 Mar 2021 06:04:08 +0000Answered: TIFR-GS2021 Question
https://csedoubts.gateoverflow.in/28915/tifr-gs2021-question?show=28931#a28931
$\frac{1}{a^2 - 1} = \frac{1}{(a+1)(a-1)} = \frac{1}{2} \left (\frac{1}{a-1} - \frac{1}{a+1} \right )$<br />
<br />
So, I can write the given sum as :<br />
<br />
$\frac{1}{2} \left [ \left (\frac{1}{2-1} - \frac{1}{2+1} \right ) + \left (\frac{1}{4-1} - \frac{1}{4+1} \right ) + \left (\frac{1}{6-1} - \frac{1}{6+1} \right ) +……. + \left (\frac{1}{40-1} - \frac{1}{40+1} \right ) \right ]$<br />
<br />
$\frac{1}{2} \left [ \left (\frac{1}{1} - \frac{1}{3} \right ) + \left (\frac{1}{3} - \frac{1}{5} \right ) + \left (\frac{1}{5} - \frac{1}{7} \right ) + \frac{1}{7} – ……. + \left (\frac{1}{39} - \frac{1}{41} \right ) \right ]$<br />
<br />
$\frac{1}{2} \left ( \frac{1}{1} – \frac{1}{41} \right)$ $(\because \frac{1}{a+1} = \frac{1}{(a+2)-1})$<br />
<br />
$\frac{20}{41} $Calculushttps://csedoubts.gateoverflow.in/28915/tifr-gs2021-question?show=28931#a28931Wed, 24 Mar 2021 18:12:29 +0000Answered: TIRF-GS2021 Question
https://csedoubts.gateoverflow.in/28917/tirf-gs2021-question?show=28929#a28929
Suppose, the sides of the rectangle are $x$ and $y$ and radius of circle = $R$ unit then<br />
<br />
$$\max 2(x+y)$$<br />
<br />
$$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; subject \;\;to \;\; x^2 + y^2 = (2R)^2$$<br />
<br />
By Lagrangian Multiplier,<br />
<br />
Lagrangian function $\mathcal{L} = 2(x+y) – \lambda(x^2 + y^2 – (2R)^2)$<br />
<br />
Given $R=1$<br />
<br />
$\mathcal{L} = 2(x+y) – \lambda (x^2 + y^2 – 2^2)$<br />
<br />
By first order optimality condition,<br />
<br />
$\frac{\partial \mathcal{L}}{\partial x} = 0 \Rightarrow 2 - \lambda \times 2x = 0 \Rightarrow \lambda = \frac{1}{x}$ and<br />
<br />
$\frac{\partial \mathcal{L}}{\partial y} = 0 \Rightarrow 2 - \lambda \times 2y = 0 \Rightarrow \lambda = \frac{1}{y}$<br />
<br />
So, $x=y \rightarrow (1)$<br />
<br />
$\frac{\partial \mathcal{L}}{\partial \lambda} = 0 \Rightarrow x^2 + y^2 – 2^2 = 0 \Rightarrow x^2 + y^2 = 2^2 \rightarrow (2)$<br />
<br />
From $(1)$ and $(2)$<br />
<br />
$2x^2 = 2^2 \Rightarrow x = \pm \sqrt{2}$<br />
<br />
So, critical points are : $(\sqrt{2},\sqrt{2}), (-\sqrt{2},-\sqrt{2})$<br />
<br />
For $(\sqrt{2},\sqrt{2}),$ $2(x+y)$ will give maximum value.<br />
<br />
Hence, Area of rectangle = $\sqrt{2} \times \sqrt{2} = 2$<br />
<br />
$\textbf{Answer: (B)}$Calculushttps://csedoubts.gateoverflow.in/28917/tirf-gs2021-question?show=28929#a28929Wed, 24 Mar 2021 18:04:36 +0000Answered: TIFR-GS2021 Question
https://csedoubts.gateoverflow.in/28916/tifr-gs2021-question?show=28926#a28926
In the worst case we’ll choose $5$ red marbles, $6$ green marbles, $6$ blue marbles and $6$ yellow marbles, before choosing the marble that’ll be the seventh marble of the same color (either green, blue or yellow).<br />
<br />
So $5 + 6 + 6 + 6 + 1 = 24$ marbles.Combinatoryhttps://csedoubts.gateoverflow.in/28916/tifr-gs2021-question?show=28926#a28926Wed, 24 Mar 2021 10:53:53 +0000TIFR-GS2021 Question
https://csedoubts.gateoverflow.in/28925/tifr-gs2021-question
Lavanya and Ketak each flip a fair coin (i.e., both heads and tails have equal probability of appearing) $n$ times. What is the probability that Lavanya sees more heads than Ketak?<br />
<br />
In the following, the binomial conefficient $n\choose k$ counts the number of $k$-element subsets of an $n$-element set.<br />
<br />
(A) $\frac{1}{2}$<br />
<br />
(B) $\frac{1}{2}(1 – \sum_{i=0}^{n}\frac{{n\choose i}^2}{2^{2n}})$<br />
<br />
(C) $\frac{1}{2}(1 – \sum_{i=0}^{n}\frac{{n\choose i}}{2^{2n}})$<br />
<br />
(D) $\frac{1}{2}(1 – \sum_{i=0}^{n}\frac{1}{2^{2n}})$<br />
<br />
(B) $\sum_{i=0}^{n}\frac{{n\choose i}}{2^{2n}}$Probabilityhttps://csedoubts.gateoverflow.in/28925/tifr-gs2021-questionWed, 24 Mar 2021 10:49:57 +0000TIFR-GS2021 Question
https://csedoubts.gateoverflow.in/28924/tifr-gs2021-question
Fix $n\geq6$. Consider the set $C$ of binary strings $x_1x_2...x_n$ of length n such that the bits satisfy the following set of equalities, all modulo 2: $x_i + x_{i+1} + x_i+2 = 0$ for all $1\leq i\leq n-2, x_{n-1} + x_n + x_1 = 0$, and $x_n + x_1 + x_2 = 0$. What is the size of set $C$?<br />
<br />
(A) $1$ for all $n\geq6$<br />
<br />
(B) $4$ for all $n\geq6$<br />
<br />
(C) $0$ for all $n\geq6$<br />
<br />
(D) If $n \geq6$ is divisible by $3$ then $|C| = 1$. If $n\geq 6$ is not divisible by $3$ the $|C| = 4$<br />
<br />
(E) If $n \geq6$ is divisible by $3$ then $|C| = 4$. If $n\geq 6$ is not divisible by $3$ the $|C| =14$Set Theory & Algebrahttps://csedoubts.gateoverflow.in/28924/tifr-gs2021-questionWed, 24 Mar 2021 10:45:22 +0000TIFR-GS2021 Question
https://csedoubts.gateoverflow.in/28923/tifr-gs2021-question
Consider the sequence $$y_n = \frac{1}{\int_{1}^{n}\frac{1}{(1 + x/n)^3}dx}$$<br />
<br />
for $n = 2, 3, 4, ...$. Which of the following is TRUE?<br />
<br />
(A) The sequence $\{y_n\}$ does not have a limit as $n\rightarrow \infty$.<br />
<br />
(B) $y_n\leq 1$ for all $n = 2, 3, 4, ...$<br />
<br />
(C) $\lim_{n\rightarrow\infty} y_n$ exists and is equal to $6/\pi^2$.<br />
<br />
(D)$\lim_{n\rightarrow\infty} y_n$ exists and is equal to $0$.<br />
<br />
(E) The sequence $\{y_n\}$ first increases and then decreases as $n$ takes values $2, 3, 4, ...$Calculushttps://csedoubts.gateoverflow.in/28923/tifr-gs2021-questionWed, 24 Mar 2021 10:39:26 +0000TIFR-GS2021 Question
https://csedoubts.gateoverflow.in/28922/tifr-gs2021-question
Let $d$ be the number of positive square integers (that is, it is a square of some integer) that are factors of $20^5\times21^5$. Which of the following is true about $d$?<br />
<br />
(A) $50 \leq d < 100$<br />
<br />
(B) $100 \leq d < 150$<br />
<br />
(C) $150 \leq d < 200$<br />
<br />
(D) $200 \leq d < 300$<br />
<br />
(E) $300 \leq d$Combinatoryhttps://csedoubts.gateoverflow.in/28922/tifr-gs2021-questionWed, 24 Mar 2021 10:32:24 +0000TIFR-GS2021 Question
https://csedoubts.gateoverflow.in/28921/tifr-gs2021-question
A matching in a graph is a set of edges such that no two edges in the set share a common vertex. Let $G$ be a graph on $n$ vertices in which there is a subset $M$ of $m$ edges which is a matching. Consider a random process where each vertex in the graph is independently selected with probability $0 < p < 1$ and let $B$ be the set of vertices so obtained. What is the probability that there exists at least one edge from matching $M$ with both end points in the set B?<br />
<br />
(A) $p^2$<br />
<br />
(B) $1 – (1 – p^2)^m$<br />
<br />
(C) $p^{2m}$<br />
<br />
(D) $(1 – p^2)^m$<br />
<br />
(E) $1 – (1 – p(1 – p))^m$Probabilityhttps://csedoubts.gateoverflow.in/28921/tifr-gs2021-questionWed, 24 Mar 2021 10:29:09 +0000TIFR-GS2021 Question
https://csedoubts.gateoverflow.in/28920/tifr-gs2021-question
Let $n$, $m$ and $k$ be three positive integers such that $n \geq m \geq k$. Let $S$ be a subset of $\{1, 2, …, n\}$ of size $k$. Consider sampling a function uniformly at random from the set of all functions mapping $\{1, …, n\}$ to $\{1, …, m\}$. What is the probability that $f$ is not injective on the set S, i.e., there exists $i, j \in S$ such that $f(i) = f(j)$?<br />
<br />
In the following, the binomial coefficient $n\choose k$ counts the number of $k$-element subsets of an n-element set. <br />
<br />
(A) $1 – \frac{k!}{k^k}$<br />
<br />
(B) $1 – \frac{m!}{m^k}$<br />
<br />
(C) $1 – \frac{k!{m\choose k}}{m^k}$<br />
<br />
(D) $1 – \frac{k!{n\choose k}}{n^k}$<br />
<br />
(E) $1 – \frac{k!{n\choose k}}{m^k}$Combinatoryhttps://csedoubts.gateoverflow.in/28920/tifr-gs2021-questionWed, 24 Mar 2021 10:25:00 +0000TIFR-GS2021Question
https://csedoubts.gateoverflow.in/28919/tifr-gs2021question
What is the probability that at least two out of four people have their birthdays in the same month, assuming their birthdays are uniformly distributed over the twelve months?<br />
<br />
(A) $\frac{25}{48}$<br />
<br />
(B) $\frac{5}{8}$<br />
<br />
(C) $\frac{5}{12}$<br />
<br />
(D) $\frac{41}{96}$<br />
<br />
(E) $\frac{55}{96}$Probabilityhttps://csedoubts.gateoverflow.in/28919/tifr-gs2021questionWed, 24 Mar 2021 10:18:49 +0000TIFR-GS2021 Question
https://csedoubts.gateoverflow.in/28918/tifr-gs2021-question
<p>Let $M$ be a $n\times m$ real matrix. Consider the following:</p>
<ul>
<li>Let $k_1$ be the smallest number such that $M$ can be factorized as $A.B$, where $A$ is an $n\times k_1$ matrix and $B$ is a $k_1\times m$ matrix.</li>
<li>Let $k_2$ be the smallest number such that $M = \sum_{i=1}^{k_2}u_iv_i$, where $u_i$ is an $n\times1$ matrix and each $v_i$ is an $1\times m$ matrix.</li>
<li>Let $k_3$ be the column-rank of M.</li>
</ul>
<p>Which of the following statements is TRUE?</p>
<p>(A) $k_1 < k_2 < k_3$</p>
<p>(B) $k_1 < k_3 < k_2$</p>
<p>(C) $k_2 = k_3 < k_1$</p>
<p>(D) $k_1 = k_2 = k_3$</p>
<p>(E) No general relationship exists among $k_1$, $k_2$ and $k_3$</p>Linear Algebrahttps://csedoubts.gateoverflow.in/28918/tifr-gs2021-questionWed, 24 Mar 2021 10:14:06 +0000Gate2021 Normalization ≠ Reality ?
https://csedoubts.gateoverflow.in/28909/gate2021-normalization-%E2%89%A0-reality
<p>I got the <strong>Set-2 paper in GATE2021.</strong><br>
<strong>As all of you realize this year Set-2 was on the harder side</strong>.</p>
<p>According to the official answer-key, <strong>my marks were 28.<br>
Checked with GO predictor (The most accurate one)</strong></p>
<p> </p>
<p><img alt="" src="https://csedoubts.gateoverflow.in/?qa=blob&qa_blobid=1295213846281008731"></p>
<p> </p>
<p> </p>
<p>I hoped that as <strong>Set 2 was a bit tougher my marks would increase</strong>.<br>
But keep aside the raise <strong>my marks were decreased to 27.77.</strong></p>
<p> </p>
<p><img alt="" src="https://csedoubts.gateoverflow.in/?qa=blob&qa_blobid=13076859994326960873"></p>
<p> </p>
<p> </p>
<p>I do not understand how normalization works and I don't want to.</p>
<p>If marks don't increase I can understand but,<br>
It just does not make sense how a person with a difficult set has his marks reduced than the original. </p>
<p>You need not be a professor at IIT to understand this. You can ask any person strolling out. He would most likely concur with me if he just has common sense.</p>
<p><strong>Some of you may contend that with that 0.33 mark you would not land you in an IIT and I agree with you.</strong><br>
But just think what if I am correct? what if normalization was not according to reality?</p>
<p>Think briefly of an individual who had the capability of being in the top 100s and landed in the 300s or 500s he/she just missed because he got set 2 don't you think this is unjust? His/Her dream of getting into IISc and IITB just shattered.</p>
<p><u><strong>My question is straightforward "Why a person with difficult set marks are reduced?"</strong></u></p>
<p>Issued in the public interest.<br>
Please feel to correct me.</p>
<p> </p>
<p>I hope Arjun sir will clear All of My doubts. You are the only hope.</p>
<p> </p>
<p> </p>GATE Applicationhttps://csedoubts.gateoverflow.in/28909/gate2021-normalization-%E2%89%A0-realityTue, 23 Mar 2021 08:58:58 +0000Accommodation dilemma at IITB
https://csedoubts.gateoverflow.in/28910/accommodation-dilemma-at-iitb
<p>IITB aren’t providing any accommodation for their M.Tech program this year. How difficult will it be to stay outside campus?</p>
<p><u>Source</u>: IIT B information brochure: <a rel="nofollow" href="https://www.iitb.ac.in/newacadhome/MTECHBROUCHURE2021.pdf">https://www.iitb.ac.in/newacadhome/MTECHBROUCHURE2021.pdf</a></p>
<p><img alt="" src="https://csedoubts.gateoverflow.in/?qa=blob&qa_blobid=7943865562600604113"></p>IISc/IITshttps://csedoubts.gateoverflow.in/28910/accommodation-dilemma-at-iitbTue, 23 Mar 2021 08:57:36 +0000I got GATE-2021 AIR 447 & score of 742. Which colleges can I expect to call me for interview or admissions?
https://csedoubts.gateoverflow.in/28905/gate-2021-score-which-colleges-expect-interview-admissions
IISc/IITshttps://csedoubts.gateoverflow.in/28905/gate-2021-score-which-colleges-expect-interview-admissionsMon, 22 Mar 2021 15:55:42 +0000Gate 2019 Mining Question 19
https://csedoubts.gateoverflow.in/28907/gate-2019-mining-question-19
If the time to failure of a machine component is exponentially distributed, the reliability of the same at Mean Time to Failure (MTTF) is ____Operating Systemhttps://csedoubts.gateoverflow.in/28907/gate-2019-mining-question-19Mon, 22 Mar 2021 15:55:38 +0000Answered: Kenneth H Rosen
https://csedoubts.gateoverflow.in/28883/kenneth-h-rosen?show=28899#a28899
<ol>
<li>I did not buy a lottery ticket this week or I did not buy a lottery ticket.</li>
<li>I bought a lottery ticket this week or I won the million dollar jackpot.</li>
<li>If I bought a lottery ticket this week, then I won the million dollar jackpot.</li>
<li>I bought a lottery ticket this week, and I won the million dollar jackpot.</li>
<li>I won the million dollar jackpot if and only if I bout a lottery ticket this week.<br>
or<br>
If I bought a lottery ticket this week, I won the million dollar jackpot, else I didn’t win the million dollar jackpot.</li>
<li>If I did not buy a lottery ticket this week, then I did not win the million dollar jackpot.</li>
<li>I did not buy a lottery ticket this week, and I did not win the million dollar jackpot.</li>
<li>$$\lnot p \lor (p \land q) \implies (\lnot p \lor p) \land (\lnot p \lor q) \implies T\land (\lnot p \lor q) \implies p\rightarrow q$$ So same as 3.</li>
</ol>Mathematical Logichttps://csedoubts.gateoverflow.in/28883/kenneth-h-rosen?show=28899#a28899Mon, 22 Mar 2021 10:16:07 +0000Answered: Kenneth H Rosen
https://csedoubts.gateoverflow.in/28884/kenneth-h-rosen?show=28898#a28898
$$p \leftrightarrow q \implies (p \land q) \lor (\lnot p \land \lnot q)$$<br />
<br />
$$\lnot p \leftrightarrow \lnot q \implies (\lnot p \land \lnot q) \lor (\lnot \lnot p \land \lnot \lnot q) \implies (\lnot p \land \lnot q) \lor (p \land q) $$Mathematical Logichttps://csedoubts.gateoverflow.in/28884/kenneth-h-rosen?show=28898#a28898Mon, 22 Mar 2021 10:06:07 +0000