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<div style="background:#eef3fb;color:#303846;border:1px solid #c9d7ee;border-radius:12px;padding:14px 18px;margin:0 0 18px"><p style="margin:0;font-size:14px;line-height:1.6"><strong style="color:#171d29">Checked 26 September 2026.</strong> From the official GATE 2027 EC syllabus (IIT Madras) and the GATE 2026 EC syllabus (IIT Guwahati), compared word by word (our diff), and a text search of the official EC papers 2023–2026. The IIT Madras site calls the two-paper combinations tentative.</p></div>

<p style="margin:0 0 16px;line-height:1.7">IIT Madras, which organises GATE 2027, revised “most of the test papers” for the new cycle, and Electronics and Communication is one of them. The EC changes are not large — the 2027 PDF has 639 words against 628 in 2026 — but almost every one of them lands in a subject that carries marks: signals, devices, analog circuits, control and communications. None of the new terms appears in an EC paper since 2023, though related questions on sampling, controllers and information theory do. This guide lists every change, what it replaced, and how to fit the new material into the weeks left.</p>

<div style="display:flex;flex-wrap:wrap;gap:10px;margin:18px 0"><div style="flex:1 1 140px;background:#fbfaf6;border:1px solid #e4e1d8;border-radius:10px;padding:12px 14px"><div style="font-size:24px;font-weight:800;color:#171d29;line-height:1.2">8</div><div style="font-size:13px;color:#5b6472;line-height:1.4;margin-top:4px">sections — unchanged</div></div><div style="flex:1 1 140px;background:#fbfaf6;border:1px solid #e4e1d8;border-radius:10px;padding:12px 14px"><div style="font-size:24px;font-weight:800;color:#171d29;line-height:1.2">11</div><div style="font-size:13px;color:#5b6472;line-height:1.4;margin-top:4px">new or reworded items to learn (our checklist)</div></div><div style="flex:1 1 140px;background:#fbfaf6;border:1px solid #e4e1d8;border-radius:10px;padding:12px 14px"><div style="font-size:24px;font-weight:800;color:#171d29;line-height:1.2">0</div><div style="font-size:13px;color:#5b6472;line-height:1.4;margin-top:4px">EC papers 2023–26 using the new terms (our text search)</div></div><div style="flex:1 1 140px;background:#fbfaf6;border:1px solid #e4e1d8;border-radius:10px;padding:12px 14px"><div style="font-size:24px;font-weight:800;color:#171d29;line-height:1.2">6 Feb 2027</div><div style="font-size:13px;color:#5b6472;line-height:1.4;margin-top:4px">first GATE 2027 exam day</div></div></div><p style="margin:12px 0 0;font-size:13px;color:#5b6472;margin:-8px 0 18px">GATE 2026 and 2027 EC syllabi; GATE 2027 brochure; our text search of the official papers.</p>

<div style="background:#fff8e8;color:#3a3020;border:1px solid #f0d9a8;border-left:4px solid #b7791f;border-radius:12px;padding:18px 20px;margin:18px 0"><p style="margin:0 0 8px;font-size:12px;font-weight:700;letter-spacing:.08em;text-transform:uppercase;color:#b7791f">Where other pages get this wrong</p><p style="margin:0 0 10px;font-size:17px;font-weight:700;color:#171d29;line-height:1.5">The 2027 additions are FIR and IIR filter design, Nyquist sampling and reconstruction, energy bands in solids, MOSFET scaling, dominant-pole (Miller) compensation and phase margin, the PID controller, source coding, and correlation and regression. The syllabus contains no “5G”, “6G”, “IoT” or “embedded”.</p><p style="margin:0 0 8px;line-height:1.6"><strong style="color:#8a5300">Commonly published instead:</strong> Careers360: “Topics such as 5G/6G communication concepts, IoT and embedded applications have been added under communication systems”, and “IIT Madras has not deleted any topics for any GATE paper.”</p><p style="margin:0;line-height:1.6">GATE 2027 EC syllabus vs GATE 2026 EC syllabus (word-level comparison). EC did drop “discrete-time processing of continuous-time signals” and the named lag/lead/lag-lead compensation.</p></div>

Our word-level comparison of the official GATE 2026 EC syllabus (IIT Guwahati) and GATE 2027 EC syllabus (IIT Madras), page headers removed. The 2027 brochure’s EC appendix is word-for-word the standalone PDF. The Networks, Signals and Systems section also moves its LTI-systems block ahead of the signal heads — a reordering only.

Which new topics have ever been examined?

Our text search of the official EC question papers 2023–2026. “No hits” means none of the terms appears; related questions are listed where the older syllabus wording covered similar ground.

<p style="margin:0 0 16px;line-height:1.7">Treat the list in two groups. <strong>Extensions of familiar topics</strong> — PID after I and PD controllers, source coding after entropy and capacity, regression after correlation, reconstruction after sampling — can be learnt in a few focused hours each, because the surrounding theory is already on the syllabus. <strong>Genuinely new blocks</strong> — FIR/IIR filter design, Miller compensation with phase margin, MOSFET scaling and energy-band formation — need a textbook chapter each. None has a previous EC question to copy, so the safest preparation is the standard textbook problems for each.</p>

Marks by subject in the official EC papers, our classification of each question (the previous-papers guide in this series has the full count). GATE fixes only General Aptitude (15) and Engineering Mathematics (13).

<div style="background:#ffffff;color:#303846;border:1px solid #e4e1d8;border-radius:12px;padding:18px 20px;margin:18px 0" id="ecplan"><h3 style="margin:0 0 10px;font-size:17px;font-weight:700;color:#171d29">GATE EC 2027 revision planner</h3><p style="margin:0 0 12px;line-height:1.6">Choose your likely exam day and how many hours a week you can study. The planner counts the weeks left from today and splits your total hours across the paper.</p><div style="display:flex;flex-wrap:wrap;gap:10px;margin:0 0 12px"><label style="font-size:13px;font-weight:700;color:#5b6472">Exam day<br><select id="ecplan-d" style="padding:8px;border:1px solid #c9c4b5;border-radius:8px;font-size:16px"><option value="2027-02-06">6 Feb 2027</option><option value="2027-02-07">7 Feb 2027</option><option value="2027-02-13">13 Feb 2027</option><option value="2027-02-14">14 Feb 2027</option><option value="2027-02-20">20 Feb 2027</option><option value="2027-02-21">21 Feb 2027</option></select></label><label style="font-size:13px;font-weight:700;color:#5b6472">Hours per week<br><input id="ecplan-h" type="number" min="1" max="80" value="22" style="width:100px;padding:8px;border:1px solid #c9c4b5;border-radius:8px;font-size:16px"></label></div><div id="ecplan-out" style="line-height:1.7"></div><script>(function(){var R=document.getElementById('ecplan');if(!R)return;var P=[{"name":"Networks + Signals & Systems (~16 marks; incl. FIR/IIR, sampling and reconstruction)","share":0.163},{"name":"Analog Circuits (~12; incl. Miller compensation, phase margin)","share":0.117},{"name":"Engineering Mathematics (~11 by our count, 13 by rule; incl. regression)","share":0.113},{"name":"Digital Circuits (~11)","share":0.11},{"name":"Communications (~11; incl. source coding)","share":0.107},{"name":"Electronic Devices (~9; incl. energy bands, MOSFET scaling)","share":0.087},{"name":"Control Systems (~8; incl. PID)","share":0.083},{"name":"Electromagnetics (~7)","share":0.07},{"name":"General Aptitude (15)","share":0.15}];function g(x){return document.getElementById('ecplan'+x);}function go(){var d=new Date(g('-d').value+'T09:30:00+05:30'),h=parseFloat(g('-h').value),now=new Date(),o=g('-out');if(isNaN(d.getTime())||isNaN(h)||h<=0){o.innerHTML='Choose an exam day and enter your weekly hours.';return;}var days=Math.ceil((d-now)/864e5);if(days<=0){o.innerHTML='That date has passed.';return;}var w=days/7,tot=Math.round(w*h);var raw=P.map(function(p){return tot*p.share;}),fl=raw.map(Math.floor),left=tot-fl.reduce(function(a,b){return a+b;},0),ord=raw.map(function(v,i){return [v-Math.floor(v),i];}).sort(function(a,b){return b[0]-a[0];});for(var k=0;k<left&&k<ord.length;k++)fl[ord[k][1]]++;var rows=P.map(function(p,i){return '<li style="margin:4px 0">'+p.name+': <strong>'+fl[i]+' h</strong></li>';}).join('');o.innerHTML='<strong>'+days+' days ('+w.toFixed(1)+' weeks) left</strong> — about <strong>'+tot+' study hours</strong> at '+h+' h/week.<ul style="margin:8px 0 0;padding-left:20px">'+rows+'</ul>';}g('-d').addEventListener('change',go);g('-h').addEventListener('input',go);go();})();</script></div>

Pick a likely exam day (the six GATE 2027 dates; EC’s own date is not yet published — in 2026 EC ran on Sunday 15 February, forenoon). Shares are the three-year mean marks in the table above.

<div style="background:#ffffff;color:#303846;border:1px solid #e4e1d8;border-radius:12px;padding:18px 20px;margin:18px 0" id="ec27new"><h3 style="margin:0 0 10px;font-size:17px;font-weight:700;color:#171d29">New 2027 topics checklist</h3><p style="margin:0 0 12px;line-height:1.6">Tick each topic once you can solve standard textbook problems on it.</p><div style="background:#f1eee6;border-radius:6px;height:12px;overflow:hidden;margin:0 0 6px"><div id="ec27new-bar" style="width:0%;height:12px;background:#1f7a45"></div></div><p id="ec27new-txt" style="margin:0 0 14px;font-size:13px;color:#5b6472">0 of 11 done</p><div style="margin:0 0 12px" data-g="0"><div style="font-weight:700;color:#171d29;margin:0 0 6px">Signals & Systems <span data-gc="0" style="font-weight:600;color:#5b6472;font-size:13px">(0/3)</span></div><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="0" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>FIR filter design</span></label><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="1" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>IIR filter design</span></label><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="2" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>Nyquist sampling, sampling and reconstruction</span></label></div><div style="margin:0 0 12px" data-g="1"><div style="font-weight:700;color:#171d29;margin:0 0 6px">Devices & Analog <span data-gc="1" style="font-weight:600;color:#5b6472;font-size:13px">(0/4)</span></div><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="3" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>Formation of energy bands in solids</span></label><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="4" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>Scaling in MOSFETs</span></label><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="5" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>Dominant-pole (Miller) compensation</span></label><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="6" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>Phase margin</span></label></div><div style="margin:0 0 12px" data-g="2"><div style="font-weight:700;color:#171d29;margin:0 0 6px">Control, Communications, Maths <span data-gc="2" style="font-weight:600;color:#5b6472;font-size:13px">(0/4)</span></div><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="7" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>PID controller</span></label><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="8" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>Source coding</span></label><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="9" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>Correlation and regression analysis</span></label><label style="display:flex;gap:8px;align-items:flex-start;margin:0 0 6px;font-size:14px;line-height:1.5;color:#303846;cursor:pointer"><input type="checkbox" data-i="10" style="margin-top:4px;width:16px;height:16px;flex:0 0 auto"> <span>Nonhomogeneous linear ODEs, Euler-Cauchy</span></label></div><p style="margin:12px 0 0;font-size:13px;color:#5b6472">Ticks are saved only in this browser on this device.</p><script>(function(){var R=document.getElementById('ec27new');if(!R)return;var K='ec27new',N=11,bx=R.querySelectorAll('input[type=checkbox]'),s={};try{s=JSON.parse(localStorage.getItem(K)||'{}')}catch(e){}function up(){var d=0;for(var i=0;i<bx.length;i++){if(bx[i].checked)d++;}document.getElementById('ec27new-bar').style.width=(d/N*100)+'%';document.getElementById('ec27new-txt').textContent=d+' of '+N+' done';var gs=R.querySelectorAll('[data-g]');for(var j=0;j<gs.length;j++){var c=gs[j].querySelectorAll('input'),k=0;for(var q=0;q<c.length;q++){if(c[q].checked)k++;}var sp=R.querySelector('[data-gc="'+gs[j].getAttribute('data-g')+'"]');if(sp)sp.textContent='('+k+'/'+c.length+')';}}for(var i=0;i<bx.length;i++){(function(b){if(s[b.getAttribute('data-i')])b.checked=true;b.addEventListener('change',function(){s[b.getAttribute('data-i')]=b.checked?1:0;try{localStorage.setItem(K,JSON.stringify(s))}catch(e){}up();});})(bx[i]);}up();})();</script></div>

GATE 2027 Information Brochure and important-dates page. DigiLocker registration is mandatory for Indian nationals, with live facial capture. Scores are valid for three years.

<p style="margin:0 0 16px;line-height:1.7">One correction to what several pages still say: the portal did not open on 14 August 2026 and the regular window did not close on 21 September. IIT Madras has moved these dates more than once; the portal opened on 2 September and the regular window now closes on 5 October, with a late-fee window to 12 October. EC’s own exam day and session are not yet published — the paper-wise schedule was not on the site on 26 September 2026. EC has been a single-session paper every year since 2023 (each year’s final key carries one session), so it will very likely sit alone in one slot again, but that is our expectation, not a notice.</p>

GATE 2026 brochure; GATE 2027 brochure Table 4 and the two-paper combinations page. RA = the new Robotics & Automation paper.

<p style="margin:0 0 16px;line-height:1.7">The one new option is <strong>EC + RA</strong>. The Robotics & Automation paper has 15 marks of General Aptitude, a common Part A of 60 marks, and a Part B of 25 marks in which candidates choose B1 “Electrical” (analog circuits and embedded systems, signals and systems, control) or B2 “Mechanical”. An EC candidate’s signals, control and analog preparation carries into Part B1; Part A adds mechanics, actuators, PLC/CNC and Python, which are outside EC (our reading of the RA syllabus). Only consider it if you are also targeting robotics programmes that ask for RA; otherwise the hours are better spent on the new EC topics above, which are certain to be on the syllabus for everyone writing EC.</p>

<div style="background:#ecf7ef;color:#1f3a2a;border:1px solid #b9dec6;border-radius:12px;padding:18px 20px;margin:22px 0"><p style="margin:0 0 8px;font-size:12px;font-weight:700;letter-spacing:.08em;text-transform:uppercase;color:#1f7a45">Practise it, don't just read it</p><p style="margin:0 0 12px;font-size:16px;line-height:1.6;color:#171d29">The subjects around the new topics are where EC’s marks already sit. The GATE EC quizzes cover diodes, digital logic, transfer functions, signals, Maxwell’s equations and antennas.</p><p style="margin:0 0 12px;line-height:1.6">The ProSyllabus GATE EC library has topic quizzes on diode circuits and clippers, Boolean algebra and Karnaugh maps, transfer functions and block diagrams, signals and systems, Maxwell’s equations, and antennas and propagation — the first quiz is free.</p><p style="margin:0"><a href="/exam/gate-ec/practice-quiz" style="display:inline-block;background:#ffffff;color:#1f7a45;border:2px solid #1f7a45;padding:9px 18px;border-radius:8px;text-decoration:none;font-weight:700">Start a GATE EC quiz →</a></p></div>

<div style="background:#ffffff;color:#303846;border:1px solid #e4e1d8;border-radius:12px;padding:18px 20px;margin:18px 0"><h3 style="margin:0 0 10px;font-size:17px;font-weight:700;color:#171d29">More in this series</h3><ul style="margin:0;padding-left:20px"><li style="margin:6px 0;line-height:1.6"><a href="/hub/gate-ec-marks-vs-score-vs-rank-calculator" style="color:#255a45">GATE EC marks vs score vs rank, 2023–2026</a></li><li style="margin:6px 0;line-height:1.6"><a href="/hub/gate-ec-previous-year-papers-subject-wise-msq-nat" style="color:#255a45">GATE EC previous papers 2024–2026, counted question by question</a></li><li style="margin:6px 0;line-height:1.6"><a href="/hub/gate-ec-psu-recruitment-powergrid-ntpc-npcil-cutoffs" style="color:#255a45">PSUs through GATE EC: POWERGRID, NTPC, NPCIL and their cut-offs</a></li><li style="margin:6px 0;line-height:1.6"><a href="/hub/gate-ec-mtech-ccmt-vlsi-communication-closing-scores-iit-cutoffs" style="color:#255a45">M.Tech after GATE EC: CCMT and IIT cut-offs for VLSI and communication</a></li><li style="margin:6px 0;line-height:1.6"><a href="/hub/gate-ec-vs-ee-vs-in-which-paper-ece-eee-students" style="color:#255a45">GATE EC vs EE vs IN (and RA): which paper to write in 2027</a></li><li style="margin:6px 0;line-height:1.6"><a href="/hub/exam-alert-and-updates-for-gate-ec" style="color:#255a45">GATE EC notice board — official updates</a></li></ul></div>

<div style="background:#ffffff;color:#303846;border:1px solid #e4e1d8;border-radius:12px;padding:18px 20px;margin:18px 0"><h3 style="margin:0 0 10px;font-size:17px;font-weight:700;color:#171d29">Sources</h3><ul style="margin:0;padding-left:20px"><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027.iitm.ac.in/static/doc/GATE2027_Syllabus/EC_GATE2027_Syllabus.pdf" rel="nofollow noopener" style="color:#255a45">GATE 2027 EC syllabus (PDF)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2026.iitg.ac.in/doc/GATE2026_Syllabus/EC_2026_Syllabus.pdf" rel="nofollow noopener" style="color:#255a45">GATE 2026 EC syllabus (PDF, IIT Guwahati)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027ib.iitm.ac.in/GATE2027-IB.pdf" rel="nofollow noopener" style="color:#255a45">GATE 2027 Information Brochure, IIT Madras (revised 27 Sep 2026)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027.iitm.ac.in/important_dates" rel="nofollow noopener" style="color:#255a45">GATE 2027 — Important dates</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027.iitm.ac.in/application_fees" rel="nofollow noopener" style="color:#255a45">GATE 2027 — Application fees</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027.iitm.ac.in/two_paper_combinations" rel="nofollow noopener" style="color:#255a45">GATE 2027 — Two-paper combinations</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027.iitm.ac.in/static/doc/GATE2027_Syllabus/RA_GATE2027_Syllabus.pdf" rel="nofollow noopener" style="color:#255a45">GATE 2027 Robotics &amp; Automation (RA) syllabus (PDF)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2026.iitg.ac.in/doc/IB/GATE2026-IB-10102025.pdf" rel="nofollow noopener" style="color:#255a45">GATE 2026 Information Brochure, IIT Guwahati (PDF)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2026.iitg.ac.in/examination-schedule.html" rel="nofollow noopener" style="color:#255a45">GATE 2026 — examination schedule</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027.iitm.ac.in/static/doc/download/2026/QPs/EC.pdf" rel="nofollow noopener" style="color:#255a45">GATE 2026 EC question paper (PDF)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027.iitm.ac.in/static/doc/download/2025/EC2025.pdf" rel="nofollow noopener" style="color:#255a45">GATE 2025 EC question paper (PDF)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027.iitm.ac.in/static/doc/download/2024/EC24S7.pdf" rel="nofollow noopener" style="color:#255a45">GATE 2024 EC question paper (PDF)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#1f7a45;font-weight:700">official</span> — <a href="https://gate2027.iitm.ac.in/static/doc/download/2023/ec_2023.pdf" rel="nofollow noopener" style="color:#255a45">GATE 2023 EC question paper (PDF)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#8a5300;font-weight:700">reported</span> — <a href="https://engineering.careers360.com/articles/gate-2027-syllabus-changes-explained-key-updates-preparation-tips" rel="nofollow noopener" style="color:#255a45">Careers360 — GATE 2027 syllabus changes explained (reported; see corrections)</a></li><li style="margin:6px 0;line-height:1.6"><span style="color:#8a5300;font-weight:700">reported</span> — <a href="https://www.pw.live/gate/exams/gate-ece-syllabus" rel="nofollow noopener" style="color:#255a45">PW — GATE ECE syllabus 2027 (reported; see corrections)</a></li></ul><p style="margin:12px 0 0;font-size:13px;color:#5b6472"><strong style="color:#1f7a45">official</strong> = a document published by the conducting body. <strong style="color:#8a5300">reported</strong> = a news or coaching site we could not check against an original. Where sources disagree this page says so rather than picking one.</p></div>

<a href="/exam/gate-ec">This article has been published in GATE Electronics and Communication Engineering. Explore everything related to it here.</a>

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Covers geometric definitions, derivation of standard equations, properties, and graphical representations of circles, parabolas, ellipses, and hyperbolas; discusses eccentricity, axes, latus rectum, and real-life applications in physics and engineering, with examples, exercises, and historical context from Apollonius to modern analytic geometry.

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Explores the statement and proof of binomial theorem for positive integral indices, use of binomial coefficients and Pascal’s triangle, patterns in expansions, special cases, and diverse applications including numerical computations, divisibility, and historical context in Indian and world mathematics.

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Discusses the fundamental principle of counting, meaning and types of permutations and combinations, their formulas, properties, differences, solved examples, word problems, circular permutations, and real-life applications.

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