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Sunday, 25 October

JEE Main · Maths · Class 11

Binomial Theorem: JEE Main previous year questions

140 questions in 105 of the 108 JEE Main shifts Lumi analysed, asked in 8 of 8 years. Here is what this chapter tests and how.

Study this chapter
Questions
140
in 105 of 108 shifts · 8 of 8 years
Average a shift
1.1
of 25 Maths · 1.1 since 2024 -0.1
Typical range
0.9–1.4
questions a shift; fewest 0.9, most 1.7
Weighted estimate
1.2
model, recent years count more · about 4.7 marks
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

What to do

How to spend time on Binomial Theorem

Priority

Should do

One of the 6 Maths chapters that took Maths from half to 80% of its questions in the 108 shifts analysed. How bands are set

Past questions
140in 105 of 108 shifts
Study plan gives it
21 hover 12 months; 15 h over 6
Study this chapter →

Ideas asked most often

  1. Ratio of Consecutive Coefficients9×
  2. Coefficient Extraction from Products6×
  3. Sum of all Coefficients6×
  4. Hockey Stick Identity4×
  5. Sum of Even and Odd Coefficients4×

27 of the 62 ideas in Lumi’s map of this chapter have not been asked or touched in the shifts analysed. Of its idea-tagged questions from 2024 on, 22% tested an idea not asked in an earlier year, so learn the whole chapter, not just the list above.

Within each subject, chapters in NTA's 2026 syllabus are ranked by their average questions a shift over all 8 years analysed (history, not the model). Going down that list, the chapters that together held the first half of the subject's questions are Must do; the next ones, up to 80%, are Should do; the rest are Lower priority.

Key findings

Binomial Theorem at a glance

  1. 01

    78%

    of its 23 questions from 2024 on that Lumi matched to an idea tested one JEE Main had asked in an earlier year; 100% came from a topic asked in an earlier year.

  2. 02

    44%

    of the 62 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    46%

    of its questions asked for a numerical answer, 1.5 times the Maths average.

  4. 04

    28%

    of its questions were rated hard, against 26% across all Maths questions in the same shifts.

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

0240.9’171.2’201.1’211’221.7’230.9’241.4’251’26

Raw count: 2017: 1 in 1 shift · 2020: 14 in 12 shifts · 2021: 32 in 24 shifts · 2022: 29 in 24 shifts · 2023: 24 in 12 shifts · 2024: 20 in 18 shifts · 2025: 11 in 8 shifts · 2026: 9 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Numerical answer46%
  • Multi-step24%
  • Calculation16%
  • Application13%
  • Recall, single correct1%
  • Two statements1%

Most common asks: term independent of x in expansion (19); remainder of large power on division (10); sum of series with summation general term (5).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Rank, all JEE chapters
#26
of 70 by weighted estimate
Rank in Maths
#9
of 21 chapters
Share of Maths
4.6%
of its questions, all shifts analysed
Busiest year
2023
1.7 questions a shift
Year to year
Steady
varies by about 0.3 questions a shift
Long-run direction
+0.03
questions a shift, per year
Easy questions
9%
28% rated hard
Numerical answer
46%
1.5× the Maths rate
With a figure
0%
graph, diagram or structure
Study time
21 h
15 h on a 6-month plan
Marks per study hour
0.23
#46 of 70 chapters
Foundation for others
35%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 20171
  • 202014
  • 202132
  • 202229
  • 202324
  • 202420
  • 202511
  • 20269
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step47%
  • Calculation36%
  • Application16%
  • Recall1%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 62 ideas. In the 108 shifts analysed, JEE Main built a question around 28 of them. Most of the chapter has never been the main idea of a question, so past questions alone leave most of it out.

Asked as the main idea
28
Touched on in a question
7
Never asked
27

Topics

What repeats, topic by topic

This chapter's questions per topic in each year's analysed shifts. The number is the count; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. 71 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
016+questions in that year’s analysed shifts, shaded per shift
  • Binomial Coefficients

    As a topic: 67 questions in 8 of 8 years, most often single correct, 48% numerical answer. Recent asks: binomial sum via integration method; equate middle term coefficients of two expansions; numerical: n from equal coefficient condition.

  • Permutations and Combinations

    As a topic: 137 questions in 8 of 8 years, most often numerical value, 52% numerical answer. Recent asks: distribute objects with no empty box; count words with letter-type restrictions; count distributions of people to floors.

  • Arithmetico-Geometric Series

    As a topic: 22 questions in 6 of 8 years, most often single correct, 50% numerical answer.

Drill down

Topic, idea, question

Open a topic to see every idea JEE Main tested inside it, then open an idea to read the questions. Each row shows its 8 years.

  • Open66 · 47%6161471156

    28 ideas inside

    • OpenRepeated9 · 14%2222
    • OpenRepeated6 · 9%33
    • OpenRepeated6 · 9%22
    • OpenRepeated4 · 6%2
    • OpenRepeated3 · 5%2
    • OpenRepeated3 · 5%2
    • OpenRepeated3 · 5%
    • OpenRepeated3 · 5%
    • OpenRepeated3 · 5%
    • OpenRepeated3 · 5%
    • OpenRepeated2 · 3%
    • OpenRepeated2 · 3%
    • OpenRepeated2 · 3%
    • OpenRepeated2 · 3%
    • Open2 · 3%2
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
  • Open2 · 1%
  • Open1 · 1%

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

The exact ideas JEE Main has asked

Inside the topics, 29 different ideas were tested; 16 came more than once. These are the repeats, then the ideas new since 2024.

Dots are the 8 years with analysed shifts, 2017 to 2026.

Every question

All 140 Binomial Theorem questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 20269 questions

  1. 2 Apr 2026, Shift 1 · Q7The number of elements in the set…MediumSingle correct
  2. 2 Apr 2026, Shift 2 · Q6If for 3≤r≤303 \le r \le 30, (30C30−r)+3(30C31−r)+3(30C32−r)+(30C33−r)=mCr\binom{30}{C_{30-r}} + 3\binom{30}{C_{31-r}} + 3\binom{30}{C_{32-r}} + \binom{30}{C_{33-r}} = ^m C_r, then mm…MediumSingle correct
  3. 4 Apr 2026, Shift 1 · Q9Let the smallest value of k∈Nk\in\mathbb{N}, for which the coefficient of x3x^3 in…MediumSingle correct
  4. 4 Apr 2026, Shift 2 · Q9In the expansion of (9x−13x)18\left(9x-\frac{1}{3\sqrt{x}}\right)^{18}, x>0x>0, if the term independent of xx is (221)k(221)k, then kk is equal to:MediumSingle correct
  5. 5 Apr 2026, Shift 1 · Q23If the sum of the coefficients of x7x^7 and x14x^{14} in the expansion of (1x3−x4)n\left(\frac{1}{x^3} - x^4\right)^n, x≠0x \neq 0, is zero, then…MediumNumerical value
  6. 5 Apr 2026, Shift 2 · Q7The coefficient of x2x^2 in the expansion of (2x2+1x)10\left(2x^2+\frac{1}{x}\right)^{10}, x≠0x \neq 0, is :EasySingle correct
  7. 6 Apr 2026, Shift 1 · Q8If the coefficients of the middle terms in the binomial expansions of (1+αx)26(1+\alpha x)^{26} and (1−αx)28(1-\alpha x)^{28}, α≠0\alpha\neq 0, are…EasySingle correct
  8. 6 Apr 2026, Shift 2 · Q22If (1−x3)10=∑r=010arxr(1−x)30−2r(1-x^3)^{10}=\sum_{r=0}^{10}a_r x^r(1-x)^{30-2r}, then 9a9a10\frac{9a_9}{a_{10}} is equal to __________.HardNumerical value
  9. 8 Apr 2026, Shift 2 · Q8If…HardSingle correct

JEE Main 202511 questions

  1. 2 Apr 2025, Shift 1 · Q6The largest n∈Nn\in\mathbf{N} such that 3n3^n divides 50!50! is :EasySingle correct
  2. 2 Apr 2025, Shift 1 · Q16The term independent of xx in the expansion of (x+1x2/3+1−x1/3−x−1x−x1/2)10\left(\frac{x+1}{x^{2/3}+1-x^{1/3}}-\frac{x-1}{x-x^{1/2}}\right)^{10}, x>1x>1, is :MediumSingle correct
  3. 2 Apr 2025, Shift 2 · Q7If ∑r=010(10r+1−110r)⋅11Cr+1=α11−11111010\sum_{r=0}^{10}\left(\frac{10^{r+1}-1}{10^r}\right)\cdot {}^{11}C_{r+1} = \frac{\alpha^{11}-11^{11}}{10^{10}}, then α\alpha is equal…HardSingle correct
  4. 3 Apr 2025, Shift 1 · Q8If ∑r=19(r+32r)⋅9Cr=α(32)9−β\sum_{r=1}^{9}\left(\frac{r+3}{2^r}\right)\cdot {}^9C_r = \alpha\left(\frac{3}{2}\right)^9 - \beta, α,β∈N\alpha, \beta \in \mathbb{N},…MediumSingle correct
  5. 3 Apr 2025, Shift 1 · Q9The sum of all rational terms in the expansion of (2+3)8\left(2+\sqrt{3}\right)^8 isMediumSingle correct
  6. 3 Apr 2025, Shift 2 · Q21Let (1+x+x2)10=a0+a1x+a2x2+…+a20x20(1 + x + x^2)^{10} = a_0 + a_1 x + a_2 x^2 + \ldots + a_{20} x^{20}. If (a1+a3+a5+…+a19)−11a2=121k(a_1 + a_3 + a_5 + \ldots + a_{19}) - 11a_2 = 121k, then…HardNumerical value
  7. 4 Apr 2025, Shift 2 · Q7If 12⋅(15C1)+22⋅(15C2)+32⋅(15C3)+…+152⋅(15C15)=2m⋅3n⋅5k1^2\cdot({}^{15}C_1)+2^2\cdot({}^{15}C_2)+3^2\cdot({}^{15}C_3)+\ldots+15^2\cdot({}^{15}C_{15})=2^m\cdot3^n\cdot5^k, where…MediumSingle correct
  8. 7 Apr 2025, Shift 1 · Q7The remainder when ((64)(64))(64)\left((64)^{(64)}\right)^{(64)} is divided by 7 is equal toEasySingle correct
  9. 7 Apr 2025, Shift 2 · Q21The sum of the series…HardNumerical value
  10. 8 Apr 2025, Shift 2 · Q8The number of integral terms in the expansion of (512+718)1016\left(5^{\frac{1}{2}} + 7^{\frac{1}{8}}\right)^{1016} isMediumSingle correct
  11. 8 Apr 2025, Shift 2 · Q22The product of the last two digits of (1919)1919(1919)^{1919} is __________MediumNumerical value

JEE Main 202420 questions

  1. 4 Apr 2024, Shift 1 · Q8The sum of all rational terms in the expansion of (215+513)15\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15} is equal to :MediumSingle correct
  2. 4 Apr 2024, Shift 1 · Q23Let a=1+2C23!+3C24!+4C25!+…a=1+\frac{{}^2C_2}{3!}+\frac{{}^3C_2}{4!}+\frac{{}^4C_2}{5!}+\ldots,…HardNumerical value
  3. 4 Apr 2024, Shift 2 · Q4If the coefficients of x4x^4, x5x^5 and x6x^6 in the expansion of (1+x)n(1+x)^n are in the arithmetic progression, then the maximum value of…MediumSingle correct
  4. 5 Apr 2024, Shift 1 · Q24If the constant term in the expansion of (1+2x−3x3)(32x2−13x)9(1+2x-3x^3)\left(\frac{3}{2}x^2-\frac{1}{3x}\right)^9 is pp, then 108p108p is equal to ________.MediumNumerical value
  5. 5 Apr 2024, Shift 2 · Q9If the constant term in the expansion of (35x+2x53)12\left(\frac{\sqrt[5]{3}}{x}+\frac{2x}{\sqrt[3]{5}}\right)^{12}, x≠0x \neq 0, is…MediumSingle correct
  6. 6 Apr 2024, Shift 1 · Q23If the second, third and fourth terms in the expansion of (x+y)n(x+y)^n are 135135, 3030 and 103\frac{10}{3}, respectively, then 6(n3+x2+y)6(n^3+x^2+y)…MediumNumerical value
  7. 6 Apr 2024, Shift 2 · Q23If S(x)=(1+x)+2(1+x)2+3(1+x)3+⋯+60(1+x)60S(x)=(1+x)+2(1+x)^2+3(1+x)^3+\cdots+60(1+x)^{60}, x≠0x\ne 0, and (60)2S(60)=a(b)b+b(60)^2 S(60)=a(b)^b+b, where a,b∈Na,b\in\mathbb{N}, then (a+b)(a+b) equal…HardNumerical value
  8. 8 Apr 2024, Shift 1 · Q24Let α=∑r=0n(4r2+2r+1) nCr\alpha=\sum_{r=0}^{n}(4r^2+2r+1)\,{}^nC_r and β=(∑r=0nnCrr+1)+1n+1\beta=\left(\sum_{r=0}^{n}\frac{{}^nC_r}{r+1}\right)+\frac{1}{n+1}. If…HardNumerical value
  9. 8 Apr 2024, Shift 2 · Q6If the term independent of xx in the expansion of (ax2+12x3)10\left(\sqrt{a}x^2 + \frac{1}{2x^3}\right)^{10} is 105, then a2a^2 is equal to :MediumSingle correct
  10. 9 Apr 2024, Shift 1 · Q4The coefficient of x70x^{70} in x2(1+x)98+x3(1+x)97+x4(1+x)96+…+x54(1+x)46x^2(1+x)^{98}+x^3(1+x)^{97}+x^4(1+x)^{96}+\ldots+x^{54}(1+x)^{46} is 99Cp−46Cq{}^{99}C_p-{}^{46}C_q. Then a…HardSingle correct
  11. 9 Apr 2024, Shift 1 · Q25The remainder when 4282024428^{2024} is divided by 2121 is ________.MediumNumerical value
  12. 9 Apr 2024, Shift 2 · Q6The sum of the coefficient of x2/3x^{2/3} and x−2/5x^{-2/5} in the binomial expansion of (x2/3+12x−2/5)9\left(x^{2/3}+\frac{1}{2}x^{-2/5}\right)^9 isMediumSingle correct
  13. 1 Feb 2024, Shift 1 · Q23If the Coefficient of x30x^{30} in the expansion of (1+1x)6(1+x2)7(1−x3)8\left(1+\frac{1}{x}\right)^6(1+x^2)^7(1-x^3)^8 ; x≠0x\neq0 is α\alpha, then…HardNumerical value
  14. 1 Feb 2024, Shift 2 · Q6Let mm and nn be the coefficients of seventh and thirteenth terms respectively in the expansion of…MediumSingle correct
  15. 27 Jan 2024, Shift 1 · Q6If A denotes the sum of all the coefficients in the expansion of (1−3x+10x2)n(1-3x+10x^2)^n and B denotes the sum of all the coefficients in the…EasySingle correct
  16. 29 Jan 2024, Shift 1 · Q23If 11C12+11C23+…+11C910=nm\frac{{}^{11}C_1}{2}+\frac{{}^{11}C_2}{3}+\ldots+\frac{{}^{11}C_9}{10}=\frac{n}{m} with gcd⁡(n,m)=1\gcd(n,m)=1, then n+mn+m is equal to ______.MediumNumerical value
  17. 30 Jan 2024, Shift 1 · Q23Number of integral terms in the expansion of {7(12)+11(16)}824\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824} is equal to…HardNumerical value
  18. 30 Jan 2024, Shift 2 · Q24Let α=∑k=0n((nCk)2k+1)\alpha = \sum_{k=0}^{n} \left(\frac{({}^nC_k)^2}{k+1}\right) and…HardNumerical value
  19. 31 Jan 2024, Shift 1 · Q24In the expansion of (1+x)(1−x2)(1+3x+3x2+1x3)5, x≠0(1+x)(1-x^2)\left(1+\frac{3}{x}+\frac{3}{x^2}+\frac{1}{x^3}\right)^5,\ x\neq0, the sum of the coefficients of x3x^3…MediumNumerical value
  20. 31 Jan 2024, Shift 2 · Q23Let the coefficient of xrx^r in the expansion of (x+3)n−1+(x+3)n−2(x+2)+(x+3)n−3(x+2)2+…+(x+2)n−1(x+3)^{n-1}+(x+3)^{n-2}(x+2)+(x+3)^{n-3}(x+2)^2+\ldots+(x+2)^{n-1} be αr\alpha_r. If…HardNumerical value

JEE Main 202324 questions

  1. 6 Apr 2023, Shift 1 · Q5Basic nCr Properties · Easy · Single correct
  2. 6 Apr 2023, Shift 1 · Q6Open the question · Medium · Single correct
  3. 6 Apr 2023, Shift 1 · Q24Open the question · Medium · Numerical value
  4. 6 Apr 2023, Shift 2 · Q6Open the question · Hard · Two statements
  5. 6 Apr 2023, Shift 2 · Q7Open the question · Medium · Single correct
  6. 6 Apr 2023, Shift 2 · Q23Sum of Finite AGP · Hard · Numerical value
  7. 8 Apr 2023, Shift 1 · Q8Ratio of Consecutive Coefficients · Medium · Single correct
  8. 8 Apr 2023, Shift 1 · Q22Open the question · Medium · Numerical value
  9. 8 Apr 2023, Shift 2 · Q6Open the question · Medium · Single correct
  10. 8 Apr 2023, Shift 2 · Q7Open the question · Medium · Single correct
  11. 10 Apr 2023, Shift 1 · Q5Open the question · Medium · Single correct
  12. 10 Apr 2023, Shift 1 · Q25Open the question · Medium · Numerical value
  13. 10 Apr 2023, Shift 2 · Q6Open the question · Medium · Single correct
  14. 10 Apr 2023, Shift 2 · Q7Open the question · Medium · Single correct
  15. 11 Apr 2023, Shift 1 · Q21Sum of all Coefficients · Medium · Numerical value
  16. 11 Apr 2023, Shift 1 · Q27Open the question · Medium · Numerical value
  17. 11 Apr 2023, Shift 2 · Q8Ratio of Consecutive Coefficients · Medium · Single correct
  18. 12 Apr 2023, Shift 1 · Q5Alternating Binomial Series · Medium · Single correct
  19. 12 Apr 2023, Shift 1 · Q6Integration Method for Sums · Medium · Single correct
  20. 13 Apr 2023, Shift 1 · Q13Open the question · Medium · Single correct
  21. 13 Apr 2023, Shift 1 · Q23Sum of all Coefficients · Hard · Numerical value
  22. 13 Apr 2023, Shift 2 · Q7Open the question · Easy · Single correct
  23. 13 Apr 2023, Shift 2 · Q23Open the question · Medium · Numerical value
  24. 15 Apr 2023, Shift 1 · Q7Open the question · Medium · Single correct

JEE Main 202229 questions

  1. 25 Jul 2022, Shift 1 · Q23Maximum Binomial Coefficient · Hard · Numerical value
  2. 25 Jul 2022, Shift 2 · Q4Open the question · Medium · Single correct
  3. 26 Jul 2022, Shift 1 · Q25Coefficient Extraction from Products · Medium · Numerical value
  4. 26 Jul 2022, Shift 2 · Q4Double Summation of Coefficients · Medium · Single correct
  5. 27 Jul 2022, Shift 1 · Q5Open the question · Medium · Single correct
  6. 27 Jul 2022, Shift 2 · Q23Ratio of Consecutive Coefficients · Hard · Numerical value
  7. 28 Jul 2022, Shift 1 · Q13Open the question · Medium · Single correct
  8. 28 Jul 2022, Shift 2 · Q81Open the question · Medium · Numerical value
  9. 28 Jul 2022, Shift 2 · Q84Sum of all Coefficients · Medium · Numerical value
  10. 29 Jul 2022, Shift 1 · Q25Open the question · Hard · Numerical value
  11. 29 Jul 2022, Shift 2 · Q25r-Weighted Sum of Squares · Medium · Numerical value
  12. 30 Jul 2022, Shift 2 · Q66Geometric Progression of Expansions · Medium · Single correct
  13. 30 Jul 2022, Shift 2 · Q82Coefficient Extraction from Products · Hard · Numerical value
  14. 24 Jun 2022, Shift 1 · Q2Open the question · Easy · Single correct
  15. 24 Jun 2022, Shift 2 · Q25Open the question · Hard · Numerical value
  16. 25 Jun 2022, Shift 1 · Q21AP-Weighted Coefficient Sums · Hard · Numerical value
  17. 25 Jun 2022, Shift 2 · Q7Geometric Progression of Expansions · Medium · Single correct
  18. 25 Jun 2022, Shift 2 · Q24Sum of Even and Odd Coefficients · Hard · Numerical value
  19. 26 Jun 2022, Shift 1 · Q5Open the question · Medium · Single correct
  20. 26 Jun 2022, Shift 2 · Q26Hockey Stick Identity · Medium · Numerical value
  21. 27 Jun 2022, Shift 1 · Q25Open the question · Hard · Numerical value
  22. 27 Jun 2022, Shift 2 · Q24Open the question · Hard · Numerical value
  23. 28 Jun 2022, Shift 1 · Q1Product Sums with Constant Index Difference · Hard · Single correct
  24. 28 Jun 2022, Shift 1 · Q28Open the question · Medium · Numerical value
  25. 28 Jun 2022, Shift 2 · Q4Coefficient Extraction from Products · Medium · Single correct
  26. 29 Jun 2022, Shift 1 · Q16Open the question · Hard · Single correct
  27. 29 Jun 2022, Shift 2 · Q20Open the question · Hard · Single correct
  28. 29 Jun 2022, Shift 2 · Q27Open the question · Medium · Numerical value
  29. 30 Jun 2022, Shift 1 · Q6Open the question · Hard · Single correct

JEE Main 202132 questions

  1. 3 Aug 2021, Shift 1 · Q84Open the question · Medium · Numerical value
  2. 3 Aug 2021, Shift 2 · Q66Open the question · Medium · Single correct
  3. 4 Aug 2021, Shift 1 · Q65Sum of Even and Odd Coefficients · Medium · Single correct
  4. 4 Aug 2021, Shift 2 · Q64Double Summation of Coefficients · Medium · Single correct
  5. 26 Aug 2021, Shift 1 · Q66Second Derivative Method for Sums · Medium · Single correct
  6. 26 Aug 2021, Shift 2 · Q83Vandermonde's Identity · Hard · Numerical value
  7. 27 Aug 2021, Shift 1 · Q80Sum of Squares of Binomial Coefficients · Easy · Single correct
  8. 27 Aug 2021, Shift 2 · Q83Open the question · Medium · Numerical value
  9. 31 Aug 2021, Shift 1 · Q81Open the question · Medium · Numerical value
  10. 31 Aug 2021, Shift 2 · Q83Multinomial Theorem in Counting · Medium · Numerical value
  11. 24 Feb 2021, Shift 1 · Q64Zero Alternating Moments · Medium · Single correct
  12. 25 Feb 2021, Shift 2 · Q87Open the question · Medium · Numerical value
  13. 26 Feb 2021, Shift 1 · Q71Open the question · Hard · Single correct
  14. 26 Feb 2021, Shift 1 · Q90AP-Weighted Coefficient Sums · Medium · Numerical value
  15. 22 Jul 2021, Shift 2 · Q87Open the question · Easy · Numerical value
  16. 22 Jul 2021, Shift 2 · Q88Open the question · Hard · Numerical value
  17. 25 Jul 2021, Shift 1 · Q70Open the question · Hard · Single correct
  18. 25 Jul 2021, Shift 1 · Q81Open the question · Medium · Numerical value
  19. 25 Jul 2021, Shift 1 · Q83Maximum Coefficient for Odd n · Easy · Numerical value
  20. 25 Jul 2021, Shift 2 · Q62Bounding Binomial Coefficients · Hard · Single correct
  21. 25 Jul 2021, Shift 2 · Q66Open the question · Medium · Single correct
  22. 25 Jul 2021, Shift 2 · Q71Open the question · Hard · Single correct
  23. 25 Jul 2021, Shift 2 · Q83Binomial Coefficients with AP Multiplier · Medium · Numerical value
  24. 25 Jul 2021, Shift 2 · Q87Ratio of Consecutive Coefficients · Medium · Numerical value
  25. 16 Mar 2021, Shift 2 · Q87Alternating Binomial Series · Medium · Numerical value
  26. 17 Mar 2021, Shift 1 · Q66Open the question · Medium · Single correct
  27. 17 Mar 2021, Shift 1 · Q83Open the question · Medium · Numerical value
  28. 17 Mar 2021, Shift 2 · Q76Sum of Squares of Binomial Coefficients · Easy · Single correct
  29. 17 Mar 2021, Shift 2 · Q86Ratio of Consecutive Coefficients · Medium · Numerical value
  30. 18 Mar 2021, Shift 1 · Q66Sum of Even and Odd Coefficients · Hard · Single correct
  31. 18 Mar 2021, Shift 2 · Q83Open the question · Medium · Numerical value
  32. 18 Mar 2021, Shift 2 · Q89Binomial Coefficients with AP Multiplier · Medium · Numerical value

JEE Main 202014 questions

  1. 8 Jan 2020, Shift 1 · Q55Maximum Binomial Coefficient · Easy · Single correct
  2. 8 Jan 2020, Shift 2 · Q56Difference of Binomial Expansions · Medium · Single correct
  3. 9 Jan 2020, Shift 1 · Q71Open the question · Medium · Numerical value
  4. 9 Jan 2020, Shift 2 · Q56Open the question · Hard · Single correct
  5. 9 Jan 2020, Shift 2 · Q71Differentiation Method for Sums · Medium · Numerical value
  6. 2 Sep 2020, Shift 1 · Q56Open the question · Hard · Single correct
  7. 2 Sep 2020, Shift 2 · Q71Ratio of Consecutive Coefficients · Medium · Numerical value
  8. 3 Sep 2020, Shift 1 · Q55Open the question · Medium · Single correct
  9. 3 Sep 2020, Shift 2 · Q55Open the question · Medium · Single correct
  10. 4 Sep 2020, Shift 1 · Q55Hockey Stick Identity · Medium · Single correct
  11. 4 Sep 2020, Shift 1 · Q72Open the question · Hard · Numerical value
  12. 4 Sep 2020, Shift 2 · Q56Ratio of Consecutive Coefficients · Medium · Single correct
  13. 5 Sep 2020, Shift 1 · Q72Open the question · Medium · Numerical value
  14. 6 Sep 2020, Shift 2 · Q55Open the question · Medium · Single correct

JEE Main 20171 question

  1. 2 Apr 2017 (offline) · Q67Sum of all Coefficients · Medium · Single correct

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

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