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Friday, 9 October

JEE Main Maths · Class 11

Binomial Theorem: JEE Main previous year questions

Binomial Theorem had 54 questions in the 42 JEE Main shifts Lumi analysed, about 1.2 a shift, asked in 42 of 42 shifts. It ranks 10 of 22 Maths chapters by questions; 30% of its questions were hard.

Questions
54
in 42 of 42 shifts
A shift, on average
1.2
of 25 Maths questions
Since 2024
-0.1
1.2 a shift in 2017–23, 1.1 in 2024–26
Numerical answer
21
39% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
06121’175’206’214’229’239’2411’259’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20205
  • 20216
  • 20224
  • 20239
  • 20249
  • 202511
  • 20269
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

2 topics and 19 distinct ideas; 6 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

27 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
6 repeat

Study it on Lumi

Binomial Theorem: the interactive lesson

Every question

All 54 Binomial Theorem questions

Newest first. Each opens with its options and the official answer.

2026 9 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

2025 11 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

2024 9 questions

  1. 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
  2. 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
  3. 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
  4. 9 Apr 2024, Shift 1 · Q25The remainder when 4282024428^{2024} is divided by 2121 is ________.MediumNumerical value
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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

2023 9 questions

  1. 6 Apr 2023, Shift 1 · Q5If 2nC3:nC3=10:1{}^{2n}C_3 : {}^{n}C_3 = 10:1, then the ratio (n2+3n):(n2−3n+4)(n^2+3n):(n^2-3n+4) isEasySingle correct
  2. 6 Apr 2023, Shift 1 · Q6If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of…MediumSingle correct
  3. 6 Apr 2023, Shift 1 · Q24The coefficient of x18x^{18} in the expansion of (x4−1x3)15\left(x^4-\frac{1}{x^3}\right)^{15} is ____________MediumNumerical value
  4. 8 Apr 2023, Shift 2 · Q625190−19190−8190+219025^{190} - 19^{190} - 8^{190} + 2^{190} is divisible byMediumSingle correct
  5. 8 Apr 2023, Shift 2 · Q7The absolute difference of the coefficients of x10x^{10} and x7x^7 in the expansion of (2x2+12x)11\left(2x^2 + \frac{1}{2x}\right)^{11} is equal toMediumSingle correct
  6. 11 Apr 2023, Shift 1 · Q21The mean of the coefficients of x,x2,…,x7x, x^2, \ldots, x^7 in the binomial expansion of (2+x)9(2+x)^9 is ______________.MediumNumerical value
  7. 11 Apr 2023, Shift 1 · Q27The number of integral terms in the expansion of (312+514)680\left(3^{\frac{1}{2}} + 5^{\frac{1}{4}}\right)^{680} is equal toMediumNumerical value
  8. 13 Apr 2023, Shift 2 · Q7The coefficient of x5x^5 in the expansion of (2x3−13x2)5\left(2x^3-\frac{1}{3x^2}\right)^5 isEasySingle correct
  9. 13 Apr 2023, Shift 2 · Q23The remainder, when 71037^{103} is divided by 17, is ______MediumNumerical value

2022 4 questions

  1. 25 Jul 2022, Shift 1 · Q23If the maximum value of the term independent of tt in the expansion of…HardNumerical value
  2. 28 Jul 2022, Shift 1 · Q13The remainder when 72022+320227^{2022}+3^{2022} is divided by 5 is :MediumSingle correct
  3. 24 Jun 2022, Shift 1 · Q2The remainder when 320223^{2022} is divided by 5 is :EasySingle correct
  4. 29 Jun 2022, Shift 1 · Q16If the constant term in the expansion of (3x3−2x2+5x5)10\left(3x^3 - 2x^2 + \frac{5}{x^5}\right)^{10} is 2k⋅l2^k \cdot l, where ll is an odd integer,…HardSingle correct

2021 6 questions

  1. 3 Aug 2021, Shift 2 · Q66In the Binomial expansion of (2xx+3y116)33\left(2x\sqrt{x} + 3y^{\frac{1}{16}}\right)^{33}, the number of terms, having positive integral powers of…MediumSingle correct
  2. 25 Jul 2021, Shift 1 · Q70If b is very small as compared to the value of a, so that the cube and other higher powers of ba\frac{b}{a} can be neglected in the…HardSingle correct
  3. 25 Jul 2021, Shift 1 · Q81The term independent of 'xx' in the expansion of (x+1x2/3−x1/3+1−x−1x−x1/2)10\left(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\right)^{10}, where x≠0,1x\ne0,1…MediumNumerical value
  4. 25 Jul 2021, Shift 1 · Q83The ratio of the coefficient of the middle term in the expansion of (1+x)20(1+x)^{20} and the sum of the coefficients of two middle terms in…EasyNumerical value
  5. 16 Mar 2021, Shift 2 · Q87Let n be a positive integer. Let…MediumNumerical value
  6. 18 Mar 2021, Shift 1 · Q66Let (1+x+2x2)20=a0+a1x+a2x2+…+a40x40(1+x+2x^2)^{20} = a_0 + a_1x + a_2x^2 + \ldots + a_{40}x^{40}. Then, a1+a3+a5+…+a37a_1 + a_3 + a_5 + \ldots + a_{37} is equal to :HardSingle correct

2020 5 questions

  1. 8 Jan 2020, Shift 1 · Q55If a, b and c are the greatest values of 19Cp^{19}C_p, 20Cq^{20}C_q and 21Cr^{21}C_r respectively, then :EasySingle correct
  2. 9 Jan 2020, Shift 2 · Q56In the expansion of (xcos⁡θ+1xsin⁡θ)16\left(\frac{x}{\cos\theta}+\frac{1}{x\sin\theta}\right)^{16}, if l1l_1 is the least value of the term independent of…HardSingle correct
  3. 9 Jan 2020, Shift 2 · Q71If Cr≡25CrC_r\equiv{}^{25}C_r and C0+5⋅C1+9⋅C2+…+(101)⋅C25=225⋅kC_0+5\cdot C_1+9\cdot C_2+\ldots+(101)\cdot C_{25}=2^{25}\cdot k, then kk is equal to ______.MediumNumerical value
  4. 2 Sep 2020, Shift 1 · Q56Let α>0\alpha>0, β>0\beta>0 be such that α3+β2=4\alpha^{3}+\beta^{2}=4. If the maximum value of the term independent of xx in the binomial…HardSingle correct
  5. 6 Sep 2020, Shift 2 · Q55If the constant term in the binomial expansion of (x−kx2)10\left(\sqrt{x}-\frac{k}{x^2}\right)^{10} is 405, then ∣k∣|k| equals :MediumSingle correct

2017 1 questions

  1. 2 Apr 2017 (offline) · Q67The value of (21C1−10C1)+(21C2−10C2)+(21C3−10C3)+(21C4−10C4)+…+(21C10−10C10)(^{21}C_1-{}^{10}C_1)+(^{21}C_2-{}^{10}C_2)+(^{21}C_3-{}^{10}C_3)+(^{21}C_4-{}^{10}C_4)+\ldots+(^{21}C_{10}-{}^{10}C_{10})…MediumSingle correct

Pattern: Asked most years.