Binomial Theorem · JEE Main previous year questions

2026 8 questions

1. Q82026 · 6 Apr 2026 · Shift 1

   If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x{)}^{26}$ and $(1-\alpha x{)}^{28}$, $\alpha \ne 0$, are equal, then the value of $\alpha$ is:

   1. A.1
   2. B.$\frac{14}{13}$
   3. C.$\frac{27}{7}$
   4. D.$\frac{7}{27}$
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   Answer: D

2. Q232026 · 5 Apr 2026 · Shift 1· Numerical answer

   If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of ${\left(\frac{1}{x^3}-x^4\right)}^n$, $x\ne 0$, is zero, then the value of $n$ is ____.

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   Answer: 21

3. Q72026 · 5 Apr 2026 · Shift 2

   The coefficient of $x^2$ in the expansion of ${\left(2x^2+\frac{1}{x}\right)}^{10}$, $x\ne 0$, is :

   1. A.$3240$
   2. B.$3360$
   3. C.$3480$
   4. D.$3600$
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   Answer: B

4. Q92026 · 4 Apr 2026 · Shift 1

   Let the smallest value of $k\in \mathbb{N}$, for which the coefficient of $x^3$ in $(1+x{)}^3+(1+x{)}^4+(1+x{)}^5+...+(1+x{)}^{99}+(1+kx{)}^{100}$, $x\ne 0$, is $\left(43n+\frac{101}{4}\right)\left({}^{100}{\mathrm{C}}_3\right)$ for some $n\in \mathbb{N}$, be $p$. Then the value of $p+n$ is:

   1. A.10
   2. B.11
   3. C.12
   4. D.13
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   Answer: B

5. Q92026 · 4 Apr 2026 · Shift 2

   Pairs of elements with the same number of electrons in their respective 4f orbital are [Atomic number. Eu-63, Gd-64, Dy-66, Ho-67, Tm-69, Yb-70, Lu-71, Hf-72] A. (Eu and Gd) B. (Dy and Ho) C. ( Yb and Hf ) D. ( Lu and Tm) Choose the correct answer from the options given below :

   1. A.B and C Only
   2. B.A and B Only
   3. C.A and D Only
   4. D.A and C Only
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   Answer: A

6. Q202026 · 28 Jan 2026 · Shift 2

   The sum of the coefficients of $x^{499}$ and $x^{500}$ in $(1+x{)}^{1000}+x(1+x{)}^{999}+x^2(1+x{)}^{998}+\cdots +x^{1000}$ is :

   1. A.${}^{1002}{C}_{501}$
   2. B.${}^{1001}{C}_{501}$
   3. C.${}^{1000}{C}_{501}$
   4. D.${}^{1002}{C}_{500}$
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   Answer: D

7. Q162026 · 22 Jan 2026 · Shift 1

   The coefficient of $x^{48}$ in $(1+x)+2(1+x{)}^2+3(1+x{)}^3+\dots +100(1+x{)}^{100}$ is equal to

   1. A.$100\cdot {}^{100}{\mathrm{C}}_{49}-{}^{100}{\mathrm{C}}_{48}$
   2. B.$100\cdot {}^{101}{\mathrm{C}}_{49}-{}^{101}{\mathrm{C}}_{50}$
   3. C.${}^{100}{\mathrm{C}}_{50}+{}^{101}{\mathrm{C}}_{49}$
   4. D.$100\cdot {}^{100}{\mathrm{C}}_{49}-{}^{100}{\mathrm{C}}_{50}$
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   Answer: B

8. Q142026 · 21 Jan 2026 · Shift 1

   If the coefficient of $x$ in the expansion of $(a{x}^2+bx+c)(1-2x{)}^{26}$ is -56 and the coefficients of $x^2$ and $x^3$ are both zero, then $a+b+c$ is equal to :

   1. A.1483
   2. B.1300
   3. C.1500
   4. D.1403
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   Answer: D