Binomial Theorem – Most Repeated Questions for JEE Main 2026

Binomial Theorem – JEE Main 2026 PYQ Quiz

Binomial Theorem is a high-weightage chapter in JEE Main Mathematics. Questions are frequently asked from coefficient comparison, remainders, factorial powers and middle term concepts.

Q1. Sum of coefficients of first three terms in expansion of (x − 3/x²)ⁿ is 376. Find the coefficient of x⁴.
Correct Answer: 405
Q2. Coefficient of x⁷⁰ in x²(1+x)⁹⁸ + x³(1+x)⁹⁷ + x⁴(1+x)⁹⁶ is ⁹⁹Cₚ − ⁴⁶C_q. A possible value of (p+q) is:
61
83
55
68
Q3. Let (22)²⁰²² + (2022)²² leave remainder α when divided by 3 and β when divided by 7. Find α² + β².
13
10
20
5
Q4. Let K be sum of coefficients of odd powers in (1+x)⁹⁹. If (²⁰⁰C₉₉ K)/a = 2ˡᵐ/n, then ordered pair (l,n) is:
(50, 101)
(50, 51)
(51, 101)
(51, 99)
Q5. ⁿ⁻¹Cₙ = (k² − 8)ⁿCₙ₊₁ if and only if:
2√2 < k < 2√3
2√2 < k ≤ 3
2√3 < k < 3√3
2√3 < k ≤ 3√2
Q6. Largest n ∈ N such that 3ⁿ divides 50! is:
22
20
21
23
Q7. In expansion of (∛2 + 1/∛3)ⁿ, ratio of 15th term from beginning to 15th term from end is 1/6. Find nC₃.
4960
2300
1040
4060
Q8. Largest natural number n such that 3ⁿ divides 66! is:
Correct Answer: 31
Q9. Remainder when 7¹⁰³ is divided by 23 is:
9
6
14
17
Q10. Remainder when 19²⁰⁰ + 23²⁰⁰ is divided by 49 is:
Correct Answer: 29
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