Binomial Theorem PYQs - Last 10 Years

JEE Main / Mathematics / Algebra / 224 recent questions

MathematicsAlgebra2017-2026

All Binomial Theorem PYQs Last 5 Years Create chapter test

Practice 224 JEE Main Mathematics questions from Binomial Theorem. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

224

PYQs on Page

Mathematics / Algebra

2017-2026

Year Range

Based on indexed question metadata

139

Last 5 Years

2022-2026

224

Last 10 Years

2017-2026

Recent Year Trend

2021

2022

2023

2024

2025

2026

202146 max PYQs/year2026

Question Types

224PYQs

MCQ61.2%

INTEGER38.8%

Difficulty Mix

#1 Medium167

#2 Hard37

#3 Easy20

139 in last 5 years224 in last 10 years

Last 10 Years Binomial Theorem Questions

Showing 24 of 224 filtered questions.

1Binomial Theorem

The sum of the series
2.20C0
+ 5.20C1 + 8.20C2 + 11.20C3 + ... +62.20C20 is equal to :

2Binomial Theorem

The sum of the co-efficients of all even
degree terms in x in the expansion of
\({\left( {x + \sqrt {{x^3} - 1} } \right)^6}\) + \({\left( {x - \sqrt {{x^3} - 1} } \right)^6}\), (x > 1) is equal to:

3Binomial Theorem

If the fourth term in the binomial expansion of
\({\left( {\sqrt {{x^{\left( {{1 \over {1 + {{\log }_{10}}x}}} \right)}}} + {x^{{1 \over {12}}}}} \right)^6}\) is equal to 200, and x > 1,
then the value of x is :

4Binomial Theorem

A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of \({\left( {{2^{1/3}} + {1 \over {2{{\left( 3 \right)}^{1/3}}}}} \right)^{10}}\) is :

5Binomial Theorem

The total number of irrational terms in the binomial expansion of (71/5 – 31/10)60 is :

6Binomial Theorem

The coefficient of x18 in the product
(1 + x) (1 – x)10 (1 + x + x2)9
is :

7Binomial Theorem

The term independent of x in the expansion of
\(\left( {{1 \over {60}} - {{{x^8}} \over {81}}} \right).{\left( {2{x^2} - {3 \over {{x^2}}}} \right)^6}\) is equal to :

8Binomial Theorem

If 20C1 + (22) 20C2 + (32) 20C3 + ..... + (202
)
20C20 = A(2\(\beta\)), then the ordered pair (A, \(\beta\)) is equal to :

9Binomial Theorem

The value of r for which 20Cr 20C0 + 20Cr\(-\)1 20C1 + 20Cr\(-\)2 20C2 + . . . . .+ 20C0 20Cr is maximum, is

10Binomial Theorem

The sum of the real values of x for which the middle term in the binomial expansion of \({\left( {{{{x^3}} \over 3} + {3 \over x}} \right)^8}\) equals 5670 is :

11Binomial Theorem

Let Sn = 1 + q + q2 + . . . . . + qn and Tn = 1 + \(\left( {{{q + 1} \over 2}} \right) + {\left( {{{q + 1} \over 2}} \right)^2}\) + . . . . . .+ \({\left( {{{q + 1} \over 2}} \right)^n}\) where q is a real number and q \(\ne\) 1. If...

12Binomial Theorem

Let (x + 10)50 + (x \(-\) 10)50 = a0 + a1x + a2x2 + . . . . + a50x50, for all x \(\in\) R; then \({{{a_2}} \over {{a_0}}}\) is equal to

13Binomial Theorem

If \({\sum\limits_{i = 1}^{20} {\left( {{{{}^{20}{C_{i - 1}}} \over {{}^{20}{C_i} + {}^{20}{C_{i - 1}}}}} \right)} ^3} = {k \over {21}}\) then k is equal to

14Binomial Theorem

If the third term in the binomial expansion of \({\left( {1 + {x^{{{\log }_2}x}}} \right)^5}\) equals 2560, then a possible value of x is -

15Binomial Theorem

The positive value of \(\lambda\) for which the co-efficient of x2
in the expression x2 \({\left( {\sqrt x + {\lambda \over {{x^2}}}} \right)^{10}}\) is 720, is -

16Binomial Theorem

If the coefficients of x2
and x3
are both zero, in the expansion of the expression (1 + ax + bx2
) (1 – 3x)15 in
powers of x, then the ordered pair (a,b) is equal to :

17Binomial Theorem

The smallest natural number n, such that the coefficient of x in the expansion of \({\left( {{x^2} + {1 \over {{x^3}}}} \right)^n}\) is nC23, is :

18Binomial Theorem

The coefficient of x2 in the expansion of the product
(2\(-\)x2) .((1 + 2x + 3x2)6 + (1 \(-\) 4x2)6) is :

19Binomial Theorem

If n is the degree of the polynomial,
\({\left[ {{2 \over {\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8} +\) \({\left[ {{2 \over {\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8}\)
and m is the coefficient of xn in it, ...

20Binomial Theorem

The coefficien of x10 in the expansion of (1 + x)2(1 + x2)3(1 + x3)4 is equal to :

21Binomial Theorem

The sum of the co-efficients of all odd degree terms in the expansion of
\({\left( {x + \sqrt {{x^3} - 1} } \right)^5} + {\left( {x - \sqrt {{x^3} - 1} } \right)^5}\), \(\left( {x > 1} \right)\) is

22Binomial Theorem

The coefficient of x−5 in the binomial expansion of
\({\left( {{{x + 1} \over {{x^{{2 \over 3}}} - {x^{{1 \over 3}}} + 1}} - {{x - 1} \over {x - {x^{{1 \over 2}}}}}} \right)^{10}},\) where x \(\ne\) 0, 1, is :

23Binomial Theorem

If (27)999 is divided by 7, then the remainder is :

24Binomial Theorem

The value of \(\left( {{}^{21}{C_1} - {}^{10}{C_1}} \right) + \left( {{}^{21}{C_2} - {}^{10}{C_2}} \right) + \left( {{}^{21}{C_3} - {}^{10}{C_3}} \right)\)
\(\left( {{}^{21}{C_4} - {}^{10}{C_4}} \right)\)$$ + .... + \left( {{}^{21}{C_{10}} ...