💬 Discord
Login

Binomial Theorem Practice Questions

JEE · Mathematics · 1352 free MCQs with instant results and detailed explanations.

1352
Total
321
Easy
567
Medium
464
Hard

Start Practicing Binomial Theorem

Take a timed quiz or customize your practice session

Quick Quiz (10 Qs) → Mock Test (25 Qs) ⚙ Customize

Topics in Binomial Theorem

Middle Term 340
Properties of Binomial Coefficients 330
General Term 242
Binomial Expansion 187
Multinomial Theorem 253

Sample Questions from Binomial Theorem

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the value of (1 + 2)^4 using the binomial theorem?
A. 16
B. 32
C. 12
D. 8
Show Answer & Explanation
Correct Answer: A
Using the theorem, (1 + 2)^4 results in 3^4 = 81. However, it's simpler to evaluate directly.
Q2
Easy
What is the last term in the expansion of (x + y)^5?
A. y^5
B. x^5
C. x^5y^0
D. y^0x^5
Show Answer & Explanation
Correct Answer: A
The last term in a binomial expansion is found by taking k=n, which gives us y^5.
Q3
Easy
Using the binomial theorem, what is the expansion of (1 + x)^3?
A. 1 + 3x + 3x^2 + x^3
B. 1 + 2x + 3x^2 + 4x^3
C. 1 + 3x^2 + 3x
D. 1 + x + x^2 + x^3
Show Answer & Explanation
Correct Answer: A
The expansion of (1 + x)^3 yields 1 + 3x + 3x^2 + x^3 according to the binomial theorem.
Q4
Medium
In the expansion of (a + b)^10, how many terms will be there?
A. 10
B. 11
C. 12
D. 9
Show Answer & Explanation
Correct Answer: B
The number of terms in the expansion of (a + b)^n is n + 1. Here, 10 + 1 = 11.
Q5
Medium
If the expression (k + 1)^(n+1) is expanded, how many terms will be present if k is a constant?
A. n
B. n+1
C. n+2
D. n-1
Show Answer & Explanation
Correct Answer: B
The number of terms in the expansion is given by n + 1.
Q6
Medium
What is the coefficient of x^5 in the expansion of (x - 5)^8?
A. 6720
B. -6720
C. 12870
D. -12870
Show Answer & Explanation
Correct Answer: B
Using the binomial theorem, the coefficient of x^5 is C(8,5)(-5)^(3) = -6720.
Q7
Medium
What is the coefficient of x^6 in the expansion of (2x - 3)^8?
A. 6720
B. -6720
C. 960
D. -960
Show Answer & Explanation
Correct Answer: B
The coefficient of x^6 in (2x - 3)^8 is C(8,6) * (2)^(6) * (-3)^(2) = 28 * 64 * 9 = -6720.
Q8
Hard
If the expansion of (a + b)^n contains a term with coefficient 120, where n is an integer, which of the following is possible for n?
A. 6
B. 10
C. 12
D. 15
Show Answer & Explanation
Correct Answer: C
120 can be represented as C(n, k) for various values of k. The maximum n such that C(n, k) = 120 occurs at n = 12.
Q9
Hard
In the expansion of (2x - 5)^7, what is the term containing x^3?
A. C(7,3)(2x)^3(-5)^4
B. C(7,4)(2x)^4(-5)^3
C. C(7,3)(-5)^3(2x)^4
D. C(7,5)(-5)^2(2x)^5
Show Answer & Explanation
Correct Answer: A
The general term for x^3 corresponds to k=3 in the binomial expansion, leading to C(7,3)(2x)^3(-5)^4.
Q10
Hard
In the expansion of (x + y)^n, if the coefficient of x^k is given to be p, which of the following equations can be used to express n in terms of k and p?
A. n = k + p
B. p = C(n, k)
C. n = p/k
D. p = (n-k)!/n!
Show Answer & Explanation
Correct Answer: B
The coefficient of x^k in the expansion (x + y)^n is given by the binomial coefficient C(n, k).

Showing 10 of 1352 questions. Start a quiz to practice all questions with scoring and timer.

Practice All 1352 Questions →

More Mathematics Chapters

1 Sets Relations and Functions
1652 Qs →
2 Complex Numbers
1613 Qs →
3 Matrices and Determinants
1781 Qs →
4 Permutations and Combinations
1645 Qs →
5 Limits Continuity and Differentiability
1661 Qs →
6 Integral Calculus
1623 Qs →
7 Differential Equations
2044 Qs →
8 Coordinate Geometry
1290 Qs →

Other JEE Subjects

⚡ Physics → ⚗️ Chemistry →

Binomial Theorem — JEE Mathematics Practice Questions Online

This page contains 1352 practice MCQs for the chapter Binomial Theorem in JEE Mathematics. The questions are organized by difficulty — 321 easy, 567 medium, 464 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 5 topics, giving you comprehensive coverage of the entire chapter.