Binomial Theorem JEE Questions PDF with Solution, Practice Now

Binomial Theorem JEE  Questions: The Binomial Theorem is a very important topic in Algebra for both JEE Main and JEE Advanced. Every year, 1–2 questions appear in JEE Main, and advanced problems are also asked in JEE Advanced. Understanding this chapter thoroughly helps students solve expansions, coefficients, and sequence-based questions easily.

Practicing the Binomial Theorem JEE Questions regularly is crucial. By solving these questions, aspirants can improve their speed, accuracy, and confidence. These problems also help in understanding the JEE Main exam pattern, which is vital for scoring well.

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Binomial Theorem JEE  Questions Overview

The Binomial Theorem works on a simple principle. It is the sum of the terms (a+b)n(a+b)^n(a+b)n in which the coefficients of the successive terms are the numbers obtained by evaluating the combination formula. In JEE exams, often questions are asked to find the middle term or find the coefficient of a particular term, using the properties of binomial coefficients, and questions with connections to probability or sequences. 

The binomial problems in JEE Main are generally single formula questions, while JEE Advanced binomial questions can be much more difficult and will require a two or three-step reasoning. Practising the Binomial Theorem JEE Questions is also great for improving algebra skills and for getting good at questions that will show up in the tougher JEE Advanced exam. This chapter is small and scores highly with proper practice.

Practice Binomial Theorem JEE Questions 

The right way to master Binomial Theorem JEE  Questions is by solving different types of problems. Direct formula-based questions are common in JEE Main, while JEE Advanced binomial problems demand a mix of ideas and patience.

1. Let f(x) = ((x + 2017)/2018)^{2018} + (2019/2019)^{2019} + (2020/2020)^{2020} + 2019 and suppose a, b, c > 0 with abc = 1, then least value of f(a) + f(b) + f(c) is

A. 1
B. 2017
C. 3
D. 2017²

2. The coefficient of r^6 in (1 + r^5)(1 + r^7)(1 + r^{25})(1 + r^{40}) is

A. 1 + 25C5
B. 1 + 25C5 + 25C7
C. 1 + 25C7
D. 1

3. The expression (√(2x^2 + 1) + √(2x^2 - 1))^6 + (2/(√(2x^2 + 1) + √(2x^2 - 1)))^6 is a polynomial of degree

A. 6
B. 8
C. 10
D. 12

4. If n > 1 then value of the expression C_n - 2C_{n-1} + 3C_{n-2} - 4C_{n-3} + … + (-1)^n (n + 1) C_1 is

A. -1
B. 0
C. 1
D. none of these

5. If n is even, then value of the expression C_n^2 - 1/2 C_{n-1}^2 + 1/3 C_{n-2}^2 - … + (-1)^{n/2} / (n+1) C_n^2 where C_r = nCr, is

A. (-1)^n n! / ((n + 1) (n/2)!)^2
B. (-1)^{n-1} (n!) / ((n + 1) (n/2)!)^2
C. -1 / ((n + 1) (n/2)!)^2
D. (-1)^{n/2} n! / ((n + 1) (n/2)!)^2

6. Sum of the coefficients of the terms of degree m in the expansion of (1 + x)^n (1 + y)^m (1 + z)^m is

A. nCm3
B. 3 (nCm0)
C. nC3m
D. 3nCm

7. If sum of the coefficients of the first, second and third terms of the expansion of (x^2 + 1/x)^m is 46, then the coefficient of the term that does not contain x is

A. 84
B. 92
C. 98
D. 106

8. The coefficient of the term independent of x in the expansion of (1 + x + 2x^3)^9 ( (3/2) x^2 - 1/(3x) )^9 is

A. 1/3
B. 19/54
C. 17/54
D. 1/4

9. The number of rational terms in the expansion of (√2 + √3 + √5)^10 is equal to

A. 0
B. 1
C. 2
D. 3

10. Coefficient of x^10 in the product (x - 1)(x^2 - 2)(x^3 - 3)…(x^{12} - 12) is

A. 4
B. 6
C. 8
D. 12

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Binomial Theorem JEE  Questions PDF with Solution

To support aspirants, PW provides a practice question PDF with answer and solution. This Binomial Theorem JEE Questions PDF is carefully curated to help the students. The practice set includes questions from basic formula based JEE Main questions to JEE Advanced binomial questions. Step by step solutions have also been provided.