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Binomial Theorem is one of the most important chapters of Algebra in the JEE syllabus and other engineering exams. For JEE Mains, it has 4% weightage and for JEE Advanced, it has 2.42% weightage..

This section contain(s) 10 questions numbered 1 to 10. Each question contains statement 1(Assertion) and statement 2(Reason). Each question has the 4 choices (a), (b), (c) and (d) out of which only one is correct.

a)Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
b)Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
c)Statement 1 is True, Statement 2 is False
d)Statement 1 is False, Statement 2 is True

Q1.
•  (a)
•  (b)
•  (c)
•  (d)
Q2.Statement 1: If 𝑛 is an odd prime, then the integral part of (√5+2)𝑛 − 2𝑛+1 is divisible by 2𝑛) Statement 2: If 𝑛 is prime, then 𝑛𝐶1, 𝑛𝐶2,…., 𝑛𝐶𝑛−1 must be divisible by 𝑛
•  (a)
•  (b)
•  (c)
•  (d)
Q3.  Statement 1: The coefficient of 𝑥𝑛 in the binomial expansion of (1−𝑥)−2 is (𝑛+1) Statement 2: The coefficient of 𝑥𝑟 in (1−𝑥)−𝑛 when 𝑛 ∈ 𝑁 is 𝑛+𝑟−1𝐶𝑟
•  (a)
•  (b)
•  (c)
•  (d)

Q4. Statement 1: The coefficient of 𝑥3𝜆+2 in the expansion of (𝑎+𝑥)𝜆(𝑏+𝑥)𝜆+1(𝑐+𝑥)𝜆+2 ∀𝜆 ∈ 𝑁 is 𝜆(𝑎+𝑏+𝑐) Statement 2: The coefficient of 𝑥𝑚 in the expansion (𝑎+𝑥)𝑛 is 𝑛𝐶𝑚𝑎𝑛−𝑚
•  (a)
•  (b)
•  (c)
•  (d)
Q5.Statement 1: The sum of coefficients in the expansion of (3−𝑥/4 + 35𝑥/4)𝑛 is 2𝑛 Statement 2: The sum of coefficients in the expansion of (𝑥+𝑦)𝑛 is 2𝑛 when we put 𝑥 = 𝑦 = 1
•  (a)
•  (b)
•  (c)
•  (d)
Q6. Statement 1: The term independent of 𝑥 in the expansion of (𝑥 + 1/𝑥 + 2)𝑚 is (4𝑚)!/(2𝑚!)2 Statement 2: The coefficient of 𝑥6 in the expansion (1+𝑥)𝑛 is 𝑛𝐶6
•  (a)
•  (b)
•  (c)
•  (d)
Q7.Statement 1: The number of terms in the expansion (𝑥 + 1/𝑥 + 1)𝑛 is 2𝑛 + 1 Statement 2: The number of terms in the expansion (𝑎1 + 𝑎2 + 𝑎3 +...+ 𝑎𝑚)𝑛 is 𝑛+𝑚−1𝐶𝑚−1
•  (a)
•  (b)
•  (c)
•  (d)
•  (a)
•  (b)
•  (c)
•  (d)
Q9.Statement 1: Three consecutive binomial coefficients are always in A.P. Statement 2: Three consecutive binomial coefficients are not in H.P. or G.P.
•  (a)
•  (b)
•  (c)
•  (d)
Q10.Statement 1: The total number of dissimilar terms in the expansion of (𝑥1 + 𝑥2 +⋯+ 𝑥𝑛)3 is (𝑛(𝑛+1)(𝑛+2))/6 Statement 2: The total number of dissimilar terms in the expansion of (𝑥1 + 𝑥2 + 𝑥3)𝑛 is (𝑛(𝑛+1)(𝑛+2))/6
•  (a)
•  (b)
•  (c)
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