Binomial Theorem-Quiz-12

Binomial Theorem Quiz-12

Dear Readers,

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. 

Statement 1: 𝑆3=55×29 Statement 2: 𝑆1=90×28 and 𝑆2=10×28

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q2.Statement 1: If 𝑛 is an odd prime, then the integral part of (√5+2)^𝑛 − 2^𝑛+1 is divisible by 2𝑛) Statement 2: If 𝑛 is prime, then ^𝑛𝐶₁, ^𝑛𝐶₂,…., ^𝑛𝐶_𝑛−1 must be divisible by 𝑛

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q3.  Statement 1: The coefficient of 𝑥^𝑛 in the binomial expansion of (1−𝑥)⁻² is (𝑛+1) Statement 2: The coefficient of 𝑥^𝑟 in (1−𝑥)^−𝑛 when 𝑛 ∈ 𝑁 is ^{𝑛+𝑟−1}𝐶_𝑟

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q4. Statement 1: The coefficient of 𝑥^3𝜆+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 ^𝑛𝐶_𝑚𝑎^𝑛−𝑚

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q5.Statement 1: The sum of coefficients in the expansion of (3^−𝑥/4 + 3^5𝑥/4)^𝑛 is 2^𝑛 Statement 2: The sum of coefficients in the expansion of (𝑥+𝑦)^𝑛 is 2^𝑛 when we put 𝑥 = 𝑦 = 1

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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)

Solution

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 +...+ 𝑎^𝑚)^𝑛 is ^{𝑛+𝑚−1}𝐶_𝑚−1

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q8.

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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)

Solution

Q10.Statement 1: The total number of dissimilar terms in the expansion of (𝑥¹ + 𝑥² +⋯+ 𝑥^𝑛)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)
• (d)

Solution