Please refer to Chapter 8 Binomial Theorem MCQ Class 11 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 11 Mathematics. Students should refer to MCQ Questions for Class 11 Mathematics with Answers to score more marks in Grade 11 Mathematics exams. Students should read the chapter Binomial Theorem and then attempt the following objective questions.

MCQ Questions Class 11 Mathematics Chapter 8 Binomial Theorem

The Binomial Theorem MCQ Class 11 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question: If the last term in the binomial expansion of

 then the 5th term from the beginning is
(a) 210
(b) 420
(c) 105
(d) None of these 

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Question: If x^2 k occurs in the expansion of +1/X²)^n-3
(a) n – 2 k is a multiple of 2
(b) n k – 2 is a multiple of 3
(c) k = 0
(d) None of the above 

Question: The coefficient of the term independent of x in the expansion of (1+x+2x³)(3/2x²-1/3x)⁹ is
(a) 1/3
(b) 19/54
(c) 17/54
(d) 1/4   

Question: If the term free from x in the expansion of (√x-k/x²)¹⁰ is 405, then the value of k is
(a) ± 1
(b) ± 2
(c) ± 3
(d) ± 4 

Question: The coefficient of x in the expansion of(1-3x+7x²)(1-x)¹⁶
(a) 19
(b) – 19
(c) 18
(d) – 18 

Question: The term independent of x in the expansion of (3x-2/x²⁾¹⁵ is
(a) – 3003 (31⁰)(2⁵)
(b) – 3003 (3¹⁰)(2⁴)
(c) 3003 (3¹⁰)(2⁵)
(d) None of these 

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Question: If the middle term of (1/x+xsinx)¹⁰ is equal to 7 7/8, then value of x is 
(a) 2nπ+π/6
(b) nπ+π/6
(c) nπ+(-1)ⁿπ/6
(d) nπ+(-1)ⁿπ/3 

Question: If p is a real number and if the middle term in the expansion of (p/2+2)⁸  1120, then the value of p is
(a) ± 3
(b) ± 1
(c) ± 2
(d) None of these 

Question: If n is even, then the middle term in the expansion of

(a) 10
(b) 12
(c) 14
(d) None of these 

Question: The largest term in the expansion of (3 +2x) ⁵⁰ , where
x =1/5 is
(a) 5th
(b) 3th
(c) 7th
(d) 6th   

Question: If the sum of the coefficients in the expansion of (x-2y+3z)ⁿ is 128, then the greatest coefficient in the expansion of (1 + x)ⁿ is
(a) 35
(b) 20
(c) 10
(d) None of the above 

Question: The greatest value of the term independent of x, as α varies over R, in the expansion of (xcos α+sinα/x)²⁰is
(a) ²⁰C₁₀
(b) ²⁰C₁₅
(c) ²⁰C₁₉
(d) None of these 

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Question: The interval in which x must lie, so that the greatest term in the expansion of (1+x)²ⁿ has the greatest coefficient, is
(a) (n-1/n,n/n-1)
(b) (n/n+1,n+1/n)
(c) (n/n+2,n+2/n)
(d) None of these 

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Question: C₁/C₀+2C₂/C₁+3C₃/C₂…+…+15^C15/C₁₄ is equal to
(a) 100
(b) 120
(c) –120
(d) None of these 

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Question: If n is odd, then

is equal to
(a) 0
(b) 1
(c) ∞
(d) n!/(n/2)²! 

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Question: If n>(8+3√7)10,n∈N, ( )  then the least value of n is
(a) (8+3√7)¹⁰-(8-3√7) ¹⁰
(b) (8+3√7)¹⁰-(8-3√7) ¹⁰
(c) (8+3√7)¹⁰-(8-3√7) ¹⁰+1
(d)(8+3√7)¹⁰-(8-3√7) ¹⁰-1 

Question: Let R=(2+√3)2n and f = R – [R ], where [ ·] denotes the greatest integer function, then R (1-f ) is equal to
(a) 1
(b) 2 ²ⁿ-1
(c) 2²ⁿ-1 
(d) ²ⁿ_Cn 

Question: If a_r is the coefficient of x^r, in the expansion of ( 1+x+x²)ⁿ,) then a₁-2a₂+3a₃-…-2na_2n … is equal to
(a) 0
(b) n
(c) – n
(d) 2 n   a

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Question: If (1+x)¹⁵=C₀+C₁x+C₂X²+…+C₁₅x¹⁵,   then C₂+2C₃+3C₄+…+14C₁₅  … is equal to
(a) 14 ·2 ¹⁴
(b) 13· 2¹⁴  +1
(c) 13 2 1 14× –
(d) None of these 

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Question: If a and d are two complex numbers, then the sum to (n + 1) terms of the following series aC₀-(a+d) C₁+(a+2d)C₂-…+…  is
(a) a/2n
(b) na
(c) 0
(d) None of these 

Question: 49ⁿ+16n-1 is divisible by
(a) 3
(b) 19
(c) 64
(d) 29 

Question: If A = 1000¹⁰⁰⁰ and B =(1001) 999, then
(a) A >B 
(b) A B =
(c) A< B
(d) None of these 

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Question: Cube root of 217 is
(a) 6.01
(b) 6.04
(c) 6.02
(d) None of these 

Question: If the value of x is so small that x² and greater powers can be neglected, then

is equal to
(a) 1+5/6x
(b) 1-5/6x
(c) 1+2/3x
(d) 1-2/3x 

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