MCQ Questions Chapter 8 Binomial Theorem Class 11 Mathematics

Please refer to MCQ Questions Chapter 8 Binomial Theorem Class 11 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 11 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 11 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 8 Binomial Theorem in Class 11 Mathematics provided below to get more marks in exams.

Chapter 8 Binomial Theorem MCQ Questions

Please refer to the following Chapter 8 Binomial Theorem MCQ Questions Class 11 Mathematics with solutions for all important topics in the chapter.

MCQ Questions Answers for Chapter 8 Binomial Theorem Class 11 Mathematics

Question. The value of (1.0025)10 correct to five decimal places is
(a) 1.025281
(b) 1.034285
(c) 1.005293
(d) None of these

Question. The number of terms which are free from radical signs in the expansion of (y^1/5 + X^1/10)⁵⁵ is
(a) 5
(b) 6
(c) 7
(d) 4

Question. (√2+1)⁶ – (√2 1)⁶ is equal to
(a) 101
(b) 70√2
(c) 140√2
(d) 120√2

Question. If the coefficient of rth, (r+1)th and (r+2)th term in the expansion of (1+ x)¹⁴ are in AP, then the value of r is
(a) 5 or 8
(b) 4 or 9
(c) 5 or 9
(d) 6 or 7 

Question. ¹⁰C₁ +¹⁰C₃ + ¹⁰C₅ + ¹⁰C₇ + ¹⁰C₉ is equal to
(a) 2⁹
(b) 2¹⁰
(c) 2¹⁰ -1 
(d) 2⁸

Question. C₁+ 2C₂ + 3C₃ +…….nC_n is equal to
(a) (n -1)^2n-1
(b) n2^{n -1}
(c) n2ⁿ
(d) n2^n-2

Question. For all n ∈ N, 2⁴ⁿ -15N -1is divisible by
(a) 225
(b) 125
(c) 325
(d) None of these

Question. If (r+1) th term is the first negative term in the expansion of (1+X ), then the value of r is
(a) 5
(b) 6
(c) 4
(d) 7

Question. Sum of infinite series 1 +2/3 . 1/2 + 2/3 . 5/6 . 1/22 + 2/3 . 5/6 . 8/9 . 1/2² is
(a) 2^1/3
(b) 4^1/3
(c) 8^1/3
(d) None of these

Question. The approximate value of ( . ) / 7 995 13 correct to four decimal places is
(a) 1.9995
(b) 1.9996
(c) 1.9990
(d) 1.9991

Question. The number of dissimilar terms in the expansion of
(a+b-c)^2n-1 (a+b-c)²ⁿ⁺¹is
(a) (n+ 1)²
(b) (n-1)²
(c) 4n² – 1
(d) None of these

Question. The total number of terms in the expansion of (x + a)¹⁰⁰ + (x – a)¹⁰⁰ after simplification will be
(a) 202
(b) 51
(c) 50
(d) None of these 

Question. The coefficient of xn in the expansion of (1+ x)²ⁿ and (1+ x)^2n-1 n are in the ratio 
(a) 1:2
(b) 1:3
(c) 3:1
(d) 2:1

Question. The value of (1.002)¹² upto fourth place of decimal is
(a) 1.0242
(b) 1.0245
(c) 1.0004
(d) 1.0254

Question. The coefficient of x[0≤r≤n-1] in the expansion of(x+3)^n-1 + (x+3)^n-2 (x+2) + (x+3)n-3(x+2)² +………..(x+2)^n-1 is
(a) ⁿC_r(3^r -2ⁿ) 
(b) ⁿC_r(3^n-r -2^n-r) 
(c) ⁿC_r(3^n-r -2^n-1)
(d) None of these

Question. If  ^n-1C_r=(k²-3).ⁿC_r+1 , then k is belongs to
(a) (- ∞, – 2]
(b) [2, ∞)
(c) [- √3, √3]
(d) ( √3, 2]

Question. The coefficient of x⁴ in the expansion of (1+ x + x² + x³ )  n is
(a) ⁿC₄
(b) ⁿC₄ + ⁿC₂
(c)  ⁿC₄ + ⁿC₂ + + ⁿC₂ 
(d) ⁿC₄ + ⁿC₂ + + ⁿC₁.ⁿC₂

Question. In the expansion of the following expression (1+x) + (1+x)² + … + (1+x)n the coefficient of x4(0≤k≤n) is
(a) ⁿ⁺¹Ck+1
(b) ⁿCk
(c) ⁿC_n-k-1 
(d) None of these

Question. The coefficient of x⁵ in the expansion of (1+x)²¹ + (1+x)²² +……(1+x)³⁰ is
(a) ⁵¹C₅
(b) ⁹C₅
(c) ³C₆ –²¹C₆
(d) ³⁰C₅ + ²⁰C₅

Question. The coefficient of t²⁴ in the expansion of (1+t²)¹² (1+t¹²) (1+t²⁴ )is
(a) ¹²C₆ + 2
(b) ¹²C₅
(c) ¹²C₆
(d) ¹²C₇

Question. In the polynomial (x – 1) (x – 2) (x – 3) …(x – 100), the coefficient of x99 is
(a) 5050
(b) – 5050
(c) 100
(d) 99 

Question. If the coefficients of three consecutive terms in the expansion of (1 + x)ⁿ are in the ratio 1 :7 : 42, then the value of n is
(a) 60
(b) 70
(c) 55
(d) None of these

Question. The digit at the unit place in the number 19²⁰⁰⁵ + 11²⁰⁰⁵ – 9²⁰⁰⁵ is
(a) 2
(b) 1
(c) 0
(d) 8

Question. If the coefficients of p th, ( p + 1)th and ( p + 2)th terms in the expansion of (1 + x)ⁿ are in AP, then
(a) n² – 2n+ 4p²  = 0
(b) n² – n(4p+1)+4p² -2 = 0
(c) n² – n(4p+1)+4p²= 0
(d) None of the above

Question. 1/1(n!-1)! + 3!/1(n!-3)! + 5!/1(n!-5)! +…..is equal to
(a) 2ⁿ/n!
(b) 2^n-1/n!
(c) 0
(d) None of these

Question. The coefficient of xn in the polynomial (x + ⁿC₀ ) (x+3+ⁿC₁ ) (x+5+ⁿC₂ ) …[x+(2n+1) ⁿC_n ] is
(a) n.2ⁿ
(b) n.2^{n + 1}
(c) (n+1)²ⁿ
(d) n.2ⁿ+1

Question. If (1-x+x²)⁶ = 1+a₁x +a₂x² +…..+a₁₂x¹² , then the expression a₂ +a₄+a₆+…..+a₁₂ has the value
(a) 32
(b) 63
(c) 64
(d) None of these

Question. The 4th term in the expansion of (x – 2y)¹² is 
(a) 1760 x³y⁹
(b) – 1760 x⁹y³
(c) 1760 x⁹y³
(d) None of these

Question. In the expansion of (1 + a)^m+n, the coefficients of am and anare 
(a) equal
(b) not equal
(c) do not say anything
(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

Question. Given the integers, r > 1, n > 2 and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1+x)²ⁿ are equal, then 
(a) n = 2r
(b) n = 3r
(c) n = 2r + 1
(d) None of these

Question. If the coefficients of x² and x³ in the expansion of (3 )+ ax 9 are equal, then the value of a is
(a) 5/7
(b) 9/7
(c) 7/9
(d)- 9/7

Question. If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1 + x)ⁿ are in AP, then value of n is
(a) 2
(b) 7
(c) 11
(d) 14

Question. If in the expansion of (a – 2b)ⁿ the sum of 4th and 5th term is zero, then the value of a/b is
(a) (n – 4)/5
(b) (n – 3)/5
(c) 5/(n – 4)
(d) 5/2(n – 4)

Question. If (1+ax)ⁿ = 1+8x+24x² …, then the values of a and n are
(a) 2, 4
(b) 2, 3
(c) 3, 6
(d) 1, 2

Question. If (1+x)n … C₀+C₁x+C₂x² +…C_nxⁿ, then the value of C₀+2C₁x+3C₂+…….+(n+1)C_n will be
(a) (n+2)^{2n – 1}
(b) (n+1)²ⁿ
(c) (n+1)^2n-1
(d) (n+2)²ⁿ

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

Question. By using the first three terms of its expansion , the approximate value of (0.99)⁵ is
(a) 0.949
(b) 0.951
(c) 0.954
(d) None of these

Question. The 14th term from the end in the expansion of ( x – y )17 is
(a) ¹⁷C₅(-x⁶)(- √y)
(b) ¹⁷C₅(-√x)¹¹ (y3)
(c) ¹⁷C₄(x)^13/2 y²
(d) None of these

Question. The ratio of the coefficient of x¹⁰ in (1-x²)¹⁰ and the term independent of x in (x-2/x)¹⁰ is
(a) 1 : 16
(b) 1 : 8
(c) 64 : 1
(d) 1: 32

Question. The value of x in the expression (x+x^log10x)⁵, if the third term in the expansion is 1000000, is
(a) 10
(b) 11
(c) 12
(d) None of these

Question. The first 3 terms in the expansion of (1 + ax)ⁿ (n ≠ 0) are 1, 6x and 16 2 x . Then, the values of a and n are respectively
(a) 2 and 9
(b) 3 and 2
(c) 2/3 and 9
(d) 3/2 and 6

Question. The coefficients of x² y² yzt², and xyzt in the expansion of (x + y + z + t)⁴ are in the ratio
(a) 4 : 2 : 1
(b) 1 : 2 : 4
(c) 2 : 4 : 1
(d) 1 : 4 : 2

Question. If sum of the coefficients of the first, second and third terms of the expansion of (x²+1) is 46, then the coefficient of the term that does not contain x is
(a) 84
(b) 92
(c) 98
(d) 106

Question. If the last term in the binomial expansion of (2^1/3 -1/√2)n 18(1/3^5/3), then the 5th term from the beginning is
(a) 210
(b) 420
(c) 105
(d) None of these

Question. If x²k occurs in the expansion of (x+1/x²), then
(a) n – 2 k is a multiple of 2
(b) n – 2 k 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+2x )(3/2x²-1/3x 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 is
(a) 19
(b) – 19
(c) 18
(d) – 18

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