Class 11 Mathematics Binomial Theorem MCQs

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) 4n^2-1 
(d) None of these

Answer :  A
 

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

Answer :  B

Question. If A and B are coefficients of xⁿ in the expansion of (1+ x)²ⁿ and (1+ x)^{2n –1} then :
(a) A = B
(b) 2A = B
(c) A = 2B
(d) AB = 2

Answer :  C


Question. In the expansion of (1 + x)ⁿ, the binomial coefficients of three consecutive terms are respectively 220, 495 and 792. The value of n is:
(a) 10
(b) 11
(c) 12
(d) 13

Answer :  C


Question. The coefficient of xk in the expansion of A = 1 + (1 + x) + (1 + x)² + .... + (1 + x)n is :
(a) ⁿC_k
(b) ⁿ⁺¹C_k
(c) ⁿ⁺¹C_k–1
(d) none of these

Answer :  D
 

Question. What is the coefficient of x³ in (3 2x) / (1 3x)³
(a) – 272
(b) – 540
(c) – 870
(d) – 918

Answer :  D
 

Question. In the expansion of (1 + x)50, the sum of the coefficients of odd powers of x is :
(a) 0
(b) 249
(c) 250
(d) 251

Answer :  B
 

Question. 5 [( √5 +1)⁵⁰ – (√5 –1)⁵⁰ ] is
(a) an irrational number
(b) 0
(c) a natural number
(d) None of these

Answer :  C


Question. The minimum positive integral value of m such that (1073)⁷¹ – m may be divisible by 10, is
(a) 1
(b) 3
(c) 7
(d) 9

Answer :  C
 

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

Answer :  C
 

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

Answer :  C

Question. If 'n' is positive integer and three consecutive co-efficient in the expansion of (1 + x)n are in the ratio 6 : 33 : 110, then n is equal to :
(a) 9
(b) 6
(c) 12
(d) 16

Answer :  C

Question. The remainder left out when 8²ⁿ – (62)²ⁿ⁺¹ is divided by 9 is :
(a) 2
(b) 7
(c) 8
(d) 0

Answer :  A
 

Question. (1 + √2 x²)⁹ – 1 – 9√2 x² – 70x⁴ is divisible by
(a) x⁶
(b) x⁸
(c) x¹⁰
(d) none of these

Answer :  D
 

Question. If x is positive, the first negative term in the expansion of (1+ x)27 5 is
(a) 6th term
(b) 7th term
(c) 5th term
(d) 8th term

Answer :  D
 

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

Answer :  A
 

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

Answer :  B
 

Question. If in the expansion of (2^x + 1/4^x)n , T3 = 7T2 and sum of the binomial coefficients of second and third terms is 36, then the value of x is –
(a) –1/3
(b) – 1/2
(c) 1/3
(d) 1/2

Answer :  A
 

Question. The coefficient of the middle term in the binomial expansion in powers of x of (1+ ax)4 and of (1- ax)6 is the same if a equals
(a) 3/5
(b) 10/3
(c) -3/10
(d) -5/3

Answer :  C


Question. If x = 9950 + 10050 and y = (101)50 then
(a) x = y
(b) x < y
(c) x > y
(d) None of these

Answer :  B


Question. If the third term in the expansion of [x + xlog10x ]5 is 106, then x may be
(a) 1
(b) √10
(c) 10
(d) 10^{-2 / 5}

Answer :  C


Question. If 7⁹ + 9⁷ is divided by 64 then the remainder is
(a) 0
(b) 1
(c) 2
(d) 63

Answer :  A


Question. The number of term in the expansion of
[(x + 4y)³ (x – 4y)³]² is
(a) 6
(b) 7
(c) 8
(d) 32

Answer :  B
 

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

Answer :  A
 

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

Answer :  B
 

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

Answer :  B
 

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

Answer :  A
 

Question. If (r+1) th term is the first negative term in the expansion of (1+X)^7/2 then the value of r is      
(a) 5
(b) 6
(c) 4
(d) 7

Answer :  A
 

Question. The approximate value of( 7.995 )1/3 correct to four decimal places is     
(a) 1.9995
(b) 1.9996
(c) 1.9990
(d) 1.9991

Answer :  B 
 

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

Answer :  A