NCERT Solutions for class 11 Maths | Chapter 8 - Binomial Theorem

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Questions
1 The coefficient of xn in the expansion (1 + x + x² + …..)-n is
A 1
B (-1)n
C n
D n+1

Answer:(-1)n
2 In the expansion of (a + b)n, if n is even then the middle term is
A (n/2 + 1)th term
B (n/2)th term
C nth term
D (n/2 – 1)th term

Answer:(n/2 + 1)th term
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3 If the third term in the binomial expansion of (1 + x)m is (-1/8)x² then the rational value of m is
A 2
B 1/2
C 3
D 4

Answer:1/2
4 In the expansion of (a + b)n, if n is odd then the number of middle term is/are
A 0
B 1
C 2
D More than 2

Answer:2
5 The general term of the expansion (a + b)n is
A Tr+1 = nCr × ar × br
B Tr+1 = nCr × ar × bn-r
C Tr+1 = nCr × an-r × bn-r
D Tr+1 = nCr × an-r × br

Answer:Tr+1 = nCr × an-r × br
6 The greatest coefficient in the expansion of (1 + x)10 is
A 10!/(5!)
B 10!/(5!)²
C 10!/(5! × 4!)²
D 10!/(5! × 4!)

Answer:10!/(5!)²
7 The value of n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively is
A 2
B 4
C 6
D 8

Answer:6
8 If n is a positive integer, then (√3+1)2n+1 + (√3−1)2n+1 is
A an even positive integer
B a rational number
C an odd positive integer
D an irrational number

Answer:an irrational number
9 The coefficient of xn in the expansion of (1 – 2x + 3x² – 4x³ + ……..)-n is
A (2n)!/n!
B (2n)!/(n!)²
C (2n)!/{2×(n!)²}
D None of these

Answer:(2n)!/(n!)²
10 In the binomial expansion of (71/2 + 51/3)37, the number of integers are
A 2
B 4
C 6
D 8

Answer:6
11 In the binomial expansion of (a + b)n, the coefficient of fourth and thirteenth terms are equal to each other, then the value of n is
A 10
B 15
C 20
D 25

Answer:15
12 The fourth term in the expansion (x – 2y)12 is
A -1670 x9 × y³
B -7160 x9 × y³
C -1760 x9 × y³
D -1607 x9 × y³

Answer:-1760 x9 × y³
13 If the third term in the binomial expansion of (1 + x)m is (-1/8)x² then the rational value of m is
A 2
B 1/2
C 3
D 4

Answer:1/2
14 The number of ordered triplets of positive integers which are solution of the equation x + y + z = 100 is
A 4815
B 4851
C 8451
D 8415

Answer:4851
15 The coefficient of y in the expansion of (y² + c/y)5 is
A 10c
B 10c²
C 10c³
D None of these

Answer:10c³
16 The greatest coefficient in the expansion of (1 + x)10 is
A 10!/(5!)
B 10!/(5!)²
C 10!/(5! × 4!)²
D 10!/(5! × 4!)

Answer: 10!/(5!)²
17 if n is a positive ineger then 23nn – 7n – 1 is divisible by
A 7
B 9
C 49
D 81

Answer:49
18 (1.1)10000 is _____ 1000
A greater than
B less than
C equal to
D None of these

Answer:greater than
19 If α and β are the roots of the equation x² – x + 1 = 0 then the value of α2009 + β2009 is
A 0
B 1
C -1
D 10

Answer:1
20 If n is a positive integer, then (√5+1)2n + 1 − (√5−1)2n + 1 is
A an odd positive integer
B not an integer
C none of these
D an even positive integer

Answer:not an integer

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