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

Questions
1 8n - 7n - 1 is always divisible by ____.
A 64
B 7
C 49
D 8

Answer:49
2 The sum of the coefficients nc1 + nc2 + nc3 + ...ncn is equal to ____
A 2n
B 2n+ 1
C 2n + 1
D 2n - 1

Answer:2n - 1
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3 The middle term in the expansion of [x3 /3 - 2/x2 ]11is ____.
A 5th term
B 6th term
C 5th and 6th terms
D 6th and 7th terms

Answer:6th and 7th terms
4 (2 + 5)2 - (2 - 5)2= ____.
A 820
B 1455
C 410
D 2905

Answer:2905
5 The 6th term from the end, in the expansion of (x + a)14 is ____
A 10th term from the beginning
B 9th term from the beginning
C 6th term from the beginning
D 8th term from the beginning

Answer:10th term from the beginning
6 The expression 7c0 + 7c1 + 7c2 + 7c3 + ... + 7c7is equal to ____
A 64
B 128
C 63
D 127

Answer:128
7 If the coefficients of the 6th and 9th terms in the expansion of (x + y)n are equal, then n is ____.
A 15
B 13
C 6
D 9

Answer:13
8 The ratio of the coefficient of xn in the expansion of (1 + x)3n to the coefficient of xn in the expansion of (1 + x)3n-1is ____
A 2
B 3/2
C 2/3
D 1/2

Answer:3/2
9 If the coefficient of x3y8 and x8y3 in the expansion of (x + y)n is the same, then the value of n is ____.
A 10
B 11
C 5
D 13

Answer:11
10 The number of terms in the expansion of (x+y)6 + (x-y)6is ____
A 14
B 7
C 4
D 3

Answer:4
11 If the expansion of (x + a)n,n ε N has 22 terms, then, n is equal to ____
A 22
B 24
C 21
D 23

Answer:21
12 Number of terms in the expansion of (y2 + 2xy + x2) 30is ____
A 31
B 43
C 61
D 91

Answer:61
13 If in the expansion of (1- x)2n - 1, the coefficient of xγ is Aγ, then Aγ - 1 + A2n - γ is ____.
A 1
B 5
C 0
D 3

Answer:0
14 The coefficient of x6 in the expansion (1 + x2 + x) (2 + x2)6is ____.
A 420
B 300
C 200
D 400

Answer:400
15 The coefficient of x5 in the expansion [1+X+X2+x3]13 is—
A 300
B 1000
C 2000
D 2728

Answer:2728
16 If 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

Answer:n = 2r
17 The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1 : 4 are
A 3rd and 4th
B 4th and 5th
C 5th and 6th
D 6th and 7th

Answer: 5th and 6th
18 The coefficients of xn in the expansion of (1 + x)2n and (1 + x)2n ~1 are in the ratio
A 1 : 2
B 1 : 3
C 3 : 1
D 2:1

Answer:2:1
19 If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1 + x)n are in A.P., then the value of n is
A 2
B 7
C 11
D 14

Answer:7
20 If A and B are coefficients of  xn   in the expansions of (1 + x)2n and (1 + x)2n–1  respectively, then A/B  equals to
A 1
B 2
C 1/2
D 1/n

Answer:2

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