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

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Questions
1 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
2 The smallest positive integer for which the statement 3n+1 < 4n is true for all
A 4
B 3
C 1
D 2

Answer:4
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3 If the sum of the coefficients in the expansion of (a + b)n is 4096, then the greatest coefficient in the expansion is
A 924
B 792
C 1594
D None of these

Answer:924
4 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
5 The value of ∑(3r * nCr ) where 0 ≤ r ≤ 4
A 2n
B 3n
C 4n
D 5n

Answer:4n
6 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
7 The value of 1/81n - (10/81n ) * 2nC1 + (102 /81n ) * 2nC2 - (103 /81n ) * 2nC3 + ....... +  102n /81n is 

A 2
B 0
C 1/2
D 1

Answer:1
8 If n is positive integer, then (√3+1)2n−(√3−1)2n is

A an irrational number
B an odd positive integer
C none of these
D a rational number

Answer:an irrational number
9 If the fourth term in the expansion (ax + 1/x)n is 5/2, then the value of x is
A 4
B 6
C 8
D 5

Answer:6
10 The sum of the coefficient of the polynomial (1 + x - 3x2 )2143 is
A -1
B 1
C 0
D None of these

Answer:-1
11 Which one the following is the common factor of (4743 + 4343 ) and (4747 + 4347 )
A 47 - 43
B 47 + 43
C (4743 + 4343 )
D (4747 + 4347 )

Answer:47 + 43
12 If n is a positive integer, then (3 + √i)n+(3 -√i)n is
A a non real number
B a positive real number
C a real number
D none of these

Answer:a non real number
13 The coefficient of y in the expansion of (y2 + c/y)5 is
A 29c
B 10c
C 10c3
D 20c2

Answer:10c3
14 The number 111111…………..1 (91 times) is
A not an odd number
B none of these
C not a prime
D an even number

Answer:not a prime
15 The remainder when (17)200 is divided by 18 is
A 0
B 1
C 2
D 17

Answer:1
16 The value of 1/81n - (10/81n ) * 2nC1 + (102 /81n ) * 2nC2 - (103 /81n ) * 2nC3 + ....... +  102n /81n is 

A 2
B 0
C 1/2
D 1

Answer:4
17 The coefficient of a-6 b4 in the expansion (1/a - 2b/3)10 is
A 1102/27
B 1120/72
C 1120/27
D 1120/37

Answer:1120/27
18 The term independent of x in (√x - 2/x)18 is
A 18C4 * 24
B 18C5 * 25
C 18C6 * 26
D None of these

Answer:18C6 * 26
19 The number (101)100 - 1 is divisible by
A 100
B 1000
C 10000
D All the above

Answer:All the above
20 The coefficient of a4 * b5 in the expansion of (a + b)9 is
A 9C4
B 9C3
C 8C4
D 8C3

Answer:9C4

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