Class 11 Mathematics Binomial Theorem MCQs Set 03

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

Question: 1+2.1/3.2 +2.5/3.6(1/2)² + 2·5 ·8/3·6·9·(1/2)³+...is equal to
(a) 2^1/3
(b) 3^1/4
(c) 4^1/3
(d) 3^1/3 
Answer: c

Question: The coefficient of x⁷ in (1+3x- 2x³)¹⁰ ) is equal to
(a) 62640
(b) 26240
(c) 64620
(d) None of these 
Answer: a

Question: The number of terms in the expansion of (a+ b+ c)ⁿ will be
(a) n + 1
(b) n + 3
(c) (n+1 ) (n+2)/2 
(d) None of the above
Answer: c

Question: Let T_n denotes the number of triangles which can be formed using the vertices of a regular polygon of n sides. If T_{n +1}-T_n=21, then n is equal to
(a) 5
(b) 7
(c) 6
(d) 4 
Answer: b

Question: Ifn-1Cr=(k2-3).n Cr+1,then k is belongs to
a) (-∞, -2]
(b) [2,∞)
(c) [- √3,√3] 
(d) (√3 ,2] 
Answer: d

Question: The coefficient of xn in the polynomial (x+ⁿC_o)(x+3ⁿC₁)(x+5ⁿC₂)...[x+(2n+1)ⁿC_n] ) is
(a) n· 2ⁿ
(b) n· 2ⁿ+1 
(c) (n+1)2ⁿ 
(d) n·2ⁿ+1 
Answer: c

Question: Which of the following is/are correct?
(a) 101⁵⁰-99⁵⁰> 100⁵⁰ 
(b) 101⁵⁰- 100⁵⁰> 99 ⁵⁰ 
(c) (1000) ¹⁰⁰⁰> (1001)⁹⁹⁹ 
(d) (1001)⁹⁹⁹> (1000) ¹⁰⁰⁰ 
Answer: a,b,c 

Question: Let[ x] denote the greatest integer less than or equal to x. If x = (√3+1)⁵ then [x ] x is equal to
(a) 75
(b) 50
(c) 76
(d) 152 
Answer: d

Question: The number 101¹⁰⁰ - is divisible by
(a) 100
(b) 1000
(c) 10000
(d) 100000
Answer: a,b,c 

Question: 1+1/3x+1.4/3.6 x² +1·4·7/3·6·9 x³+... is equal to
(a) x
(b) (1+x)^1/3
(c) (1-x)^1/3
(d) (1-x)^-1/3
Answer: d

The 2nd, 3rd and 4th terms in the expansion of( ) x a n + are 240, 720 and 1080, respectively.

Question: The value of (x-a) ⁿ can be
(a) 64
(b) -1
(c) -32
(d) None of these
Answer: b

Question: The sum of odd numbered terms is
(a) 1664
(b) 2376
(c) 1562
(d) 1486 
Answer: c

Question: The value of least term in the expansion is
(a) 16
(b) 160
(c) 32
(d) 81 
Answer: c

Assertion and Reason
Each of these questions contains two statements: Statement (Assertion) and Statement II(Reason).
Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

Question: Three consecutive binomial coefficients are given.
Statement I They cannot be in GP and HP.
Statement II They always are in AP.
Answer: b

Question: Statement I (√2+ 1)ⁿ can be expressed as of √N- √N -1) for all N > 1 and n is positive integer.
Statement II (√2- 1)ⁿ can be expressed as A+ B √2, where A and Bare integers and is positive integer. 
Answer: b

Question: Statement I The number of terms in the expansion of
[x+1/x+1]ⁿ is 2n +1

Question: Statement I The term independent of x in the expansion of (x+1/x+2)^m is (4m)!/2m!)²·
Statement II The coefficient of x⁶ in the expansion of (1+x)ⁿ is ⁿC₆. 
Answer: d

Question: Statement I If n is an odd prime, then the integral part of (√5+2)ⁿ-2ⁿ⁺¹ is divisible by 2n
Statement II If n is prime, then ⁿC₁,ⁿC_2,...ⁿC_n-1 must be divisible by n. 
Answer: a