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

Free download in PDF Class 11 Maths Chapter 8 Binomial Theorem Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries./p>

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(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
(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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