Class 11 Mathematics Binomial Theorem MCQs Set D

Question. If (1 + ax)ⁿ = 1 + 8x + 24 x² + … then the values of a and n are
(a) n = 4, a = 2
(b) n = 5, a = 1
(c) n = 8, a = 3
(d) n = 8, a = 2
Answer: a

Question. The number of term in the expansion of [(x + 4y)³ (x – 4y)³]² is
(a) 6
(b) 7
(c) 8
(d) 32
Answer: b

Question. What are the values of k if the term independent of x in the expansion of (√x + k/x²)¹⁰ is 405?
(a) ± 3
(b) ± 6
(c) ± 5
(d) ± 4
Answer: a

Question. If in the binomial expansion of (1 + x)ⁿ where n is a natural number, the coefficients of the 5^th, 6^th and 7^th terms are in A.P., then n is equal to:
(a) 7 or 13
(b) 7 or 14
(c) 7 or 15
(d) 7 or 17
Answer: b

Question. In the expansion of (1 + x)¹⁸ , if the coefficients of (2r + 4)^th and (r – 2)^th terms are equal, then the value of r is :
(a) 12
(b) 10
(c) 8
(d) 6
Answer: d

Question. The coefficient of xn in expansion of (1+ x)(1– x)ⁿ is
(a) (–1)^n–1n
(b) (–1)ⁿ (1– n)
(c) (–1)^n–1(n –1)²
(d) (n –1)
Answer: b

Question. One value of α for which the coefficients of the middle terms in the expansion of (1 + αx)4 and (1 – αx)6 are equal, is –3/10 . Other value of ‘α’ is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: a

Question. 1/√5+ 4x can be expanded by binomial theorem, if 
(a) x < 1
(b) | x | < 1
(c) | x | < 5/4
(d) | x | < 4/5
Answer: c

 Question. The expansion of 1/(4 – 3x)^{1/ 2} by binomial theorem will be valid, if
(a) x < 1
(b) | x | < 1
(c) –2/√3 <x<2/√3
(d) None of these
Answer: d

Question. If the rth term in the expansion of (x/3 – 2/x²)¹⁰ contains x⁴, then the value of r is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: b

Question. If A and B are coefficients of xn in the expansion of (1+ x)²ⁿ and (1+ x)^{2n –1} then :
(a) A = B
(b) 2A = B
(c) A = 2B
(d) AB = 2
Answer: c

Question. The term independent of x in the expansion of (1 – x/1 + x)² is
(a) 4
(b) 3
(c) 1
(d) None of these
Answer: c

Question. Coefficient of x¹³ in the expansion of (1 – x)⁵ (1 + x + x² + x³)⁴ is
(a) 4
(b) 6
(c) 32
(d) 5
Answer: a

Question. If the fourth term in the expansion of (ax + 1/x)ⁿ is 5/2 , then the value of a × n is
(a) 2
(b) 6
(c) 3
(d) 4
Answer: c

Question. The term independent of x in the expansion of (⁶√x – 1/³√x )⁹ is
(a) – ⁹C₃
(b) – ⁹C₄
(c) – ⁹C₅ 
(d) – ⁸C₃
Answer: a

Question. In the expansion of (³√x/3 – √3/x)¹⁰ , x > 0, the constant term is
(a) –70
(b) 70
(c) 210
(d) –210
Answer: c

Question. r and n are positive integers r > 1, n > 2 and coefficient of (r+2)^th term and 3r^th term in the expansion of (1 + x)²ⁿ are equal, then n equals
(a) 3r
(b) 3r + 1
(c) 2r
(d) 2r + 1
Answer: c

Question. The coefficient of x–12 in the expansion of (x + y/x³)²⁰
(a) ²⁰C₈
(b) ²⁰C₈ y⁸
(c) ²⁰C₁₂
(d) ²⁰C₁₂ y¹²
Answer: b

Question. In every term, the sum of indices of a and b in the expansion of (a + b)ⁿ is
(a) n
(b) n + 1
(c) n + 2
(d) n – 1
Answer: a

Question. The approximation of (0.99)5 using the first three terms of its expansion is
(a) 0.851
(b) 0.751
(c) 0.951
(d) None of these
Answer: c

Question. The coefficient of x^–7 in the expansion of [ax – 1/bx²]^–11 will be :
(a) 462a⁶/b⁵ 
(b) 462a⁵/b⁶ 
(c) –462a⁵/b⁶
(d) –462a⁶/b⁵ 
Answer: b

STATEMENT TYPE QUESTIONS

Question. Consider the following statements.
I. General term in the expansion of (x² – y)⁶ is ( – 1)^r x^{12 – 2r} · y^r
II. 4th term in the expansion of (x – 2y)¹² is –1760x⁹y³.
Choose the correct option.
(a) Only I is false
(b) Only II is false
(c) Both are false
(d) Both are true
Answer: a

Question. Consider the following statements.
Binomial expansion of (x + a)ⁿ contains (n + 1) terms.
I. If n is even, then (n/2 + 1)th term is the middle term.
II. If n is odd, then (n + 1/2)th is the middle term.
Choose the correct option.
(a) Only I is true
(b) Only II is true
(c) Both are true
(d) Both are false
Answer: a

Question. Consider the following statements.
I. Coefficient of xr in the binomial expansion of (1 + x)ⁿ is ⁿC_r.
II. Coefficient of (r + 1)th term in the binomial expansionof (1 + x)ⁿ is ⁿC_r.
Choose the correct option.
(a) Only I is correct
(b) Only II is correct
(c) Both are correct.
(d) Both are incorrect.
Answer: c

Question. The largest term in the expansion of (3 + 2x)⁵⁰, where x=1/5 , is
I. 5^th
II. 3^rd
III. 7^th
IV. 6^th
Choose the correct option
(a) Only I
(b) Only II
(c) Both I and IV
(d) Both III and IV
Answer: d