JEE Mathematics Binomial Theorem MCQs Set 05

Question. The tenth term in the expansion of (1+ x)^–3 is -
(a) – 55 x⁹
(b) – 66 x¹⁰
(c) 55 x⁹
(d) 66 x¹⁰

Answer: A

Question. The value of √99 upto three decimals is -
(a) 9.949
(b) 9.948
(c) 9.958
(d) None of these

Answer: A

Question. The coefficient of x⁴ in the expansion of 1+2x+3x²/1-x² is-
(a) 22
(b) 14
(c) 13
(d) 20

Answer: A

Question. If the coefficients of rth and (r +1)^th terms in the expansion of (3+7x)²⁹ are equal, then r equals-
(a) 21
(b) None of these
(c) 15
(d) 14

Answer: A

Question. If the fourth term in the expansion of (px + 1/x)ⁿ is 5/2 then the value of n and p are respectively-
(a) 6, 1/2
(b) 3,1
(c) 1/2, 6
(d) 3, 1/2

Answer: A

Question. The coefficient of x⁴ in the expansion of
(1+ x + x²+ x³)ⁿ is -
(a)  ⁿC₄+ ⁿC₂ + ⁿC₁.ⁿC₂
(b)  ⁿC₄+ ⁿC₂
(c) None of these
(d)  ⁿC₄

Answer: A

Question. If (2– x – x² )²ⁿ = a₀ + a₁x+a₂x²+ a₃x³ + ..., then the value of a₀ + a₂+ a₄ + .... is-
(a) 2 ^2n–1
(b) 2^n–1
(c) 2²ⁿ
(d) None of these

Answer: A

Question. The term independent of x in the expansion of (1-x/1+x)2 is
(a) 252
(b) – 1260
(c) 1260
(d) – 252

Answer: B

Question. The value of cube root of 1001 upto five decimal places is–
(a) 10.00333
(b) None of these
(c) 10.03333
(d) 10.00033

Answer: A

Question. The greatest integer which divides 101¹⁰⁰ – 1 is -
(a) 10,000
(b) 100
(c) 1000
(d) 100,000

Answer: A

Question. If in the expansion of (1+ y)ⁿ, the coefficient of 5th, 6th and 7th terms are in A.P., then n is equal to-
(a) 7, 14
(b) None of these
(c) 7, 11
(d) 8, 16

Answer: A

Question. The sum of the coefficient of the terms of the expansion of polynomial (1+ x– 3x² )²¹⁴³ is-
(a) –1
(b) 2²¹⁴³
(c) 1
(d) 0

Answer: A

Question. If (1+x)ⁿ = C₀ +C₁x+ C₂x²+ ...+ C_nxⁿ. then C₀+ 2C₁+ 3C₂ + ....+ (n+1) C_n is equal to-
(a) 2^n–1 (n+2)
(b) 2ⁿ(n+1)
(c) 2^n–1 (n+ 1)
(d) 2ⁿ (n+2)

Answer: A

Question. In the expansion of (4–3x)⁷, the numerically greatest term at x = 2/3 is -
(a) T₃
(b) T₄
(c) T₅
(d) T₂

Answer: A

Question. If the sum of the cofficients in the expansion of (2 + 3cx + c² x² )12 vanishes then c equals
(1) – 2 (2) 2
(3) – 1 (4) 1
(a) 1 and 3 are correct
(b) 1 and 2 are correct
(c) 1, 2 and 3 are correct
(d) 2 and 4 are correct

Answer: A

Question. Statement 1 : If x = ⁿC_n–1 + ⁿ⁺¹C_n–1 + ⁿ⁺²C_n–1 + ........ +²ⁿC_n–1, then x+1/ 2n+1 is integer.
Statement 2 : ⁿC_r + ⁿC_r–1 = ⁿ⁺¹C_r and ⁿC_r is divisible by n if n and r are co-prime.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(c) Statement-1 is False, Statement-2 is True.
(d) Statement-1 is True, Statement-2 is False.

Answer: A

Question. If (1+ x) ⁿ = C₀+ C₁x + C₂ x² + ....+ C_nxⁿ, then 3C₀ – 5C₁ + 7C₂ + ...+ (–1)ⁿ (2n+ 3) C_n equals-
(a) 0
(b) 2 (2n + 3) 2ⁿ
(c) 1
(d) (2n + 3) 2^n–1

Answer: A

Question. The middle term in the expansion of (x + 4) ⁴ is
(a) 96x²
(b) None of these
(c) 96x³
(d) -96x³

Answer: A

Question. The middle terms in the expansion (x+6)⁷ is-
(a) 7560 x⁴, 45360 x³
(b) None of these
(c) –7560 x⁴, –45360 x³
(d) 7560 x⁴, – 45360 x³

Answer: A

Question. The term which has the greatest coefficient in the expansion of (x² + 2/x)⁶ is–
(a) 4th
(b) 6th
(c) 3rd
(d) 5th

Answer: A

Question. The co-efficient of x³⁹ in the expansion of (x⁴ –1/x³) ¹⁵ is–
(a) – 455
(b) None of these
(c) 455
(d) 105

Answer: A

Question. The 4th term from the end in the expansion of (2x – 1/x²)¹⁰ is–
(a) –960 x^–11
(b) 960 x^–12
(c) 960 x^–11
(d) –960 x^–12

Answer: A

Question. The term which has the greatest coefficient in the expansion of (x + a)⁸ is–
(a) 5th
(b) 3rd
(c) 4th
(d) 6th

Answer: A

Question. The greatest term in the expansion of (2x + 7)¹⁰, when x = 3 is-
(a) T₆
(b) None of these
(c) T₅
(d) T₇

Answer: A

Question. The first four terms in the expansion of (3x + 1/x)⁴ is -
(a) 81x⁴+108x² + 54 + 12x^–2
(b) – 81x⁴ –108x² – 54 – 12x^–2
(c) Both
(d) None of these

Answer: A

Question. The tenth term in the expansion of (2x²+ 1/x)¹² is –
(a) 1760/x³
(b) 1760/x²
(c) –1760/x³
(d) None of these

Answer: A

Question. The number of terms in the expansion of (x + y + 2z)⁸ is -
(a) 45
(b) 48
(c) 46
(d) 50

Answer: A