JEE Mathematics Binomial Theorem MCQs Set E

Question: If | x | < 1/2, then expansion of (1–2x)^1/2 is-

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

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: – 55 x⁹

Question: The value of √99 upto three decimals is -

• a) 9.949
• b) 9.948
• c) 9.958
• d) None of these

Answer: 9.949

Question:

• a)

  

• b) 1√5
• c) 1√2
• d) √5

Answer:

Question: The coefficient of x⁴ in the expansion of 1+2x+3x²/1-x² is-

• a) 22
• b) 14
• c) 13
• d) 20

Answer: 22

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: 21

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: 6, 1/2

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: ⁿC₄+ ⁿC₂ + ⁿC₁.ⁿC₂

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: 2 ^2n–1

Question:

• a) 7
• b) 5
• c) 6
• d) 8

Answer: 7

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

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: – 1260

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: 10.00333

Question:

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question:

• a) 10
• b) 10²
• c) 10³
• d) No such x exists

Answer: 10

Question: The greatest integer in the expansion of (1+x)²ⁿ⁺² is -

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The greatest integer which divides 101¹⁰⁰ – 1 is -

• a) 10,000
• b) 100
• c) 1000
• d) 100,000

Answer: 10,000

Question:

(1) the number of irrational terms = 19
(2) middle term is irrational
(3) the number of rational term = 2
(4) 8th term is rational

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: The largest coefficient in the expansion of (4 + 3x)²⁵ is

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question:

(1) positive if a > 0
(2) positive if c > 0
(3) negative if a < 0 and n is odd
(4) positive if c < 0 and n is odd

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

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: 7, 14

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: –1

Question:

• a) 10
• b) 8
• c) 9
• d) None of these

Answer: 10

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: 2^n–1 (n+2)

Question:

• a) (n+1)n/n!
• b) nⁿ/(n +1)!
• c) nⁿ/n!
• d) None of these

Answer: (n+1)n/n!

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: T₃

Question:

(1) an ≥2  (2) an < 3
(3) an < 4 (4) an < 2

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

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: 1 and 3 are correct

Question:

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

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: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• b) Statement-1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is False.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Question:

• 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: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

• a) 17/54
• b) 1/3
• c) 19/54
• d) 1/4

Answer: 17/54

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: 0

Question:

• a) √2
• b) √3
• c) 2^3/2
• d) 1√2

Answer: √2

Question:

• a) 1120
• b) 560
• c) –560
• d) –1120

Answer: 1120

Question: The term independent from x in the expansion of

• a) 405
• b) 3240
• c) – 3240
• d) – 405

Answer: 405

Question: The middle term in the expansion of (x + 4) ⁴ is

• a) 96x²
• b) None of these
• c) 96x³
• d) -96x³

Answer: 96x²

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: 7560 x⁴, 45360 x³

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: 4th

Question: The term independent of x in the expansion of

• a) 7th
• b) 5th
• c) 6th
• d) 8th

Answer: 7th

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: – 455

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: –960 x^–11

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: 5th

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: T₆

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

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: 81x⁴+108x² + 54 + 12x^–2

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: 1760/x³

Question: The number of terms in the expansion of (x + y + 2z)⁸ is -

• a) 45
• b) 48
• c) 46
• d) 50

Answer: 45