BITSAT Mathematics Bionomial Theorem MCQs

Question: The integer just greater than (3+ √5)²ⁿ is divisible by (n € N)

• a) 2^n–1
• b) 2ⁿ⁺¹
• c) 2ⁿ⁺²
• d) Not divisible by 2

Answer: 2ⁿ⁺¹

Question: If

 then n =

• a) 8
• b) 4
• c) 6
• d) 5

Answer: 5

Question: If the sum of odd numbered terms and the sum of even numbered terms in the expansion of (x +a)n are A and B respectively, then the value of (x² – a²)ⁿ is

• a) A² – B²
• b) A² + B²
• c) 4AB
• d) None of these

Answer: A² – B²

Question: If the third term in the expansion of [x + x^{log10 x} ]⁵ is 10⁶, then x may be

• a) 1
• b) √10
• c) 10
• d) 10^{-2 / 5}

Answer: 10

Question: The coefficient of x⁴ in the expansion of (1 + x + x² + x³)¹¹, is

• a) 440
• b) 770
• c) 990
• d) 1001

Answer: 990

Question: If T₀,T₁,T₂....T_n represent the terms in the expansion of (x + a)ⁿ, then (T₀ –T₂ + T₄ – .......)²+ (T₁ – T₃ + T₅ – .....)² =

• a) (x² + a² )
• b) (x² + a² )ⁿ
• c) (x² + a² )^{1/ n}
• d) (x² + a² )^{-1/ n}

Answer: (x² + a² )ⁿ

Question: The coefficient of the middle term in the expansion of(2 + 3x)⁴ is :

• a) 6
• b) 5!
• c) 8!
• d) 216

Answer: 216

Question: If C₀, C₁, C₂, .............. C_n denote the binomial coefficients in the expansion of (1 + x)ⁿ, then the value of C₀ + (C₀ + C₁) + (C₀+ C₁ + C₂) + .... + (C₀+ C₁ +.....+ C_n–1)

• a) n.2^n–1
• b) n.2ⁿ
• c) (n – 1).2^n–1
• d) (n – 1).2ⁿ

Answer: n.2^n–1

Question: The coefficient of x²⁰ in the expansion of

is

• a) ³⁰C₁₀
• b) ³⁰C₂₅
• c) 1
• d) None of these

Answer: ³⁰C₂₅

Question: The term independent of x in the expansion of

is a times the corresponding binomial coefficient. Then a is

• a) 3
• b) 1/3
• c) –1/3
• d) None of these

Answer: None of these

Question: In the binomial (2^1/3 + 3^-1/3)ⁿ, if the ratio of the seventh term from the beginning of the expansion to the seventh term from its end is 1/6 , then n equal to

• a) 6
• b) 9
• c) 12
• d) 15

Answer: 9 

Question: The coefficient of x³² in the expansion of :

 is

• a) ^–15C₃
• b) ¹⁵C₄
• c) ^–15C₅
• d) ¹⁵C₂

Answer: ¹⁵C₄

Question: If in the expansion of

 T₃ = 7T₂ and sum of the binomial coefficients of second and third terms is 36, then the value of x is –

• a) –1/3
• b) – 1/2
• c) 1/3
• d) 1/2

Answer: –1/3

Question: If the second, third and fourth terms in the expansion of (a + b)ⁿ are 135, 30 and 10/3 respectively, then find the value of n.

• a) 3
• b) 4
• c) 5
• d) 6

Answer: 5

Question: If the middle term in the expansion of

is 924 x⁶, then find n.

• a) 58
• b) 18
• c) 12
• d) 20

Answer: 12

Question: If the third term in the expansion of [x + x^{log10 x} ]⁵ is 10⁶, then x may be

• a) 1
• b) √10
• c) 10
• d) 10^{-2 / 5}

Answer: 10

Question:

is a polynomial of the order of

• a) 5
• b) 6
• c) 7
• d) 8

Answer: 7

Question: if 

 then a₀ + a₂ + a₄ + .... + a_2n equals

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:  Find the term independent of x in the expansion of

• a) 4
• b) 7
• c) 8
• d) 10

Answer: 7

Question: In the binomial (2^1/3 + 3^-1/3)ⁿ, if the ratio of the seventh term from the beginning of the expansion to the seventh term from its end is 1/6 , then n equal to

• a) 6
• b) 9
• c) 12
• d) 15

Answer: 9