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## MCQ for BITSAT Mathematics Bionomial Theorem

BITSAT Mathematics students should refer to the following multiple-choice questions with answers for Bionomial Theorem in BITSAT. These MCQ questions with answers for BITSAT Mathematics will come in exams and help you to score good marks

### Bionomial Theorem MCQ Questions with Answers

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

- a) 2
^{n–1} - b) 2
^{n+1} - c) 2
^{n+2} - d) Not divisible by 2

**Answer: ****2 ^{n+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 (x^{2} – a^{2})^{n} is

- a) A
^{2}– B^{2} - b) A
^{2}+ B^{2} - c) 4AB
- d) None of these

**Answer: ****A ^{2} – B^{2}**

#### Question: If the third term in the expansion of [x + x^{log10 x} ]^{5} is 10^{6}, then x may be

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

**Answer: ****10**

#### Question: The coefficient of x^{4} in the expansion of (1 + x + x^{2} + x^{3})^{11}, is

- a) 440
- b) 770
- c) 990
- d) 1001

**Answer: ****990**

#### Question: If T_{0},T_{1},T_{2}....T_{n} represent the terms in the expansion of (x + a)^{n}, then (T_{0} –T_{2} + T_{4} – .......)^{2}+ (T_{1} – T_{3} + T_{5} – .....)^{2} =

- a) (x
^{2}+ a^{2}) - b) (x
^{2}+ a^{2})^{n} - c) (x
^{2}+ a^{2})^{1/ n} - d) (x
^{2}+ a^{2})^{-1/ n}

**Answer: ****(x ^{2} + a^{2} )^{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 C_{0}, C_{1}, C_{2}, .............. C_{n} denote the binomial coefficients in the expansion of (1 + x)^{n}, then the value of C_{0} + (C_{0} + C_{1}) + (C_{0}+ C_{1} + C_{2}) + .... + (C_{0}+ C_{1} +.....+ C_{n–1})

- a) n.2
^{n–1} - b) n.2
^{n} - c) (n – 1).2
^{n–1} - d) (n – 1).2
^{n}

**Answer: ****n.2 ^{n–1}**

#### Question: The coefficient of x^{20} in the expansion of

#### is

- a)
^{30}C_{10} - b)
^{30}C_{25} - c) 1
- d) None of these

**Answer: **^{30}C_{25}

#### 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 x^{32} in the expansion of :

#### is

- a)
^{–15}C_{3} - b)
^{15}C_{4} - c)
^{–15}C_{5} - d)
^{15}C_{2}

**Answer: **^{15}C_{4}

#### Question: If in the expansion of

#### T_{3} = 7T_{2} 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 x^{6}, 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 10^{6}, 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 a_{0} + a_{2} + a_{4} + .... + 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**