### Binomial Theorem Quiz:

**Ques. **The total number of terms in the expansion of (x + a)^{100} + (x – a)^{100} after simplification will be

(a) 202

(b) 51

(c) 50

(d) None of these

Ans. (b)

Related: Digestive system questions

**Ques. **Let T_{n} denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If T_{n + 1} –T_{n} = 21, then n equals

(a) 5

(b) 7

(c) 6

(d) 4

Ans. (b)

**Ques. **If *A* and *B* are the coefficients of x^{n} in the expansions of (1 + x)^{2n} and (1 + x)^{2n–1} respectively, then

(a) A = B

(b) A = 2B

(c) 2A = B

(d) None of these

Ans. (b)

**Ques. **The number 111……1 (91 times) is

(a) Not a prime

(b) An even number

(c) Not an odd number

(d) None of these

Ans. (a)

Related: permutation and combination quiz

**Ques. **In the expansion of (1 + x)^{5}, the sum of the coefficient of the terms is

(a) 80

(b) 16

(c) 32

(d) 64

Ans. (c)

**Ques. **If *p* and *q* be positive, then the coefficients of x^{p} and x^{q} in the expansion of (1 + x)^{p + q} will be

(a) Equal

(b) Equal in magnitude but opposite in sign

(c) Reciprocal to each other

(d) None of these

Ans. (a)

**Ques. **Coefficient of t^{24} in (1 + t^{2})^{12} (1 + t^{12}) (1 + t^{24}) is

(a) ^{12}C_{6} + 3

(b) ^{12}C_{6} + 1

(c) ^{12}C_{6}

(d) ^{12}C_{6} + 2

Ans. (d)

Related: Relations and functions objective questions

**Ques. **The sum of all the coefficients in the binomial expansion of (x^{2} + x – 3)^{319} is

(a) 1

(b) 2

(c) – 1

(d) 0

Ans. (c)

**Ques. **If in the expansion of (1 + x)^{m} (1 – x)^{n}, the coefficient of *x* and x^{2 }are 3 and – 6 respectively, then *m* is

(a) 6

(b) 9

(c) 12

(d) 24

Ans. (c)

**Ques. **Cube root of 217 is

(a) 6.01

(b) 6.04

(c) 6.02

(d) None of these

Ans. (a)

Related: wave optics quiz

**Ques. **If the coefficients of 5^{th}, 6^{th} and 7^{th} terms in the expansion of (1 + x)^{n} be in A.P., then *n* =

(a) 7 only

(b) 14 only

(c) 7 or 14

(d) None of these

Ans. (c)

**Ques. **If in the expression of (1 + x)^{m} (1 – x)^{n}, then coefficient of x and x^{2} are 3 and – 6 respectively, then m is

(a) 6

(b) 9

(c) 12

(d) 24

Ans. (c)

**Ques. **In the expansion of (1 + x)^{n} the sum of coefficients of odd powers of *x* is

(a) 2^{n} + 1

(b) 2^{n} – 1

(c) 2^{n}

(d) 2^{n – 1}

Ans. (d)

**Ques. **If the three consecutive coefficient in the expansion of (1 + x)^{n} are 28, 56 and 70, then the value of *n* is

(a) 6

(b) 4

(c) 8

(d) 10

Ans. (c)

Related: Nuclear Chemistry Sample paper

**Ques. **In the expansion of (1 + x + x^{3} + x^{4})^{10}, the coefficient of x^{4} is

(a) ^{40}C_{4}

(b) ^{10}C_{4
}(c) 210

(d) 310

Ans. (d)

**Ques. **The sum of coefficients in (1 + x – 3x^{2})^{2134} is

(a) – 1

(b) 1

(c) 0

(d) 2^{2134}

Ans. (b)

**Ques. **The expression {(x + (x^{3} – 1)^{1/2})^{5}} + {x – (x^{3} – 1)^{1/2}}^{5} is polynomial of degree

(a) 5

(b) 6

(c) 7

(d) 8

Ans. (c)

Related: objective questions on Quantum Numbers

**Ques. **If the coefficients of second, third and fourth term in the expansion of (1 + x)^{2n} are in A.P., then 2n^{2} – 9n + 7 is equal to

(a) – 1

(b) 0

(c) 1

(d) 3/2

Ans. (b)

**Ques. **In the expansion of (1 + 3x + 2x^{2})^{6} the coefficient of x^{11} is

(a) 144

(b) 288

(c) 216

(d) 576

Ans. (d)

**Ques. **The sum of coefficients in the expansion of (x + 2y + 3z)^{8} is

(a) 3^{8}

(b) 5^{8
}(c) 6^{8}

(d) None of these

Ans. (c)

Related: Ratio and proportion quiz

**Ques. **The greatest integer which divides the number 101^{100} – 1, is

(a) 100

(b) 1000

(c) 10000

(d) 100000

Ans. (c)

**Ques. **If the second, third and fourth term in the expansion of (x + a)^{n} are 240, 720 and 1080 respectively, then the value of *n* is

(a) 15

(b) 20

(c) 10

(d) 5

Ans. (d)

**Ques. **Given positive integers r > 1, m > 2, and that the coefficients of (3r)^{th} term and (r + 2)^{th} terms in the binomial expansion of (1 + r)^{2n} are equal. Then

(a) n = 2r

(b) n = 2r + 1

(c) n = 3r

(d) none of these

Ans. (a)

Related: Percentage problems and solutions

**Ques. **If coefficient of (2r + 3)^{th} and (r – 1)^{th} terms in the expansion of (1 + x)^{15} are equal, then value of *r* is

(a) 5

(b) 6

(c) 4

(d) 3

Ans. (a)

**Ques. **The coefficient of x^{5} in the expansion of (x^{2} – x – 2)^{5} is

(a) – 83

(b) – 82

(c) – 81

(d) 0

Ans. (c)

**Ques. **The coefficient of x^{5} in the expansion of (x + 3)^{6} is

(a) 18

(b) 6

(c) 12

(d) 10

Ans. (a)

Related: syllogism worksheet

**Ques. **The last digit in 7^{300} is

(a) 7

(b) 9

(c) 1

(d) 3

Ans. (c)

**Ques. **The digit in the unit place of the number (183!) + 3^{183} is

(a) 7

(b) 6

(c) 3

(d) 0

Ans. (a)