Please refer to MCQ Questions Chapter 8 Binomial Theorem Class 11 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 11 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 11 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 8 Binomial Theorem in Class 11 Mathematics provided below to get more marks in exams.

**Chapter 8 Binomial Theorem MCQ Questions**

Please refer to the following **Chapter 8 Binomial Theorem MCQ Questions Class 11 Mathematics** with solutions for all important topics in the chapter.

**MCQ Questions Answers for Chapter 8 Binomial Theorem Class 11 Mathematics**

**Question. The value of (1.0025)10 correct to five decimal places is**

(a) 1.025281

(b) 1.034285

(c) 1.005293

(d) None of these

## Answer

A

**Question. The number of terms which are free from radical signs in the expansion of (y ^{1/5} + X^{1/10})^{55} is**

(a) 5

(b) 6

(c) 7

(d) 4

## Answer

B

**Question. (√2+1) ^{6} – (√2 1)^{6} is equal to**

(a) 101

(b) 70

**√**2

(c) 140√2

(d) 120

**√**2

## Answer

C

**Question. If the coefficient of rth, (r+1)th and (r+2)th term in the expansion of (1+ x) ^{14} are in AP, then the value of r is**

(a) 5 or 8

(b) 4 or 9

(c) 5 or 9

(d) 6 or 7

## Answer

C

**Question. ^{10}C_{1} +^{10}C_{3} +^{ 10}C_{5} +^{ 10}C_{7} + ^{10}C_{9} is equal to**

(a) 2

^{9}

(b) 2

^{10}

(c) 2

^{10}-1

(d) 2

^{8}

## Answer

A

**Question. C _{1}+ 2C_{2} + 3C_{3} +…….nC_{n }is equal to**

(a) (n -1)

^{2n-1}

(b) n2

^{n -1}

(c) n2

^{n}

(d) n2

^{n-2}

## Answer

B

**Question. For all n ∈ N, 2 ^{4n} -15N -1is divisible by**

(a) 225

(b) 125

(c) 325

(d) None of these

## Answer

A

**Question. If (r+1) th term is the first negative term in the expansion of (1+X ), then the value of r is**

(a) 5

(b) 6

(c) 4

(d) 7

## Answer

A

**Question. Sum of infinite series 1 +2/3 . 1/2 + 2/3 . 5/6 . 1/22 + 2/3 . 5/6 . 8/9 . 1/2 ^{2} is**

(a) 2

^{1/3}

(b) 4

^{1/3}

(c) 8

^{1/3}

(d) None of these

## Answer

B

**Question. The approximate value of ( . ) / 7 995 13 correct to four decimal places is**

(a) 1.9995

(b) 1.9996

(c) 1.9990

(d) 1.9991

## Answer

B

**Question. The number of dissimilar terms in the expansion of****(a+b-c) ^{2n-1} (a+b-c)^{2n+1}is**

(a) (n+ 1)

^{2}

(b) (n-1)

^{2}

(c) 4n

^{2}– 1

(d) None of these

## Answer

A

**Question. 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

## Answer

B

**Question. The coefficient of xn in the expansion of (1+ x) ^{2n} and (1+ x)^{2n-1} n are in the ratio **

(a) 1:2

(b) 1:3

(c) 3:1

(d) 2:1

## Answer

D

**Question. The value of (1.002) ^{12} upto fourth place of decimal is**

(a) 1.0242

(b) 1.0245

(c) 1.0004

(d) 1.0254

## Answer

A

**Question. The coefficient of x[0≤r≤n-1] in the expansion of(x+3) ^{n-1} + (x+3)^{n-2} (x+2) + (x+3)n-3(x+2)^{2} +………..(x+2)^{n-1} is**

(a)

^{n}C

_{r}(3

^{r}-2

^{n})

(b)

^{n}C

_{r}(3

^{n-r}-2

^{n-r})

(c)

^{n}C

_{r}(3

^{n-r}-2

^{n-1})

(d) None of these

## Answer

B

**Question. If ^{n-1}C_{r}=(k^{2}-3).^{n}C_{r+1} , then k is belongs to**

(a) (- ∞, – 2]

(b) [2, ∞)

(c) [- √3, √3]

(d) ( √3, 2]

## Answer

D

**Question. The coefficient of x ^{4} in the expansion of (1+ x + x^{2} + x^{3} ) n is**

(a)

^{n}C

_{4}

(b)

^{n}C

_{4}+

^{n}C

_{2}

(c)

^{n}C

_{4}+

^{n}C

_{2 }+ +

^{n}C

_{2}

(d)

^{n}C

_{4}+

^{n}C

_{2 }+ +

^{n}C

_{1}.

^{n}C

_{2}

## Answer

D

**Question. In the expansion of the following expression (1+x) + (1+x) ^{2} + … + (1+x)n the coefficient of x4(0≤k≤n) is**

(a)

^{n+1}Ck+1

(b)

^{n}Ck

(c)

^{n}C

_{n-k-1}

(d) None of these

## Answer

A

**Question. The coefficient of x ^{5} in the expansion of (1+x)^{21} + (1+x)^{22} +……(1+x)^{30} is**

(a)

^{51}C

_{5}

(b)

^{9}C

_{5}

(c)

^{3}C

_{6}–

^{21}C

_{6}

(d)

^{30}C

_{5}+

^{20}C

_{5}

## Answer

C

**Question. The coefficient of t ^{24} in the expansion of (1+t^{2})^{12} (1+t^{12}) (1+t^{24} )is**

(a)

^{12}C

_{6}+ 2

(b)

^{12}C

_{5}

(c)

^{12}C

_{6}

(d)

^{12}C

_{7}

## Answer

A

**Question. In the polynomial (x – 1) (x – 2) (x – 3) …(x – 100), the coefficient of x99 is**

(a) 5050

(b) – 5050

(c) 100

(d) 99

## Answer

B

**Question. If the coefficients of three consecutive terms in the expansion of (1 + x) ^{n} are in the ratio 1 :7 : 42, then the value of n is**

(a) 60

(b) 70

(c) 55

(d) None of these

## Answer

C

**Question. The digit at the unit place in the number 19 ^{2005} + 11^{2005} – 9^{2005} is**

(a) 2

(b) 1

(c) 0

(d) 8

## Answer

B

**Question. If the coefficients of p th, ( p + 1)th and ( p + 2)th terms in the expansion of (1 + x) ^{n} are in AP, then**

(a) n

^{2}– 2n+ 4p

^{2 }= 0

(b) n

^{2}– n(4p+1)+4p

^{2}-2 = 0

(c) n

^{2}– n(4p+1)+4p

^{2}= 0

(d) None of the above

## Answer

B

**Question. 1/1(n!-1)! + 3!/1(n!-3)! + 5!/1(n!-5)! +…..is equal to**

(a) 2^{n}/n!

(b) 2^{n-1}/n!

(c) 0

(d) None of these

## Answer

B

**Question. The coefficient of xn in the polynomial (x + ^{n}C_{0} ) (x+3+^{n}C_{1} ) (x+5+^{n}C_{2} ) …[x+(2n+1) ^{n}C_{n} ] is**

(a) n.2

^{n}

(b) n.2

^{n + 1}

(c) (n+1)

^{2n}

(d) n.2

^{n}+1

## Answer

C

**Question. If (1-x+x ^{2})^{6} = 1+a_{1}x +a_{2}x^{2} +…..+a_{12}x^{12} , then the expression a_{2} +a_{4}+a_{6}+…..+a_{12} has the value**

(a) 32

(b) 63

(c) 64

(d) None of these

## Answer

D

**Question. The 4th term in the expansion of (x – 2y) ^{12} is **

(a) 1760 x

^{3}y

^{9}

(b) – 1760 x

^{9}y

^{3}

(c) 1760 x

^{9}y

^{3}

(d) None of these

## Answer

B

**Question. In the expansion of (1 + a) ^{m+n}, the coefficients of am and anare **

(a) equal

(b) not equal

(c) do not say anything

(d) None of these

## Answer

A

**Question. 49 ^{n} +16n -1 is divisible by**

(a) 3

(b) 19

(c) 64

(d) 29

## Answer

C

**Question. If A = 1000 ^{1000} and B = (1001)^{999} , then**

(a) A > B

(b) A = B

(c) A < B

(d) None of these

## Answer

A

**Question. Given the integers, r > 1, n > 2 and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1+x) ^{2n} are equal, then **

(a) n = 2r

(b) n = 3r

(c) n = 2r + 1

(d) None of these

## Answer

A

**Question. If the coefficients of x ^{2} and x^{3} in the expansion of (3 )+ ax 9 are equal, then the value of a is**

(a) 5/7

(b) 9/7

(c) 7/9

(d)- 9/7

## Answer

B

**Question. If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1 + x) ^{n} are in AP, then value of n is**

(a) 2

(b) 7

(c) 11

(d) 14

## Answer

B

**Question. If in the expansion of (a – 2b) ^{n} the sum of 4th and 5th term is zero, then the value of a/b is**

(a) (n – 4)/5

(b) (n – 3)/5

(c) 5/(n – 4)

(d) 5/2(n – 4)

## Answer

B

**Question. If (1+ax) ^{n} = 1+8x+24x^{2} …, then the values of a and n are**

(a) 2, 4

(b) 2, 3

(c) 3, 6

(d) 1, 2

## Answer

A

**Question. If (1+x)n … C _{0}+C_{1}x+C_{2}x^{2} +…C_{n}x^{n}, then the value of C_{0}+2C_{1}x+3C_{2}+…….+(n+1)C_{n }will be**

(a) (n+2)

^{2n – 1}

(b) (n+1)

^{2n}

(c) (n+1)

^{2n-1}

(d) (n+2)

^{2n}

## Answer

A

**Question. If n > (8 +3√7) ^{10} , n ∈ N, then the least value of n is**

(a) (8+3√7) – (8-3√7)

^{10}

(b) (8+3√7) + (8-3√7)

^{10}

(c) (8+3√7) – (8-3√7)

^{10}+1

(d) (8+3√7) – (8-3√7)

^{10}-1

## Answer

B

**Question. By using the first three terms of its expansion , the approximate value of (0.99) ^{5} is**

(a) 0.949

(b) 0.951

(c) 0.954

(d) None of these

## Answer

B

**Question. The 14th term from the end in the expansion of ( x – y )17 is**

(a) ^{17}C_{5}(-x^{6})(- √y)

(b) ^{17}C_{5}(-√x)^{11} (y3)

(c) ^{17}C_{4}(x)^{13/2} y^{2}

(d) None of these

## Answer

D

**Question. The ratio of the coefficient of x ^{10} in (1-x^{2})^{10} and the term independent of x in (x-2/x)^{10} is**

(a) 1 : 16

(b) 1 : 8

(c) 64 : 1

(d) 1: 32

## Answer

D

**Question. The value of x in the expression (x+x ^{log10x})^{5}, if the third term in the expansion is 1000000, is**

(a) 10

(b) 11

(c) 12

(d) None of these

## Answer

A

**Question. The first 3 terms in the expansion of (1 + ax) ^{n} (n ≠ 0) are 1, 6x and 16 2 x . Then, the values of a and n are respectively**

(a) 2 and 9

(b) 3 and 2

(c) 2/3 and 9

(d) 3/2 and 6

## Answer

C

**Question. The coefficients of x ^{2} y^{2} yzt^{2}, and xyzt in the expansion of (x + y + z + t)^{4} are in the ratio**

(a) 4 : 2 : 1

(b) 1 : 2 : 4

(c) 2 : 4 : 1

(d) 1 : 4 : 2

## Answer

B

**Question. If sum of the coefficients of the first, second and third terms of the expansion of (x ^{2}+1) is 46, then the coefficient of the term that does not contain x is**

(a) 84

(b) 92

(c) 98

(d) 106

## Answer

A

**Question. If the last term in the binomial expansion of (2 ^{1/3} -1/√2)n 18(1/3^{5/3}), then the 5th term from the beginning is**

(a) 210

(b) 420

(c) 105

(d) None of these

## Answer

A

**Question. If x ^{2}k occurs in the expansion of (x+1/x^{2}), then**

(a) n – 2 k is a multiple of 2

(b) n – 2 k is a multiple of 3

(c) k = 0

(d) None of the above

## Answer

B

**Question. The coefficient of the term independent of x in the expansion of (1+x+2x )(3/2x ^{2}-1/3x is**

(a) 1/3

(b) 19/54

(c) 17/54

(d) 1/4

## Answer

C

**Question. If the term free from x in the expansion of (x -k/x ^{2})^{10} is 405, then the value of k is**

(a) ± 1

(b) ± 2

(c) ± 3

(d) ± 4

## Answer

C

**Question. The coefficient of x in the expansion of (1-3x+7x ^{2} ) (1-x)^{16} is**

(a) 19

(b) – 19

(c) 18

(d) – 18

## Answer

B

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