# Binomial Theorem VBQs Class 11 Mathematics

VBQs Binomial Theorem Class 11 Mathematics with solutions has been provided below for standard students. We have provided chapter wise VBQ for Class 11 Mathematics with solutions. The following Binomial Theorem Class 11 Mathematics value based questions with answers will come in your exams. Students should understand the concepts and learn the solved cased based VBQs provided below. This will help you to get better marks in class 11 examinations.

## Binomial Theorem VBQs Class 11 Mathematics

Question. Let (x + 10)50 + (x – 10)50 = a0 + a1x + a2x2 + …. + a50x50, for all x ∈ R; then a2/a0 is equal to :
(a) 12.50
(b) 12.00
(c) 12.25
(d) 12.75

C

Question. If the third term in the binomial expansion of (1 + xlog2x)equals 2560, then a possible value of x is:
(a) 1/4
(b) 4√2
(c) 1/8
(d) 2√2

A

Question. The number of terms in the expansion of (1 + x)101 (1 + x2 – x)100 in powers of x is:
(a) 302
(b) 301
(c) 202
(d) 101

C

Question. If for positive integers r > 1, n > 2, the coefficients of the (3r)th and (r + 2)th powers of x in the expansion of (1 + x)2n are equal, then n is equal to :
(a) 2r + 1
(b) 2r –1
(c) 3r
(d) r + 1

A

Question. If the fourth term in the Binomial expansion of (2/x + xlog8x)6 (x > 0) is 20 × 87, then a value of x is:
(a) 83
(b) 82
(c) 8
(d) 8–2

B

Question. If the fourth term in the binomial expansion of

is equal to 200, and x > 1, then the value of x is:
(a) 100
(b) 10
(c) 103
(d) 104

B

Question. The positive value of l for which the co-efficient of x2 in the expression x2(√x + λ/x2)10 is 720, is:
(a) 4
(b) 2√2
(c) √5
(d) 3

A

Question. If the fractional part of the number 2403/15 is k/15 , then k is equal to:
(a) 6
(b) 8
(c) 4
(d) 14

B

Question. The natural number m, for which the coefficient of x in the binomial expansion of (xm + 1/x2)22 is 1540, is ______.

13

Question. If n is the degree of the polynomial,

and m is the coefficient of xn in it, then the ordered pair (n, m) is equal to
(a) (12 , (20)4)
(b) (8, 5 (10)4)
(c) (24 , (10)8)
(d) (12, 8 (10)4)

D

Question. If α and β be the coefficients of x4 and x2 respectively in the expansion of (x + √(x2 – 1))6 + (x – √(x2 – 1))6 , then:
(a) α + β = 60
(b) α + β = –30
(c) α – β= 60
(d) α – β = –132

D

Question. If {4n – 3n – 1 : n ∈ N } and Y = {9(n -1) : nε N}, where N is the set of natural numbers, then X ∪ Y is equal to:
(a) X
(b) Y
(c) N
(d) Y – X

B

Question. The coefficient of x2 in the expansion of the product (2 – x2). ((1 + 2x + 3x2)6 + (1 – 4x2)6) is
(a) 106
(b) 107
(c) 155
(d) 108

A

Question. If (27)999 is divided by 7, then the remainder is :
(a) 1
(b) 2
(c) 3
(d) 6

D

Question. Statement – 1 : For each natural number n, (n + 1)7–1 is divisible by 7.
Statement – 2 : For each natural number n, n7 – n is divisible by 7.
(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 true, Statement-2 is false
(d) Statement-1 is false, Statement-2 is true

A

Question. In the expansion of (x/cosθ + 1/sinθ)16, if l1 is the least value of the term independent of x when π/8 ≤ 0 ≤ π/4 and l2 is the least value of the term independent of x when π/16 ≤ 0 ≤ π/8 , then the ratio l2 : l1 is equal to :
(a) 1 : 8
(b) 16 : 1
(c) 8 : 1
(d) 1 : 16

B

Question. The number of integral terms in the expansion of (√3 + 8√5)256 is
(a) 35
(b) 32
(c) 33
(d) 34

C

Question. If the constant term in the binomial expansion of

is 405, then |k| equals:
(a) 9
(b) 1
(c) 3
(d) 2

C

Question. If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1 + x)n+5 are in the ratio 5 : 10 : 14, then the largest coefficient in this expansion is :
(a) 462
(b) 330
(c) 792
(d) 252

A

Question. In the binomial expansion of (a – b)n, n ≥ 5, the sum of 5th and 6th terms is ero, then a/b equals
(a) (n – 5) / 6
(b) (n – 4) / 5
(c) 5/ (n – 4)
(d) 6/ (n – 5)

B

Question. For natural numbers m, n if (1 – y)m (1 + y)n = 1+ a1y + a2y2 + ……. and a1 = a2 = 10, then (m,n) is
(a) (20, 45)
(b) (35, 20)
(c) (45, 35)
(d) (35, 45)

D

Question. If the number of integral terms in the expansion of (31/2 + 51/8)n is exactly 33, then the least value of n is :
(a) 264
(b) 128
(c) 256
(d) 248

C

Question. The total number is irrational terms in the binomial expansion of (71/5 – 31/10)60 is :
(a) 55
(b) 49
(c) 48
(d) 54

D

Question. The coefficient of x18 in the product (1+x)(1–x)10 (1+x+x2)9 is :
(a) 84
(b) –126
(c) –84
(d) 126

A

Question. The ratio of the coefficient of x15 to the term independent of x in the expansion of (x2 + 2/x)15 is :
(a) 7 : 16
(b) 7 : 64
(c) 1 : 4
(d) 1 : 32

D

Question. The middle term in the expansion of (1 – 1/x)n (1 – x)n in power of x is
(a) –2nCn–1
(b) – 2nCn
(c) 2nCn–1
(d) 2nCn

D

Question. If x is so small that x3 and higher powers of x may be neglected, then

may be approximated as
(a) 1 – 3/8 x2
(b) 3x + 3/8 x2
(c) – 3/8 x2
(d) x/2 – 3/8 x2

C

Question. If x is positive, the first negative term in the expansion of (1+ x)27/5 is
(a) 6th term
(b) 7th term
(c) 5th term
(d) 8th term

D

Question. The coefficient of the middle term in the binomial expansion in powers of x of (1+ αx)4 and of (1 – αx)6 is the same if
α equals
(a) 3/5
(b) 10/3
(c) -3/10
(d) -5/3

C

Question. A ratio of the 5th term from the begining to the 5th term from the end in the binomial expansion of (21/3 + 1/2(3)1/3)10 is:
(a) 1 : 2(6)1/3
(b) 1/1 : 4(16)1/3
(c) 4(36)1/3 : 1
(d) 2(36)1/3 : 1

C

Question. If 20C1 + (22) 20C2 +(32) 20C3+ ………. + (202) 20C20 = A(2β), then the ordered pair (A, β) is equal to :
(a) (420, 19)
(b) (420, 18)
(c) (380, 18)
(d) (380, 19)

B

Question.

Statement – 1 : S3 = 55 × 29.
Statement – 2 : S1 = 90 × 28 and S2 = 10 × 28.
(a) Statement -1 is true, Statement -2 is true ; Statement – 2 is not a correct explanation for Statement -1.
(b) Statement -1 is true, Statement -2 is false.
(c) Statement -1 is false, Statement -2 is true .
(d) Statement – 1 is true, Statement 2 is true ; Statement -2 is a correct explanation for Statement -1.

B

Question. In a shop there are five types of ice-creams available. A child buys six ice-creams.
Statement – 1 : The number of different ways the child can buy the six ice-creams is 10C5.
Statement – 2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row.
(a) Statement -1 is false, Statement-2 is true
(b) Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c) Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d) Statement -1 is true, Statement-2 is false

A

Question. The value of

is equal to :
(a) 51C730C7
(b) 50C730C7
(c) 50C630C6
(d) 51C7 + 30C7

A

Question. The term independent of x in the expansion of (1/60 – x8/81) · (2x2 – 3/x2)6 is equal to :
(a) –72
(b) 36
(c) –36
(d) –108

D

Question. The coefficient of x7 in the expansion of (1– x – x2 + x3 )6 is
(a) –132
(b) –144
(c) 132
(d) 144

B

Question. If the coefficients of x–2 and x–4 in the expansion of

(x > 0), are m and n respectively, then m/n is equal to :
(a) 27
(b) 182
(c) 5/4
(d) 4/5

B

Question. The remainder left out when 82n – (62)2n+1 is divided by 9 is:
(a) 2
(b) 7
(c) 8
(d) 0

A

Question. The coefficient of x10 in the expansion of (1 + x)2 (1 + x2)3 (1 + x3)4 is equal to
(a) 52
(b) 44
(c) 50
(d) 56

A

Question. If {p} denotes the fractional part of the number p, then {3200/8}, is equal to :
(a) 5/8
(b) 7/8
(c) 3/8
(d) 1/8

D

Question.

(a) Statement -1 is false, Statement-2 is true
(b) Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c) Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d) Statement -1 is true, Statement-2 is false

B

Question. If the coefficients of the three successive terms in the binomial expansion of (1 + x)n are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is:
(a) 8th
(b) 6th
(c) 7th
(d) 9th

C

Question. If some three consecutive coefficients in the binomial expansion of (x + 1)n in powers of x are in the ratio 2:15:70, then the average of these three coefficients is:
(a) 964
(b) 232
(c) 227
(d) 625

B

Question. The sum of the co-efficients of all even degree terms in x in the expansion of (x + √(x3-1))6 + (x – √(x3-1))6 , (x > 1) is equal to :
(a) 29
(b) 32
(c) 26
(d) 24

D

Question. If the coefficents of x3 and x4 in the expansion of (1+ ax + bx2) (1- 2x)18 in powers of x are both ero, then
(a, b) is equal to:
(a) (14 , 272/3)
(b) (16 , 272/3)
(c) (16 , 251/3)
(d) (14 , 251/3)

B

Question. Let

Then a7 / a13 is equal to ___________.

800

Question.

(a) – 4
(b) 6
(c) – 8
(d) 10

A

Question. If the 7th term in the binomial expansion of

is equal to 729, then x can be :
(a) e2
(b) e
(c) e/2
(d) 2e

B

Question. If n is a positive integer, then (√3+1)2n – (√3 –1)2n is :
(a) an irrational number
(b) an odd positive integer
(c) an even positive integer
(d) a rational number other than positive integers

A

Question. If (2+x/3)55 is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive terms of the expansion are equal, then these terms are:
(a) 7th and 8th
(b) 8th and 9th
(c) 28th and 29th
(d) 27th and 28th

A

Question. The sum of the rational terms in the binomial expansion of (21/2 + 31/5)10 is :
(a) 25
(b) 32
(c) 9
(d) 41

D

Question. The coefficient of x4 in the expansion of (1 + x + x2 + x3)6 in powers of x, is ____________.

120

Question. The smallest natural number n, such that the coefficient of x in the expansion of (x2 + 1/x3)n is nC23, is :
(a) 38
(b) 58
(c) 23
(d) 35

A

Question. The number of terms in the expansion of (y1/5 + x1/10)55 , in which powers of x and y are free from radical signs are
(a) six
(b) twelve
(c) seven
(d) five

A

Question. If ƒ(y) = 1 – (y – 1) + (y – 1)2 – (y – 1)3 + … – (y – 1)17, then the coefficient of y2 in it is
(a) 17C2
(b) 17C3
(c) 18C2
(d) 18C3

D

Question. The sum of the co-efficients of all odd degree terms in the expansion of (x+ √x3–1) + (x– √x3 -1) ,(x >1) is :
(a) 0
(b) 1
(c) 2
(d) – 1

C

Question. The coefficient of x–5 in the binomial expansion of

(a) 1
(b) 4
(c) – 4
(d) – 1

A

Question. If the coefficients of x2 and x3 are both ero, in the expansion of the expression (1 + ax + bx2) (1–3x)15 in powers of x, then the ordered pair (a, b) is equal to:
(a) (28, 861)
(b) (–54, 315)
(c) (28, 315)
(d) (–21, 714)

C

Question. If the coefficient of x7 in [ ax2 + (1/bx) ]11 equals the coefficient of x7 in [ ax – (1/bx) ]11 , then a and b satisfy the relation
(a) a – b = 1
(b) a + b = 1
(c) a/b = 1
(d) ab = 1

D

Question. For a positive integer n, (1 + 1/x)n is expanded in increasing powers of x. If three consecutive coefficients in this expansion are in the ratio, 2 : 5 : 12, then n is equal to __________.

118

Question. The coefficient of xn in expansion of (1 + x)(1 – x)n is
(a) ( –1)n–1n
(b) ( – 1)n(1 – n)
(c) ( – 1)n–1(n – 1)2
(d) (n – 1)

B

Question. The sum of the series 2 · 20C0 + 5 · 20C1 + 8 · 20C2 + 11 · 20C3 + … + 62 · 20C20 is equal to :
(a) 226
(b) 225
(c) 223
(d) 224

B

Question. If the sum of the coefficients in the expansion of (a + b)n is 4096, then the greatest coefficient in the expansion is
(a) 1594
(b) 792
(c) 924
(d) 2924

C

Question. The coefficient of t4 in the expansion of ( 1 – t6 / 1 – t )3
(a) 14
(b) 15
(c) 10
(d) 12

B

Question. The sum of the real values of x for which the middle term in the binomial expansion of (x3/3 + 3/x)8 equals 5670 is :
(a) 0
(b) 6
(c) 4
(d) 8

A

Question. If the term independent of x in the expansion of

is k, then 18k is equal to :
(a) 5
(b) 9
(c) 7
(d) 11

C

Question. If the number of terms in the expansion of ( 1 – 2/x + 4/x2 )n , x ≠ 0, is 28, then the sum of the coefficients of all the terms in this expansion, is :
(a) 243
(b) 729
(c) 64
(d) 2187

B

Question. The sum of coefficients of integral power of x in the binomial expansion (1–2√x)50 is :
(a) 1/2(350 – 1)
(b) 1/2(250 – 1)
(c) 1/2(350 + 1)
(d) 1/2(350)

C

Question. Let α > 0, β > 0 be such that α32 = 4. If the maximum value of the term independent of x in the binomial expansion of (αx1/9 + βx1/6)10 is 10k, then k is equal to :
(a) 336
(b) 352
(c) 84
(d) 176

A

Question. The value of r for which 20Cr20C020Cr-120C1 + 20Cr-220C2 + … +20C020Cr is maximum, is :
(a) 15
(b) 20
(c) 11
(d) 10

B

Question. If

then K is equal to:
(a) (25)2
(b) 225 – 1
(c) 224
(d) 225

D

Question. The positive integer ust greater than (1 + 0.0001)10000 is
(a) 4
(b) 5
(c) 2
(d) 3

D

Question. The value of (21C110C1) + (21C210C2) + (21C310C3) + (21C410C4) + …. + (21C1010C10) is :
(a) 220 – 210
(b) 221 – 211
(c) 221 – 210
(d) 220 – 29

A

Question. The coefficient of x1012 in the expansion of (1 + xn + x253)10, (where n ≤ 22 is any positive integer), is
(a) 1
(b) 10C4
(c) 4n
(d) 253C4

B

Question. The sum of the series 20C0 – 20C1 + 20C2 – 20C3 + …. – …. + 20c10 is
(a) 0
(b) 20C10
(c) – 20C10
(d) 1/220C10

D

Question. r and n are positive integers r > 1, n > 2 and coefficient of (r+2)th term and 3rth term in the expansion of (1 + x)2n are equal, then n equals
(a) 3r
(b) 3r + 1
(c) 2r
(d) 2r + 1

C

Question. The coefficients of xp and xq in the expansion of (1+ x )p+q are
(a) equal
(b) equal with opposite signs
(c) reciprocals of each other
(d) none of these

A

Question. The coefficient of x4 in the expansion of (1 + x + x2)10 is _______.

615

Question. If the sum of the coefficients of all even powers of x in the product (1 + x + x2 + … + x2n) (1 – x + x2 – x3 + … + x2n) is 61, then n is equal to_______.

30

Question. The term independent of x in the binomial expansion of (1 – 1/x + 3x5)(2x2 – 1/X)8 is :
(a) 496
(b) –496
(c) 400
(d) –400