Class 11 Mathematics Binomial Theorem MCQs Set 02

Question: The approximate value of(7.995)^1/3 correct to four decimal places is
a) 1.9995
b) 1.9996
c) 1.9990
d) 1.9991
Answer: b

Question:

Answer: a

Question: (√2+1)⁶-(√2 -1)⁶)is equal to
a) 101
b) 70√2
c) 140√2
d) 120√2
Answer: c

Question:

Answer: d

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: If x is so small that its square and higher powers may be neglected, then the value of (8+3x)^2/3/(2+3x)4-5x)^1/2is
a) 1-3/2x
b) 1+5/8x
c) 1-5/8x
d) None of the options
Answer: c

Question: The ratio of the coefficient of x¹⁰ in (1-X²)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(1.0025)¹⁰ correct to five decimal places is
a) 1.025281
b) 1.034285
c) 1.005293
d) None of the options
Answer: a

Question:

Answer: b

Question: The coefficient of xⁿ in the expansion of(1+x)²ⁿ and (1+x)^2n-1 are in the ratio
a) 1:2
b) 1:3
c) 3:1
d) 2:1
Answer: d

Question: If (+x-2x²)⁶=1+a₁x+a₂x²+..+a₁₂x₁₂,then the expression a₂+a₄+a₆+…+a₁₂ has the value
a) 32
b) 63
c) 64
d) None of the options
Answer: d

Question:

Answer: b

Question:

Answer: a

Question: If (1+ax)ⁿ=1+8x+24x²+..,, then the values of a and n are
a) 2, 4
b) 2, 3
c) 3, 6
d) 1, 2
Answer: a

Question: In the expansion of the following expression

Answer: a

Question: The two successive terms in the expansion of( 1+x)²⁴ whose coefficients are in the ratio 1:4 are
a) 3rd and 4th
b) 4th and 5th
c) 5th and 6th
d) 6th and 7th
Answer: c

Question:

Answer: c

Question:

Answer: c

Question: The coefficient of x⁴ in the expansion of

Answer: d

Question: C₁+2C₂+3C₃+..+nC_n is equal to
a) (n-1)^2n-1
b) n2^n-1
c) n2ⁿ
d) n2^n-2
Answer: b

Question:

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 the options
Answer: b

Question: The term independent of x in the expansion of

Answer: a

Question: The first 3 terms in the expansion of (1+ax)ⁿ(n≠0) are 1,6x and 16x² .Then, the values of a and n are respectively
a) 2 and 9
b) 3 and 2
c) 2/3and 9
d) 3/2and 6
Answer: c

Question: If in the expansion of (1+x)^m(1-x)ⁿ,) the coefficient of x and x² are 3 and – 6 respectively, then m is
a) 6
b) 9
c) 12
d) 24
Answer: c

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: For all n ∈N,2⁴ⁿ-15n-1is divisible by
a) 225
b) 125
c) 325
d) None of the options
Answer: a

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 the options
Answer: c

Question: The 4th term in the expansion of (x-2y)¹² is
a) 1760x³y⁹
b) – 1760x⁹y³
c) 1760x⁹y³
d) None of the options
Answer: b

Question: If the coefficients of x²and x³ 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: 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: The rth term in the expansion of (a+2x)ⁿ ) is

Answer: b

Question:

Answer: c

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 the options
Answer: a

Question: The coefficient of x⁵ in the expansion of

Answer: c

Question:

Answer: c

Question: The value of (1.002)¹² up to fourth place of decimal is
a) 1.0242
b) 1.0245
c) 1.0004
d) 1.0254
Answer: a

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: Given the integers, r>1, n > 2 and coefficients of (3)r 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 the options
Answer: a

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) 4n²-1
d) None of the options
Answer: a

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 the options
Answer: b

Question: In the expansion of (1 +a)^{m+ n}, the coefficients of a ^m and aⁿ are
a) equal
b) not equal
c) do not say anything
d) None of the options
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: 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) n²-2np+4p²=0
b) n²-n(4p+1)+4p²-2=0
c) n²-n(4p+1)+4p²=0
d) None of the options
Answer: b

Question: The( r+1)th term in the expansion of(1-x)^-4 will be
a) xr/r!
b) (r+1) (r+2) (r+3)/6 ) xr
c) (r+2) (r+3)/2xr
d) None of the options
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 – 3/2
c) 5/n – 4
d) 5/ 2(n -4)
Answer: b

Question: The digit at the unit place in the number 19 ²⁰⁰⁵ +11²⁰⁰⁵-9 ²⁰⁰⁵ – is
a) 2
b) 1
c) 0
d) 8
Answer: b