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CBSE Questions for Class 11 Engineering Maths Binomial Theorem Quiz 1 - MCQExams.com

The sum of coefficient of integral powers of x in the binomial expansion of (12x)50 is :
  • 12(350+1)
  • 12(350)
  • 12(3501)
  • 12(250+1)
If (2+x3)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 :
  • 7th and 8th
  • 8th and 9th
  • 28th and 29th
  • 27th and 28th
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 (x2a2)n is
  • A2B2
  • A2+B2
  • 4AB
  • None
15C3+15C5+....+15C15 will be equal to
  • 214
  • 21415
  • 214+15
  • 2141
Find the sum of coefficient of middle terms of the expansion \left(3x-\dfrac{x^3}{6}\right)^7:
  • \dfrac {595}{48}
  • -\dfrac {595}{48}
  • -\dfrac {595}{24}
  • None of the above
The total number of terms in the expansion of (x+y)^{50}+(x-y)^{50} is
  • 51
  • 26
  • 102
  • 25
In the expansion of (\sqrt 2+\sqrt [3]{5})^{20} the number of rational terms will be:
  • 3
  • 10
  • 4
  • 8
What is \displaystyle\sum _{ r=0 }^{ n }{ C\left( n,r \right)  } equal to?
  • {2}^{n} - 1
  • n
  • n!
  • {2}^{n}
The number of rational terms in the expansion of (9^{1/4} + 8^{1/6})^{1000} is:
  • 500
  • 400
  • 501
  • none of the above
The 3rd term of {\left( {3x - \dfrac{{{y^3}}}{6}} \right)^4} is
  • ^4{C_2}{\left( {3x} \right)^2}{\left( { - \dfrac{{{y^3}}}{6}} \right)^2}
  • ^4{C_2}{\left( {3x} \right)^2}{\left( { - \dfrac{{{y^2}}}{6}} \right)^2}
  • ^4{C_2}{\left( {3x} \right)^3}{\left( { - \dfrac{{{y^3}}}{6}} \right)^2}
  • ^4{C_2}{\left( {3x} \right)^3}{\left( { - \dfrac{{{y^2}}}{6}} \right)^2}
[AS 1] If A = \dfrac{1}{3} B \, and \, B = \dfrac{1}{2} C, then A : B : C = .. 
  • 1 : 3 : 6
  • 2 : 3 : 6
  • 3 : 2 : 6
  • 3 : 1 : 2
The expression ^{n}\textrm{C}_{0}+4\ ^{n}\textrm{C}_{1}+4^{2}\ ^{n}\textrm{C}_{2}+..........+4^{n}\ ^{n}\textrm{C}_{n}, equals 
  • 2^{2n}
  • 2^{3n}
  • 5^{n}
  • None of these
The number of zeroes at the end of (101)^{11}-1 is
  • 8
  • 4
  • 1100
  • 2
The middle terms in the expansion of (x^{2}-a^{2})^{5} is
  • 10x^{6}a^{4},\ -10x^{4}a^{6}
  • -10x^{6}a^{4},\ 10x^{4}a^{6}
  • 10x^{6}a^{4},\ 10x^{4}a^{6}
  • -10x^{6}a^{4},\ -10x^{4}a^{6}
If sum of the coefficients in the expansion of (2+3cx+c^2x^2)^{12} vanishes, then c equals to
  • -1,2
  • 1,2
  • 1,-2
  • -1,-2
^{100}C_{0}-^{100}C_{2}+^{100}C_{4}+^{100}C_{8}-........+^{100}C_{100}=__
  • 2^{-49}
  • -2
  • 2^{50}
  • -2^{50}
If the sum of binomial coefficient in the expansion (1+x)^{n} is 256, then n is
  • 6
  • 7
  • 8
  • 9
The coefficient of { x }^{ 3 } in the polynomial (x-1) (x-2) (x-4) is
  • 1
  • -1
  • 7
  • None of these
If the constants term in the expansions of (\sqrt{x}-\dfrac{k}{x^2})^{10} is 405, then what can be the value of k ?
  • \pm 2
  • \pm 3
  • \pm 5
  • \pm 9
The middle term in {\left( {{x^2} + \dfrac{1}{{{x^2}}} + 2} \right)^n} is 
  • \dfrac{{n!}}{{{{\left( {\left( {\frac{n}{2}} \right)!} \right)}^2}}}
  • \dfrac{{\left( {2n} \right)!}}{{{{\left( {\left( {\frac{n}{2}} \right)!} \right)}^2}}}
  • \dfrac{{1.3.5....\left( {2n + 1} \right)}}{{n!}}{2^n}
  • \dfrac{{\left( {2n} \right)!}}{{{{\left( {n!} \right)}^2}}}
The term containing x^3 in the expansion of (x - 2y)^7 is

  • 3rd
  • 4th
  • 5th
  • 6th
The greatest coefficient in the expansion of \left ( 1+X \right )^{2n+2} is


  • \frac{\left ( 2n \right )!}{\left ( n! \right )^{2}}
  • \frac{\left ( 2n+2 \right )!}{\left (( n+1 \right )!)^{2}}
  • \frac{\left ( 2n+2 \right )!}{n!\left (n+1 \right )!}
  • \frac{\left ( 2n \right )!}{n!\left (n+1 \right )!}
In the expansion of (2+\dfrac{x}{3})^n , coefficients of x^7 and x^8 are equal. Then n =
  • 49
  • 50
  • 55
  • 56
The middle term in the expansion of \left (\displaystyle \frac{x^{\frac{3}{2}}}{\sqrt{a}} - \frac{y^{\frac{5}{2}}}{b^{\frac{3}{2}}} \right )^8 is 
  • ^8C_4. \dfrac{x^6.y^{10}}{a^2b^6}
  • ^8C_4. \dfrac{x^6.y^{8}}{a^2b^4}
  • ^8C_5. \dfrac{x^5.y^{10}}{a^2b^5}
  • ^8C_1. \dfrac{x^5.y^{10}}{a^2b^5}
The middle term in the expansion of \left ( x + \dfrac{1}{x} \right )^{10} is
  • ^{10}C_{4}.\dfrac{1}{x}
  • ^{10}C_{5}
  • ^{10}C_{5}.\dfrac{1}{x}
  • ^{10}C_{6}.x
The middle term in the expansion of (1+x)^{2n} is
  • ^{2n}C_{n}
  • ^{2n}C_{n-1}.x^{n+1}
  • ^{2n}C_{n-1}.x^{n-1}
  • ^{2n}C_{n}.x^n
The middle term of \left ( x - \dfrac{1}{x} \right )^{2n+1} is
  • ^{2n+1}C_n.x
  • ^{2n+1}C_n
  • (-1)^{n}.^{2n+1}C_{n}
  • (-1)^{n}.^{2n+1}C_{n}.x
If the coefficients of (r+2)^{th} and (2r+1) ^{th} terms (r \neq 1) are equal in the expansion of (1+x)^{43} , then r =
  • 12
  • 13
  • 14
  • 15
Sum of the coefficients of (1+x)^n is always a
  • an integer
  • positive integer
  • negative integer
  • zero
The number of terms in the expansion of (1+x)^{21} is
  • 20
  • 21
  • 22
  • 24
The ratio of the { r }^{ th } term and the ({ r+1 })^{ th } term in the expansion of (1+ x)^n is 
  • \displaystyle \frac{r}{(n-r+1)x}
  • \displaystyle \frac{1}{(n-r+1)x}
  • \displaystyle \frac{r}{(n-r+1)}
  • \displaystyle \frac{(n-r+1)x}{r}
In the binomial expansion of (a-b)^n , n \geq{5} , the sum of
5th and 6th terms is zero then a/b equal to

  • \frac{5}{n-4}
  • \frac{6}{n-5}
  • \frac{n-5}{6}
  • \frac{n-4}{5}
If the middle term of (1+x)^{2n} is the greatest term then x lies between
  • n - 1 < x < n
  • \dfrac{n}{n + 1} < x < \dfrac{n+1}{n}
  • n < x < n+1
  • \dfrac{n+1}{n} < x < \dfrac{n}{n+1}
In the expansion of (a+b)^n , the ratio of the binomial coefficients of { 2 }^{ nd } and { 3 }^{ rd } terms is equal to the ratio of the binomial coefficients of { 5 }^{ th } and { 4 }^{ th } terms, then n =
  • 4
  • 5
  • 6
  • 7
The ratio of (r+1)th and rth terms in the expansion of (1-x)^n is

  • \dfrac{-r}{(n-r+1)x}
  • \dfrac{r}{(n-r+1)x}
  • \dfrac{-(n-r+1)x}{r}
  • \dfrac{(n-r+1)x}{r}
In the expansion of \left ( a^2\sqrt{a} + \frac{\sqrt[3]{a}}{a} \right )^n the binomial coefficient of 3rd term isThe 7th term is :
  • 84a^3\sqrt{a}
  • 84a^2\sqrt{a}
  • 84 a^2
  • 84 a^3
In the expansion of \displaystyle  \left ( \sqrt{a} + \frac{1}{\sqrt{(3a)}} \right )^n  , if the ratio of the binomial coefficient of the 4^{th} term to the binomial coefficient of the 3^{rd} term is \dfrac{10}{3} , the 5^{th} term is
  • \dfrac{88a}{\sqrt 3}
  • \dfrac {88a}{3}
  • 50a^2
  • 55a^2
Sum of the coefficients of (1 - x)^{25} is

  • -1
  • 1
  • 0
  • 2^{25}
The product of two middle terms in the expansion of  \left (\displaystyle \frac{3x^2}{2} - \frac{1}{3x} \right )^9 is 
  • (^9C_4)^2.\displaystyle \frac{x^9}{512}
  • ^{-9}C_4.^9C_5.\displaystyle \frac{x^8}{512}
  • -^{9}C_4.^9C_5.\displaystyle \frac{x^9}{512}
  • ^9C_4.^9C_5.\displaystyle \frac{x^9}{256}
The 3rd, 4th and 5th terms in the expansion of (1+x)^n are 60, 160 and 240 respectively, then x =

  • 2
  • 4
  • 5
  • 6
\displaystyle \frac{^{15}C_1}{^{15}C_0}+2.\frac{^{15}C_2}{^{15}C_1}+3.\frac{^{15}C_3}{^{15}C_2}+\ldots+15.\frac{^{15}C_{15}}{^{15}C_{14}} =
  • 105
  • 91
  • 120
  • 15
The number of terms in the expansion of (1+5\sqrt{2}x)^9 + (1-5\sqrt{2}x)^9 is :
  • 5
  • 10
  • 18
  • 20
A. ^{2n}C_n = C_0^2 + C_1^2 + C_2^2 + C_3^2 + \dots \dots + C_n^2

B. ^{2n}C_n = term independent of x in (1+x)^n \left(1+\frac{1}{x} \right)^n

C. ^{2n}C_n = \dfrac{1.3.5.7 \ldots \ldots (2n-1)}{n!} then
  • A, B are false, C is true
  • A is false, B and C are true
  • A and B are true; C is false
  • A, B, C are true
The total number of terms in the expansion of (x+a)^{100}+(x-a)^{100} after simplification is

  • 202
  • 51
  • 101
  • 50
C_0^2+3.C_1^2+5.C_2^2 + \ldots\ldots +(2n+1).C_n^2 =
  • (n+1)2^n
  • (2n+1) ^{2n}C_n
  • (n+1). ^{2n}C_n
  • (2n-1) ^{2n}C_n
^nC_0 + ^nC_2 + ^nC_4 + \dots \dots + ^nC_{2[n/2]} , where [ ] denotes greatest integer
  • 2^{2n-1}
  • 2^{2n-1}-1
  • 2^{n-1}
  • 2^{n-1}-1
^5C_0+2.^5C_1+2^2.^5C_2+2^3.^5C_3 +2^4.^5C_4+2^5.^5C_5 =


  • 32
  • 243
  • 64
  • 729
Evaluate the following:
C_1+2C_2+3C_3+\ldots\dots+nC_n 
  • n2^n
  • n2^{n-1}
  • (n+1)2^n
  • (n+1)2^{n-1}
(1+x)^{15}=a_0+a_1x+\ldots\ldots+a_{15}x^{15} \Rightarrow \sum_{r=1}^{15}r\frac{a_r}{a_{r-1}}=
  • 110
  • 115
  • 120
  • 135
If n\geq2 then (a-1).C_1-(a-2).C_2+(a-3).C_3-\ldots\ldots(-1)^{n-1}(a-n).C_n=
  • 0
  • a-1
  • a
  • a+1
0:0:1


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