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CBSE Questions for Class 11 Engineering Maths Binomial Theorem Quiz 7 - MCQExams.com

The value of C21+C22....+C2n (where Ci is the ith coefficient of (1+x)n expansion), is:
  • nnn!
  • 2n!n!n!
  • 2n!n!
  • n!×2n2n!
If f(n)=ns=1nr=snCrrCs, then f(3)=
  • 27
  • 19
  • 1
  • 5
The value of (n+2)C02n+1(n+1)C12n+nC22n1+.... is equal to:
(Cr=nCr)
  • 4n
  • 4
  • 2n+4
  • 4+4n
If n1Cr=(k23)nCr+1, then kϵ
  • (,2]
  • [2,)
  • [3,3]
  • (3,2]
If Pn denotes the product of all the coefficients in the expansion of (1+x)n, then Pn+1Pn is equal to:
  • (n+2)nn!
  • (n+1)n+1n+1!
  • (n+1)n+1n!
  • (n+1)nn+1!
The value of 50C4+6r=156rC3 is
  • 55C4
  • 55C3
  • 56C3
  • 56C4
The coefficient of x53 in the following expansions.
100m=0100Cm(x3)100m2m is
  • 100C47
  • 100C53
  • 100C53
  • 100C100
The coefficient of x2012 in 1+x(1+x2)(1x) is.
  • 1
  • 2
  • 3
  • 4
Let n be a positive integer and, (1+x)n=a0+a1x+a2x2++anxn. What is a0+a1+a2++an equal to?
  • 1
  • 2n
  • 2n1
  • 2n+1
5th term from the end in the expansion of (x222x2)12 is
  • 7920x4
  • 7920x4
  • 7920x4
  • 7920x4
Consider the expansion of (1+x)2n+1
The average of the coefficients of the two middle terms in the expansion is
  • 2n+1Cn+2
  • 2n+1Cn
  • 2n+1Cn1
  • 2nCn+1
In the expansion of (x31x2)n,nN, if the sum of the coefficient of x5 and x10 is 0, then n is :
  • 25
  • 20
  • 15
  • None of these
The value of nC0nC1+nC2....+(1)nnCn is:
  • 1
  • 0
  • 2n
  • n
The value of the expression k1Ck1+kCk1+....n+k2Ck1 is given by :
  • n+k1Ck1
  • n+k1Ck
  • n+kCk
  • None of these
How many terms are there in the expansion of (1+2x+x2)10?
  • 11
  • 20
  • 21
  • 30
Consider the expansion of (1+x)2n+1
The sum of the coefficients of all the terms in the expansion is
  • 22n1
  • 4n1
  • 2×4n
  • None of the above
What is n equal to ? 
  • 5
  • 10
  • 15
  • None of the above
In the expansion of (x+1x)n, then the coefficient of the term indepenent of x is
  • n!(r!)2
  • n!(r+1)!(r1)!
  • n!(n+r2)!(nr2)!
  • n![(n2)!]2
The sum of the series 20C020C1+20C220C3+...+20C10 is 
  • 20C10
  • 1220C10
  • 0
  • 20C10
If Tr=2016Crx2016r, for r=0,1,,....2016, then (T0T2+T4....+T2016)2+(T1T3+T5....T2015)2 is equal to - 
  • (X21)1008
  • (X+1)2016
  • (X21)2016
  • (X2+1)2016
If C0,C1,C2,....,Cn are binomial coefficients of order n, then the value of C12+C34+C56+....=
  • 2n+1n+1
  • 2n1n+1
  • 2n+1n1
  • 2nn+1
The total number of terms in the expansion of (x+a)47(xa)47 after simplification is
  • 24
  • 47
  • 48
  • 96
Let ((1+x)+x2)9=a0+a1x+a2x2+.....+a18x18. Then
  • a0+a2+.....+a18=a1+a3+.....+a17
  • a0+a2+.....+a18 is even
  • a0+a2+.....+a18 is divisible by 9
  • a0+a2+.....+a18 is divisible by 3 but not by 9
Let n5 and b0. In the binomial expansion of (ab)n, the sum of the 5th and 6th terms is zero then a/b equals
  • 5n4
  • 15(n4)
  • n56
  • n45
In the expansion of (3x1x2)10, the 5th term from the end is
  • 16486x8
  • 17010x8
  • 13486x8
  • None of these
The coefficient of x49 in the product (x1)(x2)(x3)....(x50) is
  • 2250
  • 1275
  • 1275
  • 2250
  • 49
If C0,C1,C2,C3,.... are binomial coefficients in the expansion of (1+x)n , then C03C14++... is equal to :
  • 1n+12n+2+1n+3
  • 1n+1+2n+23n+3
  • 1n+21n+1+1n+3
  • 2n+11n+2+2n+3
  • 1n+22n+1+3n+3
The value of r for which the coefficients of (r5)th and (3r+1)th terms in the expansion of (1+x)1/2 are equal, is
  • 4
  • 9
  • 12
  • None of these
If (1+x+x2)n=1+a1x+a2x2+...+a2nx2n, then 2a13a2+...(2n+1)a2n is equal to
  • n
  • n
  • n+1
  • n1
  • n+1
The middle term in the expansion of (10x+x10)10 is
  • 10C5
  • 10C6
  • 10C51x10
  • 10C5x10
  • 10C51010
If the term free from x in the expansion of (xkx2)10 is 405, then the value of k is
  • ±1
  • ±3
  • ±4
  • ±2
Sum of coefficients of the last 6 terms in the expansion of (1+x)11 when the expansion is in ascending powers of x, is
  • 2048
  • 32
  • 512
  • 64
  • 1024
If C0,C1,C2,,C15 are binomial coefficients in (1+x)15, then C1C0+2C2C1+3C3C2++15C15C14 is equal to
  • 60
  • 120
  • 64
  • 124
  • 144
The middle term in the expansion of (1+x)2n is
  • 1.3.5....(2n1)2nn!
  • 1.2.3....(2n1)2nxnn!
  • 1.3.5....(2n1)xnn!
  • 1.3.5....(2n1)2nxnn!
If nϵN and (1+4x+4x2)n=r=2nr=0arxr then value of 2nr=0a2r equals
  • 9n1
  • 9n+1
  • 3n+1
  • 3n1
The sum of the co-efficients of all odd degree terms in the expansion of (x+x31)5+(xx31)5,(x>1) is
  • 1
  • 2
  • 1
  • 0
If Cr denotes the binomial coefficient nCr then (1)C20+2C21+5C22+......(3n1)C2n=
  • (3n2)2nCn
  • (3n22)2nCn
  • (5+3n)2nCn
  • (3n52)2nCn+1
Given (1-2x+5x^2-10x^3)(1+x)^n=1+a_1x+a_2x^2+... and that a_1^2=2a_2 then the value of n is-
  • 6
  • 2
  • 5
  • 3
If { C }_{ 0 },{ C }_{ 1 },{ C }_{ 2 },.....{ C }_{ r } are binomial coefficients in the expansion of {(1+x)}^{n} then
{ C }_{ 1 }-\cfrac { { C }_{ 2 } }{ 2 } +\cfrac { { C }_{ 3 } }{ 3 } -\cfrac { { C }_{ 4 } }{ 4 } +....{ \left( -1 \right)  }^{ n-1 }\cfrac { { C }_{ n } }{ n } equals
  • \sum _{ r=1 }^{ n }{ { \left( -1 \right) }^{ n-1 } } \cfrac { { C }_{ r } }{ r }
  • \sum _{ r=1 }^{ n }{ \cfrac { 1 }{ r } }
  • \sum _{ r=2 }^{ n }{ \cfrac { 1 }{ r-1 } }
  • None of these
Prove that the coefficient of middle  term  in the  expansion  of ( 1 + x ) ^{2n}   is equal  to the sum  of the coefficient  of two middle  terms in (1 + x)^{2n - 1}.
  • True
  • False
State true or false.
The middle term in the expansion of 
\left(\dfrac{x}{a} \, - \, \dfrac{a}{x}\right)^{10}=-252
  • True
  • False
Find the term of the expansion of \displaystyle\, \left ( \sqrt[3]{x^{-2}} + x \right )^7 containing x in the second power.
  • T_4
  • T_5
  • T_6
  • T_7
Sum of coefficients in the expression of (x+2y+z)^{10} is
  • 2^{10}
  • 3^{10}
  • 1
  • None of these
The 6^{th} coefficient in the expansion of \left (2x^2 - \dfrac {1}{3x^2}\right)^{10}
  • -\dfrac{986}{27}
  • \dfrac{986}{27}
  • \dfrac{896}{27}
  • - \dfrac{896}{27}
Prove that C_0+C_1+C_2+.....C_n=2^n
  • 2^n
  • 2^{n-1}
  • 2^{n+1}
  • None of the above.
In the expansion of (\sqrt[5]{3}+\sqrt[7]{2})^{24}, the rational term is 
  • T_{14}
  • T_{16}
  • T_{15}
  • T_7
 the coefficients of x^{49} in the polynomial. 
\left (x \, - \, \dfrac{C_1}{C_0}\right) \, \left (x \, - \, 2^2 \, \dfrac{C_2}{C_1}\right) \, \left (x \, - \, 3^2 \, \dfrac{C_3}{C_2}\right) \, ..... \,  \, \left (x \, - \, 50^2 \, \dfrac{C_{50}}{C_{49}}\right) is
  • 50\displaystyle \sum _{ r=1 }^{ 50 }{ r-{ r }^{ 2 } }
  • 51\displaystyle \sum _{ r=1 }^{ 50 }{ { r }^{ 2 } } -\displaystyle \sum _{ r=1 }^{ 50 }{ r }
  • 51\displaystyle \sum _{ r=1 }^{ 50 }{ { r } } -\displaystyle \sum _{ r=1 }^{ 50 }{ r^{ 2 } }
  • none\ of\ these
If the sum of the co-efficient in the expansion of (a+b)^n is 1024, then the greatest co-efficient in the expansion is 
  • 252
  • 352
  • 452
  • 552
If n\ge 2 then 3.{ C }_{ 1 }-4.{ C }_{ 2 }+5.{ C }_{ 3 }-......+{ \left( -1 \right)  }^{ n-1 }\left( n+2 \right) .{ C }_{ n } is equal to
  • -1
  • 2
  • -2
  • 1
The sum ^{10}C_3 + ^{11}C_3 + ^{12}C_3 + .... + ^{20}C_3 is equal to
  • ^{21}C_4
  • ^{21}C_4 - ^{10}C_4
  • ^{21}C_4 - ^{11}C_4
  • ^{21}C_{17}
0:0:1


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