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CBSE Questions for Class 11 Engineering Maths Binomial Theorem Quiz 13 - MCQExams.com

Coefficient of x11 in the extension of (1+x2)4(1+x3)7(1+x4)12 is 
  • 1051
  • 1106
  • 1113
  • 1120
If the variable takes the values 0,1,2,....., n with frequericies proportional to the binomial coefficients C(n,0),C(n,1),C(n,2)...,C(n,n) respectively, then the variance of the distribution is :-
  • n
  • n2
  • n2
  • n4
In the expansion of (1+x1x)2 , the coefficient of xn will be 
  • 4n
  • 4n3
  • 4n1
  • none of these
Coefficient of t12 in (1+t2)6(1+t6)(1+t12) is:
  • 24
  • 21
  • 22
  • 23
The coefficient of xn in the binomial expansion of (1x)2, is
  • 2n2!
  • n+1
  • n
  • 2n
The coefficient of x24 in the expansion of (1+x2)12(1+x12)(1+x24) is
  • 12C6
  • 12C6+2
  • 12C6+4
  • 12C6+6
The term independent of x in the expansion of ((x3)+(32x2))10 is:-
  • 5/12
  • 10C1
  • 1
  • none of these
If xm occurs in the expansion of (x+1x2)2n, the coefficient of xm, is 
  • (2n)!m!(2nm)!
  • (2n)!3!3!(2nm)!
  • (2n)!(2nm3)!(4n+m3)!
  • none of these
The coefficient of a3b4c in the expansion of (1+a+bc)9 is 
  • 29C77C4
  • 29C77C3
  • 9C77C3
  • 9C77C3
The 4th term in the expansion of (x+1x)2 is
  • 110x32
  • 220x32
  • 220x2
  • 110x2
In how many terms in the expansion of (x1/5+y1/10)55 do not have fractional power of the variable :
  • 6
  • 7
  • 8
  • 10
The coefficient of x4 in 3x2+2x(x2+2)(x3) is
  • 1127
  • 77324
  • 77324
  • 1127
In the expansion of (x+1x2/3x1/3+1x1xx1/2)10, the term which does not contain x is
  • 10C0
  • 10C7
  • 10C4
  • none
The coefficient of x2 in (1+3x2+x4)(1+1x)8 is
  • 266
  • 161
  • 162
  • none of these
(10)2+(21)2+(32)2+...+(n+1n)2=
  • (n+1)(2nn)
  • (n+22)(2nn)
  • (n+2).2n1
  • (n)(2nn)
Number of irrational terms in the expansion of (2+3)15 are 
  • 9
  • 7
  • 16
  • 10
Coefficient of x8 in (x1)(x2)(x3)..(x10) is?
  • 980
  • 1395
  • 1320
  • None of these
The sum of the coefficient in the expansion of (x+y)n is 4096. The greatest coefficient in the expansion is-
  • 1024
  • 924
  • 824
  • 724
The coefficient of xn in x+1(x1)2(x2) is
  • 12n32n+1
  • 12n32n1
  • 1+2n+32n+1
  • 1+2n32n1
The coefficient of the middle term in the binomial expansion in power of x of (1+αx)4 and of (1αx)6 is the same if α equals-
  • 53
  • 103
  • 310
  • 35
The number of terms which are free from radical signs in the expansion of (y1/5+x1/10)55 is
  • 5
  • 6
  • 7
  • None of these
The number of irrational terms in the expansion of  (51/6+21/8)100  is :
  • 96
  • 97
  • 98
  • 99
The value of the sum 8j=0(8j)1(j+1)(j+2) is
  • 100390
  • 101390
  • 102390
  • 103390
Find the number of terms in the expression 5x2x2y+2xy+7
  • 3
  • 4
  • 1
  • 2
The coefficient of x2 in expansion of the product
(2 x2).((1+2x+3x2)6 + (14x2)6) is :
  • 107
  • 106
  • 108
  • 155
The sum of the co-efficients of all odd degree terms in the expansion of (x+x31)5+(xx31)5, (x>1)
  • 2
  • 1
  • 0
  • 1
26C0+26C1+26C2+...+26C13 is equal to
  • 225
  • 225+1226C13
  • 213
  • 213+1226C13
Number of terms which are rational in the expansion of (45+34)100 is 
  • 10
  • 8
  • 9
  • 11
If | x | < 2 / 3 then the fourth term in the expansion of \left( 1 + \frac { 3 } { 2 } x \right) ^ { 1 / 2 } is
  • \frac { 27 } { 128 } x ^ { 3 }
  • -\frac { 27 } { 128 } x ^ { 3 }
  • \frac { 81 } { 256 } x ^ { 3 }
  • -\frac { 81 } { 256 } x ^ { 3 }
If { (1+x-{ 2x }^{ 2 }) }^{ 6 }=1+{ C }_{ 1 }x+{ C }_{ 2 }{ x }^{ 2 }+{ C }_{ 3 }{ x }^{ 3 }+...+{ C }_{ 12 }{ x }^{ 12 }, then the value of { C }_{ 2 }+{ C }_{ 4 }+{ C }_{ 6 }+...+{ C }_{ 12 } is
  • 30
  • 32
  • 31
  • None of these
The sum of the coefficients in the expansion (6a-5b) when n is a positive integer, is 
  • { 10 }^{ \circ }
  • 1
  • { 11 }^{ n }
  • 0
Coefficient of { x }^{ 2009 }in(1+x+{ x }^{ 2 }+{ x }^{ 3 }+{ x }^{ 4 }{ ) }^{ 1001 }{ \left( 1-x \right)  }^{ 1002 } IS...
  • { 4. }^{ 1001 }{ c }_{ 501 }
  • - 2009
  • 0
  • None of these
The number of terms which are free from radical signs in the expansion of \left( \frac { 1 }{ { y }^{ 4 } } +\frac { 1 }{ { y }^{ 8 } }  \right) is:
  • 5
  • 6
  • 7
  • non of these
If sum of the coefficient in the expression of { (-3{ x }^{ 2 }+\frac { 2 }{ x } ) }^{ 2n+1 } is 'a' then the values of 'b' for which roots of the equation { x }^{ 2 }+bx+6a=0 are integral
  • {-7,-5,5,7}
  • {-7,-1,1,7}
  • {-5,-1,1,5}
  • none of these
If \left | x \right | < 1, then the coefficient of x^n in the expansion of (1 + x + x^2 + x^3 + .....)^2 is
  • n
  • n 1
  • n + 2
  • n + 1
If the number of terms in the expansion of { \left( 1-\dfrac { 2 }{ X } +\dfrac { 4 }{ { X }^{ 2 } }  \right)  }^{ n },x\neq 0, is 28, then sum coefficients of all the terms in this expansion,is:
  • 2187
  • 243
  • 729
  • 64
Coefficient of x^ {15} in (1+x+x^ {3}+x^ {4})^ {n} is
  • \displaystyle \sum _{ r=0 }^{ 5 }{ ^{ n } } { C }_{ 5-r }.^{ n }{ C }_{ 3r }
  • \displaystyle \sum _{ r=0 }^{ 5 }{ ^{ n } } { C }_{ 5r }
  • \displaystyle \sum _{ r=0 }^{ 5 }{ ^{ n } } { C }_{ 2r }
  • \displaystyle \sum _{ r=0 }^{ 3 }{ ^{ n } } { C }_{ 3-r }.^{ n }{ C }_{ 5r }
The 11^{th} term from last, in expansion of (2x+\frac{1}{^{x2}} is
  • ^{25}C_{15}\frac{2^{10}}{x^{20}}
  • ^{-25}C_{15}\frac{2^{10}}{x^{20}}
  • ^{25}C_{14}\frac{2^{11}}{x^{11}}
  • ^{25}C_{15}\frac{2^{10}}{x^{20}}
The sum of rational terms in (\sqrt{2}+\sqrt[3] {3} +\sqrt[6] {5})^{10}
  • 12632
  • 1260
  • 126
  • none of these
The number of distinct terms in the expansion of { \left( { x+y }^{ 2 } \right)  }^{ 13 }+{ \left( { x }^{ 2 }+y \right)  }^{ 14 } is...
  • 29
  • 28
  • 25
  • 27
The number of terms whose values depend on x in the expansion of \left( x ^ { 2 } - 2 + \frac { 1 } { x ^ { 2 } } \right) ^ { n } is 
  • 2 n + 1
  • 2n
  • n
  • None of these
Find the middle terms of the equation of \left(x^4 - \dfrac{1}{x^3}\right)^{11}.
  • -462\ x^9, 462\ x^2
  • -462\ x^8, 462\ x^4
  • 462\ x^7, -462\ x^3
  • None of these
The coefficient of   x^{5}  in the expansion of \left(x^{2}-x-2\right)^{5}  is
  • -83
  • -82
  • -81
  • 0
In the expansion of \left(1+3 x+2 x^{2}\right)^{6}  the coefficient of   x^{11}  is
  • 144
  • 288
  • 216
  • 576
The coefficient of { x }^{ 1 } in the expansion of \left( 1-2x \right) ^{ -1/2 } is 
  • \dfrac { \left( 2r \right) ! }{ \left( r! \right) ^{ 2 } }
  • \dfrac { \left( 2r \right) ! }{ { 2 }^{ r }\left( r! \right) ^{ 2 } }
  • None of these
  • \dfrac { \left( 2r \right) ! }{ { 2 }^{ r }\left( r+1 \right) !\left( c-1 \right) ! }
The coefficient of  x^m in the expansion of  (1+)^{m+n} is -

  • \frac { m!n! }{ (m+n)! }
  • (m+n)!
  • \frac { (m+n)! }{ m!n! }
  • none of these
The fifth term of \left(1 - \dfrac{2x}{3}\right)^{3/4} is
  • \dfrac{-5x^4}{1152}
  • \dfrac{5x^4}{1152}
  • -\dfrac{5x^4}{1052}
  • \dfrac{5x^4}{1052}
If the middle term in the expansion of { \left( { x }^{ 2 }+\dfrac { 1 }{ x }  \right)  }^{ n } is 924{ x }^{ 6 } then n=
  • 10
  • 12
  • 14
  • None of these
the number of terms in the expansion of {\left( {x + y - x} \right)^3} is  
  • 4
  • 6
  • 9
  • 10
The value of   x,  for which the 6 th term in the expansion of \int 2^{\log 2 \sqrt{\left(9^{x-1}+7\right)}}+\frac{1}{_{0}^{(1 / 5) \log _{2}\left(3^{x-1}+1\right)}} )^{7}  is 84 is equal to
  • 4,3
  • 0,3
  • 0,2
  • 1,2
0:0:2


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