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CBSE Questions for Class 11 Engineering Maths Binomial Theorem Quiz 8 - MCQExams.com

nrk=1nkCr=xCy
  • x=n+1;y=r
  • x=n;y=r+1
  • x=n;y=r
  • x=n+1;y=r+1
If (1+x)n=C0+C1x+C2x2.......Cnxn, then C20+C21+C22+C23+.......+C2n is equal to
  • n!n!n!
  • (2n)!n!n!
  • (2n)!n!
  • None of these
Find the 13th terms in the expansion of (9x13x)18,x0.
  • 18564
  • 87328
  • 17374
  • 35546
The co-efficient of x in  the expansion of (12x3+3x5)(1+1x)8 is :
  • 56
  • 65
  • 154
  • 62
The third term from the end in the expansion of (3x552x)8 is
  • 3545115x4
  • 4545516x4
  • 3937215x4
  • 3937516x4
The co-efficient of x5 in the expansion of (1+x)21+(1+x)22+........+(1+x)30 is: 
  • 51C5
  • 9C5
  • 31C621C6
  • 30C5+20C5
If Sn=nr=01nCrandtn=nr=0rnCr,thentnsn= 
  • 12n
  • 2n12
  • n1
  • 2n
In the expansion of (1+ax)n, nN, then the coefficient of x and x2 are 8 and 24 respectively. Then?
  • a=2,n=4
  • a=4,n=2
  • a=2,n=6
  • None of these
If \left| x \right| < 1 then the coefficient of {x^n} in expansion of {\left( {1 + x + {x^2} + {x^3}....} \right)^2} is
  • n
  • n - 1
  • n + 2
  • n + 1
{c_0},{c_1},{c_2} denotes coefficents expansion of {(1 + x)^n} , then {c_1} + {c_1}{c_2} + {c_2}{c_3} + .......{c_{n - 1}}{c_n} = \frac{{(2n)!}}{{(n + 1)!(n - 1)!}}
  • True
  • False
The sum of rational term in the expansion of {(3^{\frac{1}{5}}+2^{\frac{1}{3}})}^{15} is
  • 31
  • 59
  • 51
  • 61
The middle term (s) in the expansion of { \left( 1+x \right)  }^{ 2n+1 } is (are)
  • _{ }^{ 2n+1 }{ { C }_{ n } }{ X }^{ n } and _{ }^{ 2n+1 }{ { C }_{ n+1 } }{ X }^{ n+1 }
  • _{ }^{ 2n+1 }{ { C }_{ n } }{ X }^{ n+1 } and _{ }^{ 2n+1 }{ { C }_{ n+1 } }{ X }^{ n }
  • ^{ 2n+1 }{ { C }_{ n+1 } }{ X }^{ n }
  • ^{ 2n+1 }{ { C }_{ n+1 } }{ X }^{ n+1 }
If 6^{th} term in the expansion of \left[\dfrac{1}{x^{8/3}}+x^{2 }\log_{10}x\right]^{8} is 5600, then x is equal to 
  • 5
  • 4
  • 8
  • none\ of\ these
 \sum _{ r=0 }^{ n } \left( \dfrac {r+2}{r+1} \right) .^nCr is equal to :
  • \dfrac {2^n (n+2)-1}{(n+1)}
  • \dfrac {2^n (n+1)-1}{(n+1)}
  • \dfrac {2^n (n+4)-1}{(n+1)}
  • \dfrac {2^n (n+3)-1}{(n+1)}
The value of \displaystyle\sum^{10}_{r=0} ^{20}C_r is equal to?
  • \dfrac{1}{2}(2^{20}+ ^{20}C_{10})
  • \dfrac{1}{2}(2^{28}+ ^{19}C_{10})
  • 20(2^{18}+ ^{19}C_{11})
  • 10(2^{18}+ ^{19}C_{11})
In the binomial expansion of (a-b)^{n}, n\ge 5, the sum of the 5^{th} and 6^{th} terms is zero, then a/b is equals:
  • \dfrac{n-5}{6}
  • \dfrac{n-4}{5}
  • \dfrac{5}{n-4}
  • \dfrac{6}{n-5}
The first 3 terms in the expansion of (1+ax)^{n}(n\neq 0) are 1, 6x and 16x^{2}. Then the value of a and n are respectively 
  • 2 and 9
  • 3 and 2
  • 2/3 and 9
  • 3/2 and 6
If f ( x ) + 2 f ( 1 - x ) = x ^ { 2 } + 2 , \forall x \in R, then find f ( x )
  • \dfrac{(x+3)^2}{3}
  • \dfrac{(x-3)^2}{3}
  • \dfrac{(x-2)^2}{4}
  • \dfrac{(x-2)^2}{3}
The number of non-zero terms in the expansion of (\sqrt{7}+1)^{75}-(\sqrt{7}-1)^{75} is
  • 36
  • 37
  • 38
  • 39
The coefficient of {x^5} in the expansion of {\left( {1 + {x^2}} \right)^5}{\left( {1 - x} \right)^4} is   
  • {4.^6}{C_4}
  • {2.^6}{C_4}
  • {2.^6}{C_2}
  • {4.^6}{C_2}
The number of rational terms in the expansion of \quad { \left( { 3 }^{ \cfrac { 1 }{ 4 }  }+{ 7 }^{ \cfrac { 1 }{ 6 }  } \right)  }^{ 144 } is
  • 33
  • 23
  • 12
  • 13
In the expansion of (y^{1/5}+x^{1/10})^{55}, the number of terms free of a radical sign is
  • 5
  • 6
  • 50
  • 56
For r=0,1,2,,....10 let {A}_{r},{B}_{r} and {C}_{r} denote respectively the coefficient of {x}^{r} in the expansions of {(1+x)}^{10},{(1+x)}^{20} and {(1+x)}^{30}. Then \sum _{ r=1 }^{ 10 }{ { A }_{ r }\left( { B }_{ 10 }{ B }_{ r }-{ C }_{ 10 }{ A }_{ r } \right)  } is equal to
  • {B}_{10}-{C}_{10}
  • {A}_{10}({B}_{10}^{2}-{C}_{10}{A}_{10})
  • 0
  • {C}_{10}-{B}_{10}
 The coefficient of the middle term in the expansion of \left(1+x\right)^{2n} is equal to the sum of the coefficient of middle terms in the expansion of \left(1+x\right)^{2n-1}
the statement is true and false
  • True
  • False
The numerical value of middle terms in { \left( 1-\cfrac { 1 }{ x }  \right)  }^{ n }{(1-x)}^{n} is
  • { _{ }^{ 2n }{ C } }_{ n }
  • { _{ }^{ n }{ C } }_{ n }
  • \left( { _{ }^{ 2n }{ C } }_{ n } \right)
  • \left( { _{ }^{ n }{ C } }_{ n } \right)
The value of
\left( { _{  }^{ 7 }{ C } }_{ 0 }+{ _{  }^{ 7 }{ C } }_{ 1 } \right) +\left( { _{  }^{ 7 }{ C } }_{ 1 }+{ _{  }^{ 7 }{ C } }_{ 2 } \right) +.....\left( { _{  }^{ 7 }{ C } }_{ 6 }+{ _{  }^{ 7 }{ C } }_{ 7 } \right) is
  • {2}^{7}-1
  • {2}^{8}-2
  • {2}^{8}-1
  • {2}^{8}
The number of rational terms in the expansion of { \left( \sqrt [ 4 ]{ 5 } +\sqrt [ 5 ]{ 4 }  \right)  }^{ 100 } is
  • 50
  • 5
  • 6
  • 51
The rth term of series 2\dfrac{1}{2} + 1\dfrac{7}{{13}} + 1\dfrac{1}{9} + \dfrac{{20}}{{23}} + ..... is
  • \dfrac{{20}}{{5r + 3}}
  • \dfrac{{20}}{{5r - 3}}
  • 20\left( {5r + 3} \right)
  • \dfrac{{20}}{{5{r^2} + 3}}
^{m}C_r.^{n}C_0+{}^{m}C_{r-1}.{}^{n}C_{1}+{}^{m}C_{r-2}.^{n}C_2+..........+^{m}C_0.^{n}C_r={}^{m+n}Cr
  • True
  • False
If rth term is middle term in { \left( { x }^{ 2 }-\cfrac { 1 }{ 2x }  \right)  }^{ 20 } then (r+3)th term is:
  • \cfrac { { _{ }^{ 20 }{ C } }_{ 7 }x }{ { 2 }^{ 13 } }
  • -\left( \cfrac { { _{ }^{ 20 }{ C } }_{ 5 }x }{ { 4 }^{ 13 } } \right)
  • -\left( \cfrac { { _{ }^{ 20 }{ C } }_{ 7 }x }{ { 2 }^{ 13 } } \right)
  • -\left( \cfrac { { _{ }^{ 20 }{ C } }_{ 14 }x }{ { 4 }^{ 13 } } \right)
The middle term in the expansion of (1-3x+3x^{2}-x^{3})^{6} is
  • ^{18}C_{10}\ {x}^{10}
  • ^{18}C_{9}( {-x})^{9}
  • ^{18}C_{9}\ {x}^{9}
  • None\ of\ these
The value of \displaystyle\frac { { C }_{ 0 } }{ 1.3 } -\frac { { C }_{ 1 } }{ 2.3 } +\frac { { C }_{ 2 } }{ 3.3 } -\frac { { C }_{ 3 } }{ 4.3 } +.........+{ \left( -1 \right)  }^{ n }\frac { { C }_{ n } }{ (n+1).3 }  is :
  • \displaystyle\frac { 3 }{ n+1 }
  • \displaystyle\frac { n+1 }{ 3 }
  • \displaystyle\frac { 1 }{ 3n+3 }
  • none of these
The sum of  the series ^{20}{C_0}{ - ^{20}}{C_1}{ + ^{20}}{C_2}{ - ^{20}}{C_3}{ + _{......}}{ - _{......}}{ + ^{20}}{C_{10}}\,is -
  • \frac{1}{2}{20_{{C_{10}}}}
  • 0
  • { - ^{20}}{C_{10}}
  • ^{20}{C_{10}}
If the number of terms is the expansion {\left( {1 - \frac{2}{x} + \frac{4}{{{x^2}}}} \right)^n},x \ne 0, is 28, then the sum of coefficients of all the terms in this expansion, is :
  • 2187
  • 243
  • 729
  • 64
The sum of coefficients of integral powers of x in the binomial expansion of (1-2\sqrt x)^{50} is : 
  • \dfrac{1}{2}(3^{50}-1)
  • \dfrac{1}{2}(2^{50}+1)
  • \dfrac{1}{2}(3^{50}+1)
  • \dfrac{1}{2}(3^{50})
If A and B are coefficients of x ^ { n } in the expansion of ( 1 + x ) ^ { 2 n } and ( 1 + x ) ^ { 2 n - 1 } respectively, then
  • A = B
  • A = 2 B
  • 2 A = B
  • A + B = 0
If(1+x)^n=C_0+C_1x+C_2x^2+......+C_nx^n,  then C_0+5C_1+9C_2+.....+(4n+1)C_n is equal to 
  • n.2^n
  • (n+1)2^n
  • (2n+1)2^n
  • (4n+1)2^n
If the rth term in the expansion of {\left( {{x \over 3} - {2 \over {{x^2}}}} \right)^{10}} contains {x^4} then r is equal to 
  • 2
  • 3
  • 4
  • 5
If the sum of the binomial coefficients in the expansion of \left(x^{2}+\dfrac{2}{x^{3}}\right)^{n} is 243, the term independent of x is equal to 
  • 40
  • 30
  • 20
  • 10
If x^{4} occurs in the rth term in the expansion of \left(x^{4}+\dfrac{1}{x^{3}}\right)^{15}, then r=
  • 7
  • 8
  • 9
  • 10
If (1-x-x^2)^{20} = \sum _{ r=0 }^{ 40 }{ a_4,x^x }, then 
a_1+3a_3+5a_5+........+39a_{39}=
  • 40
  • -40
  • 80
  • -80
whether the sum of the coefficients in the expansion of {\left(1+x-3{x}^{2}\right)}^{2163} is -6
  • True
  • False
If the constant term in the expansion of \left(x^{2}-\dfrac{1}{x}\right)^{n} is 15 then the value of n is
  • 6
  • 9
  • 12
  • 15
In the expansion of (1+2x+3x^{2})^{10}, coefficient of x^{4} is not divisible by
  • 12
  • 7
  • 11
  • 5
Coefficient of \alpha in the expansion of (\alpha +p)^{m-1}+(\alpha +p)^{m-2}(\alpha +q)^{m-3}(\alpha +q)^{2}+....(\alpha +q)^{m-1} where \alpha \neq -q and p\neq q is: 
  • \frac{^{m}C_{1}(p^{1}-q^{1})}{p-q}
  • \frac{^{m}C_{1}(p^{m-1}-q^{m-1})}{p-q}
  • \frac{^{m}C_{1}(p^{1}+q^{1})}{p-q}
  • \frac{^{m}C_{1}(p^{m-1}+q^{m-1})}{p-q}
If the r^{th} and the (r+1)^{th} terms in the expansion of (p+q)^{n} are equal, then \dfrac{(n+1)q}{r(p+q)} is
  • 1/2
  • 1/4
  • 1
  • 0
Number of distinct terms in the expansion of (x+y-z)^{16} is 
  • 816
  • 152
  • 153
  • 136
Find the coefficient of x^{11} in the expansion of \left(x^{3}-\dfrac{2}{x^{2}}\right)^{12}
  • -25344
  • -25250
  • -25000
  • -25750
The number of terms in the expansion of (1+x)^{101}(1+x^{2}-x)^{100} in power of x is:
  • 302
  • 301
  • 202
  • 101
If (1+x+x^2)^8=a_0+a_1x+.....a_{16}x^{16} then a_1-a_3+a_5-a_7+....... -a_{15}=
  • 1
  • 2
  • 3
  • 0
0:0:1


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